Name: graphs, curve fit, and standard deviation
Uploaded: 2020-03-26T07:22:24.000Z
Duration: 4 min 34 s
Channel: JoVE

K12 Standards

Texas Essential Knowledge and Skills

High School

Chemistry

CHEM.1

CHEM.1.D

Scientific Measurement and Lab Skills

Die Übersetzung experimenteller Ergebnisse von Datenpunkten in visuelle Darstellungen wie Diagramme ist unerlässlich, um die Beziehung zwischen zwei oder mehr Eigenschaften zu bestimmen. Diese Eigenschaften werden als Variablen bezeichnet. Wenn zwei Variablen vorhanden sind, wird ein aus den Daten erstellter Graph als zweidimensional bezeichnet. Das Diagramm besteht aus zwei Achsen. Die unabhängige Variable wird auf der x-Achse und die abhängige Variable auf der y-Achse dargestellt.
Nehmen wir zum Beispiel diese Beispieldaten für die Temperatur und das Volumen eines Gases. Das Volumen des Gases hängt von der Temperatur ab. Daher würden wir die gemessene Temperatur auf der x-Achse und das Volumen auf der y-Achse darstellen.
Wenn es mehrere Datenpunkte mit demselben x-Wert gibt, z. B. wenn wir das Volumen mehrmals bei einer Temperatur gemessen haben, berechnen wir auch die Standardabweichung dieser Messungen. Die Standardabweichung ist ein statistischer Wert, der das Ausmaß der Streuung angibt, die in einer Reihe von Werten vorhanden ist.
Die Standardabweichung wird anhand dieser Formel berechnet, wobei n die Anzahl der Datenpunkte, x bar der Mittelwert der Datenpunkte und xi für jeden einzelnen Datenpunkt steht. Sie können die Standardabweichung von Hand berechnen, oder ein Tabellenkalkulationsprogramm kann sie automatisch berechnen. Je näher die Standardabweichung an 0 liegt, desto näher liegen die Datenpunkte am Mittelwert. Wenn die Standardabweichung gleich 0 ist, haben alle eingegebenen Datenpunkte den gleichen Wert.
Schauen wir uns die Mittelwerte und Standardabweichungen der Volumenmessungen bei jeder Temperatur in unserem Datensatz an. Wir können jeden Satz von Datenpunkten als Mittelwert plus oder minus der Standardabweichung zusammenfassen. Wir ermitteln die signifikanten Zahlen für jeden Mittelwert aus den entsprechenden Messungen und runden die Mittelwerte entsprechend.
Die Standardabweichung jeder Gruppe muss die gleiche Anzahl von Dezimalstellen wie der Mittelwert haben, daher runden wir jede Standardabweichung auf die Hundertstelstelle. Um die Beziehung zwischen zwei Variablen grafisch zu bestimmen, können wir die Daten mit einer Best-Fit-Funktion anpassen.
Die Funktion wird automatisch von einer Tabellenkalkulationssoftware generiert und kann die Form einer linearen Trendlinie, einer Polynomfunktion oder einer Exponential- oder Logarithmusfunktion annehmen. Im Falle unserer Temperatur- und Volumendaten ist die Beziehung eine lineare. Die Datenpunkte werden also durch die lineare Regression der kleinsten Quadrate angepasst. Ihr Tabellenkalkulationsprogramm gibt die Gleichung für die am besten passende Linie und einen r-Quadrat-Wert zurück. Je näher der R-Quadrat-Wert an 1 liegt, desto besser ist die Anpassung der Daten.
Als Nächstes können Sie mit Ihrer Tabellenkalkulationssoftware die Standardabweichungen der Steigung, des y-Achsenabschnitts und des berechneten y-Werts ermitteln. Um die signifikanten Zahlen für die Werte in der Gleichung zu bestimmen, folgen wir einer einfachen Regel. Die letzte signifikante Zahl jedes Wertes entspricht der ersten signifikanten Dezimalstelle seiner Standardabweichung.
Wir runden also die Steigung auf die Tausendstelstelle und den y-Achsenabschnitt auf die Zehntelstelle, und wir runden die Standardabweichungen entsprechend. Unsere Steigung beträgt 0,167 +/- 0,003 Liter pro Kelvin und unser y-Achsenabschnitt -40,6 +/- 1,2 Liter. Jeder berechnete y-Wert wird auf die Zehntelstelle gerundet und beträgt +/- 0,8 Liter. Diese Gleichung beschreibt den Zusammenhang zwischen Temperatur und Volumen eines Gases.
In dieser Übung erstellen Sie einen Datensatz mit abhängigen und unabhängigen Variablen, indem Sie den Durchmesser und Umfang verschiedener Größen von Bechern messen. Anschließend verwenden Sie diese Daten, um ein Streudiagramm zu erstellen und eine lineare Regression durchzuführen, wobei Sie die Bedeutung signifikanter Zahlen berücksichtigen. Sie üben auch Laborfähigkeiten, wie z. B. das Filtern und Messen des Volumens mit Pipetten, wobei Sie auf die Unsicherheit bei den Messungen und Analysen achten.

wissenschaftliche mess- und laborfähigkeiten

Zweidimensionale Graphen
Einige chemische Experimente bestehen darin, eine Eigenschaft des Systems, das Sie untersuchen, direkt zu ändern, auch bekannt als unabhängige Variable, wie die Temperatur, und die Auswirkungen auf eine andere Eigenschaft zu messen, die auch als abhängige Variable bekannt ist, wie z. B. das Volumen. Sobald die Daten gesammelt sind, muss die Wechselwirkung zwischen den beiden Parametern quantifiziert – oder in eine Form umgewandelt werden, die ausgewertet werden kann – und mit anderen Beziehungen verglichen werden.
Zweidimensionale Graphen können verwendet werden, um bestimmte Arten von mathematischen Beziehungen zwischen zwei Eigenschaften abzuleiten oder um festzustellen, dass eine solche Beziehung zwischen ihnen nicht besteht. Die Analyse bestimmt letztendlich, wie sich die abhängige Variable als Reaktion auf die unabhängige Variable ändert. Im Beispiel der Anpassung der Temperatur einer Flüssigkeit oder eines Gases und der Überwachung von Änderungen ihres Volumens ist die Temperatur die unabhängige Variable und das Volumen die abhängige Variable.
Um ein zweidimensionales Diagramm zu erstellen, muss jeder Datenpunkt einen Wert haben, der sowohl für die abhängigen als auch für die unabhängigen Variablen als Koordinate bezeichnet wird. Die unabhängige Variable wird auf der x-Achse und die abhängige Variable auf der y-Achse dargestellt. Diese Diagramme können einfach in einer Tabellenkalkulationssoftware erstellt werden, die auch zur Analyse der gezeichneten Daten verwendet werden kann.
Kurven-Anpassung
Nachdem ein Datensatz in einem zweidimensionalen Diagramm dargestellt wurde, kann die Kurvenanpassung verwendet werden, um eine Gleichung oder Funktion für die abhängige Variable in Bezug auf die unabhängige Variable zu generieren. Funktionen stellen ein mathematisches Modell dar, das die Daten, aus denen es abgeleitet wird, am besten modelliert. Kurvenanpassung ist die Technik, bei der eine Funktion gefunden wird, die eine Linie erzeugt, die gut mit dem Muster der Datenpunkte übereinstimmt. Tabellenkalkulationssoftware verfügt über verschiedene Werkzeuge zur Kurvenanpassung, die als "Best-Fit" bezeichnet werden. Dabei handelt es sich in der Regel um eine lineare Regressionsanalyse der kleinsten Quadrate, obwohl die meisten Programme auch eine nichtlineare Regression der kleinsten Quadrate anbieten.
Die Genauigkeit der am besten angepassten linearen Gleichung kann überprüft werden, indem die x-Werte für die Datenpunkte eingegeben und die "theoretischen" Ergebnisse der Gleichung mit den tatsächlichen y-Werten der Datenpunkte verglichen werden. Tabellenkalkulationssoftware berechnet in der Regel den Wert des Bestimmtheitskoeffizienten (R2) für die Funktion, der angibt, wie gut die Funktion mit den Datenpunkten übereinstimmt. Je näher derR2-Wert an 1 liegt, desto besser ist die Anpassung für eine lineare Regression. Andere Funktionen verfügen über speziellere Methoden, um zu bestimmen, wie gut die Funktion an die Daten angepasst ist.
Die Bestimmung der Unsicherheit abhängiger Werte, die aus der Best-Fit-Funktion berechnet werden, würde komplizierte "Fehlerfortpflanzungs"-Techniken erfordern. Es ist jedoch möglich, die Unsicherheit innerhalb der Gleichung in Form der Standardabweichung sowohl für die Steigung als auch für den y-Achsenabschnitt einer Best-Fit-Funktion zu berechnen. Dies wird in der Regel mit einem anderen Werkzeug durchgeführt als dem, das zum Generieren eines zweidimensionalen Diagramms verwendet wird.
Standardabweichung
Die Standardabweichung beschreibt das Ausmaß der Streuung, die in einer Reihe von Werten vorhanden ist. Die Standardabweichung der Grundgesamtheit (σ) wird verwendet, wenn Daten von jedem Mitglied einer endlichen Grundgesamtheit vorhanden sind, z. B. die Masse jeder Murmel in einem Beutel Murmeln. Die Stichprobenstandardabweichung(en) wird für alle anderen Fälle verwendet und ist die Standardberechnung der Standardabweichung in Tabellenkalkulationssoftware. 1 Sie können davon ausgehen, dass sich die "Standardabweichung" auf die Standardabweichung der Stichprobe bezieht.
Es wird davon ausgegangen, dass der zufällige Messfehler einer ungefähren "Normalverteilung" folgt, bei der etwa 68 % eines Wertesatzes innerhalb eines Bereichs von einer Standardabweichung auf beiden Seiten des Mittelwerts liegen, 95 % der Werte innerhalb von zwei Standardabweichungen auf beiden Seiten des Mittelwerts und 99,7 % der Werte innerhalb von drei Standardabweichungen auf beiden Seiten des Mittelwerts. Daher ist die Standardabweichung ein nützliches Mittel, um Fehler und Unsicherheit zu beschreiben.
Die Gleichung für die Standardabweichung der Stichprobe lautet:
<img src="/CDNSource/lm/labs/42/42_Concepts_1.jpg">
In dieser Gleichung ist N die Anzahl der Werte; <img src="/CDNSource/lm/labs/42/30034eq02.jpg"> ist der Durchschnitt (oder Mittelwert) der Werte; und xi steht für jeden einzelnen Wert. Um also die Standardabweichung von Hand zu berechnen, berechnen Sie den Mittelwert der Wertemenge, subtrahieren Sie den Mittelwert von jedem Wert, quadrieren Sie jede Differenz, addieren Sie die quadrierten Differenzen, dividieren Sie die Gesamtsumme durch eins weniger als die Anzahl der Werte und ziehen Sie die Quadratwurzel des Quotienten. Je näher s an Null liegt, desto geringer ist die Abweichung zwischen den Werten. Wenn die Werte in eine Tabellenkalkulationssoftware eingegeben werden, kann die Standardabweichung aus der Software heraus berechnet werden.
Die Anzahl der signifikanten Stellen in einer Standardabweichung hängt davon ab, für welche Werte es sich handelt. Bei der Angabe der Standardabweichung für eine Gruppe von Datenpunkten, die unter denselben Bedingungen erhoben wurden, muss zunächst die entsprechende Anzahl signifikanter Stellen im Mittelwert bestimmt werden. Die Standardabweichung wird dann auf die gleiche Anzahl von Dezimalstellen wie der Mittelwert gerundet. Für einen Satz von Volumina mit vier signifikanten Ziffern, einem Mittelwert von 15,361 ml und einer Standardabweichung von 0,2313, würden der Mittelwert und die Standardabweichung als 15,36 ml ± 0,23 ml angegeben.
Bei der Angabe der Standardabweichung des Mittelwerts und des y-Achsenabschnitts für eine Best-Fit-Funktion, die durch die Analyse der kleinsten Quadrate bestimmt wird, was die übliche Methode für Tabellenkalkulationssoftware ist, ist die erste Dezimalstelle der Standardabweichung die letzte signifikante Zahl des Mittelwerts oder y-Achsenabschnitts. Daher sollte die Standardabweichung auf eine signifikante Dezimalstelle gerundet werden, und die Steigung oder der y-Achsenabschnitt sollte auf die entsprechende Dezimalstelle gerundet werden. Wenn die Steigung z. B. 0,1691 L·K-1 beträgt und eine Standardabweichung von 0,00512 aufweist, sollte die Steigung als 0,169 L·K-1 ± 0,005 L·K-1 angegeben werden.
Wenn die Standardabweichung der Steigung oder des y-Achsenabschnitts so viel kleiner ist als der entsprechende Wert, dass die Steigung oder der y-Achsenabschnitt nach dieser Regel signifikantere Zahlen ergeben würde, als die ursprünglichen Messdaten zulassen würden, dann bestimmen Sie stattdessen die signifikanten Zahlen der Steigung oder des y-Achsenabschnitts aus den x- und y-Werten und runden Sie die Standardabweichung auf eine signifikante Zahl. Für eine Steigung von 0,1691 L·K-1, eine Standardabweichung von 0,0000512 und x- und y-Werte mit vier signifikanten Ziffern sollte die Steigung also als 0,1691 L·K-1 ± 0,00005 L·K- 1 angegeben werden. In diesem Fall ist es in Ordnung, wenn der berechnete Wert und seine Standardabweichung eine andere Anzahl von Dezimalstellen aufweisen. Beachten Sie, dass bei der Methode der kleinsten Quadrate sowohl die x- als auch die y-Werte verwendet werden, um die Steigung und den y-Achsenabschnitt zu berechnen.
Wenn Sie die Standardabweichung als Unsicherheitsbereich angeben, beachten Sie ausdrücklich, dass die Unsicherheit eine Standardabweichung darstellt. Dies sagt dem Leser, dass es eine Wahrscheinlichkeit von etwa 68 % gibt, dass der wahre Wert einer Messung innerhalb dieses Bereichs des Mittelwerts liegt, wenn eine Normalverteilung angenommen wird. Es kann oft besser sein, die Unsicherheit als zwei Standardabweichungen vom Mittelwert anzugeben, da dies die Wahrscheinlichkeit auf etwa 95% erhöht. Multiplizieren Sie dazu einfach die Standardabweichung mit zwei, bevor Sie sie auf die entsprechende Anzahl signifikanter Stellen runden.
Referenzen
<ol style="Schriftgröße:17px">
	<li style="font-size:17px">Harris, D.C. (2015). Quantitative chemische Analyse. New York, NY: W.H. Freeman und Company.</li>
</ol>

Wissenschaftliche Mess- und Laborfähigkeiten

Zweidimensionale Graphen
Einige chemische Experimente haben die Form, eine Eigenschaft des Systems, das Sie untersuchen, direkt zu ändern, auch bekannt als ...

Education

Lehre

JoVE Lab Manual

Chemie

graphs, curve fit, and standard deviation

Two-dimensional graphs help students compare an independent variable with a dependent variable in science data. In a chemistry example, temperature is the independent variable and volume is the dependent variable. After data are collected, the relationship between the two measurements must be quantified so it can be evaluated and compared with other relationships. A graph can also show when no relationship exists between the two variables.

To make a two-dimensional graph, each data point needs a coordinate for both variables. The independent variable is plotted on the x-axis, and the dependent variable is plotted on the y-axis. These plots are often made in spreadsheet software, which can also be used to analyze the data. This helps show how the dependent variable changes in response to the independent variable.

Once the data are plotted, curve fitting can turn the pattern into an equation, or function. A function is a mathematical model that best matches the data it comes from. Curve fitting looks for a line or curve that fits the data points well. In many cases, spreadsheet tools use a best-fit method based on linear least-squares regression, although nonlinear least-squares regression is also available in most software.

The quality of a best-fit line can be checked by comparing the x values in the equation with the actual y values from the data. Spreadsheet software usually reports the coefficient of determination, or R squared, which shows how well the function matches the plotted points. A value closer to 1 means a better fit for linear regression. Finding uncertainty for values calculated from the equation can be more complicated, but standard deviation can be used to describe the uncertainty in the slope and y-intercept of a best-fit line.

Standard deviation shows how much values vary in a set. Population standard deviation, written as sigma, is used when data are available for every member of a finite population, such as the mass of each marble in a bag. Sample standard deviation, written as s, is used in all other cases and is the default in spreadsheet software. For that reason, standard deviation usually means sample standard deviation. Random measurement error is assumed to follow a roughly normal distribution, where about 68% of values fall within one standard deviation of the mean, 95% fall within two, and 99.7% fall within three.

The sample standard deviation can also be calculated by hand. First find the mean. Then subtract the mean from each value, square each difference, add the squared differences, divide by one less than the number of values, and take the square root. The closer s is to zero, the less variation there is in the data. Spreadsheet software can also calculate standard deviation directly.

When reporting standard deviation, the number of significant figures depends on what it describes. For a group of measurements taken under the same conditions, the standard deviation is rounded to the same number of decimal places as the mean. For example, 15.361 mL with a standard deviation of 0.2313 should be reported as 15.36 mL ± 0.23 mL. When reporting the standard deviation of a slope or y-intercept from least-squares analysis, the first decimal place of the standard deviation becomes the last significant figure of the value. So 0.1691 L·K-1 with a standard deviation of 0.00512 is reported as 0.169 L·K-1 ± 0.005 L·K-1.

If the standard deviation is much smaller than the slope or y-intercept, this rule can give more significant figures than the original x and y data allow. In that case, use the significant figures from the data and round the standard deviation to one significant figure. For example, 0.1691 L·K-1 with a standard deviation of 0.0000512 and x and y values with four significant figures is reported as 0.1691 L·K-1 ± 0.00005 L·K-1. It is important to state whether the uncertainty represents one standard deviation. One standard deviation gives about a 68% chance that the true value lies within that range. Two standard deviations may be a better choice when a wider uncertainty range is needed, since that raises the chance to about 95%.

Graphs, Curve Fit, and Standard Deviation

lab techniques

Measuring with Accuracy in the Lab

Measuring with accuracy in the lab starts with careful records, the right tools, and correct reading of data. Scientists use lab notebooks to record how an experiment was done. These notes include the amounts of materials used and each step of the procedure. Without that record, an experiment cannot be repeated in the same way. Balances and glassware are used to measure solids and liquids for experiments. The precision of a measurement depends on the equipment used. Digital balances show the...

scientific measurement and lab skills

Two-dimensional graphs help students compare an independent variable with a dependent variable in science data. In a chemistry example, temperature is the independent variable and volume is the dependent variable. After data are collected, the relationship between the two measurements must be quantified so it can be evaluated and compared with other relationships. A graph can also show when no relationship exists between the two variables. To make a two-dimensional graph, each data point needs...

stoichiometry, product yield, and limiting reactants

stoichiometry-product-yield-and-limiting-reactants

Balancing Equations and Reactant Limits

Chemical equations show how reactants change into products during a reaction. Stoichiometry is the study of the relative amounts of reactants and products. It is based on the Law of Conservation of Mass, which says matter is neither created nor destroyed. Because atoms are only rearranged, the number and identity of atoms must match on both sides of a reaction. That is why a chemical equation must be balanced. A balanced equation has the same number of atoms for each element in the reactants...

redox reactions

Oxidation States in Redox Reactions

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ideal gas law

Gas Laws Behind the Ideal Gas Equation

The ideal gas equation brings together the main gas laws used in chemistry. Gases have molecules that are far apart, so their behavior is described with four measurable variables: pressure, volume, number of moles, and temperature. The ideal gas law links these variables with the gas constant, R, which equals 8.314 J·K−1 mol−1. Boyle’s law describes the link between pressure and volume. When temperature and the number of moles stay constant, pressure and volume change in opposite directions.

acid and base concentrations

Acids, Bases, and pH in Titration

Acids, bases, and pH explain how acidic or basic a solution is. An Arrhenius acid releases hydrogen ions when it dissolves in water, while an Arrhenius base releases hydroxide ions. These reactions also create conjugate partners: an acid forms a conjugate base after losing hydrogen, and a base forms a conjugate acid after losing hydroxyl. Every acid has a conjugate base, and every base has a conjugate acid. pH measures the amount of hydrogen ions in a solution. The pH scale runs from 0 to 14...

buffers

Buffer pH and the Common Ion Effect

Buffer solutions help keep pH steady when acids or bases are added. In water, an Arrhenius acid (HA) dissociates into hydrogen ions, H+, and a conjugate base, A-. More hydrogen ions make a solution more acidic and lower its pH. An Arrhenius base (BOH) dissociates into a conjugate acid, B+, and hydroxide ions, OH-. Strong acids and strong bases usually change pH a lot because they react completely in water and raise the amount of H+ or OH-. Buffers reduce those pH changes. A buffer usually...

enthalpy of reaction

Reaction Heat, Hess’s Law, and Calorimetry

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solubility

Solubility in Water and Other Solvents

Solubility describes how much of a solute can dissolve in a specific solvent. It is usually reported as solute mass per solvent volume or as solute mass per solvent mass. For example, sodium chloride has a solubility of 36 g per 100 mL of water at room temperature. If solubility is given by solvent mass, that mass must be converted to volume for later calculations. Temperature changes solubility. Sodium carbonate dissolves at about 7 g per 100 mL of water at 0 °C, 22 g per 100 mL at room...

metal flame emission

Flame Test Metal Color Clues

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balmer series

Hydrogen Emission Lines

Hydrogen emission lines show how electrons move between fixed energy levels in the Bohr model. Niels Bohr proposed this model for the hydrogen atom in 1913. In this model, an electron can only occupy certain orbits, and it cannot exist between them. These energy states are labeled with the quantum number n. The ground state is n = 1. Higher values, such as n = 2, 3, 4, and so on, are excited states. An electron changes state only by absorbing or emitting energy equal to the difference between...

beer's law

Absorbance Spectra and Beer-Lambert Analysis

Absorbance spectra and the Beer-Lambert Law show how light can be used to study molecules in solution. When light hits a substance, it may be absorbed, transmitted, or reflected. A substance often interacts with a range of wavelengths, and each wavelength can affect the molecules or atoms in a different way. When a molecule absorbs light, that energy can be used for translation, vibration, rotation, or electron excitement. Electron excitement is especially important in spectroscopy because it...

concentration dependence

Reaction Order and Rate Constants

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temperature dependence

Reaction Rate, Arrhenius, and Catalysts

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galvanic cells

Battery Power from Redox Reactions

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electrolytic cells

Electroplating with Electrolytic Cells

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proper lab notebook keeping

Recording a Reproducible Lab Experiment

Accurate lab notebook records are essential in science and organic chemistry labs. Without clear notes, descriptions, quantities, and observations, an experiment cannot be repeated or checked. Good record keeping supports reproducibility, which means other people can follow the same work and get similar results. A laboratory notebook is useful in school labs, research settings, and industry. It can also become a legal record when an idea, process, substance, or technique is patented and...

basic organic chemistry techniques

Organic Lab Glassware and Safe Handling

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melting points

How Impurities Change Melting Points

Melting point helps identify an organic compound by showing the temperature where a solid turns into a liquid at 1 atmosphere of pressure. It is a physical property, like solubility, density, color, and electronegativity. Because the exact start of melting is hard to measure, the result is reported as a range. The lower end is when the first drops of liquid appear. The upper end is when the last solid has melted. Scientists compare this range with literature values to help identify a compound. <br...

boiling points

Boiling Point and Vapor Pressure

Boiling point and vapor pressure are key physical properties of a liquid. For a pure compound, the boiling point can help identify the substance. In experiments, the boiling point is usually recorded as a range because exact values are hard to measure and may differ by a few degrees from the literature value. Vapor pressure explains why a liquid boils. In a sealed container, some molecules at the liquid surface gain enough energy to escape into the gas phase. At the same time, some gas...

recrystallization

Purifying Crystals by Solubility

Purifying crystals by solubility is a key organic chemistry technique. Recrystallization uses differences in solubility to separate a desired solid product from starting materials, solvent, and impurities. It is one of the three standard purification methods, along with distillation and extraction. Solubility is the maximum amount of a substance that can dissolve in a fixed volume of solvent at a given temperature. Different solutes dissolve in different solvents, and their behavior can vary...

extraction

Separating Mixtures with Solvent Extraction

Solvent extraction is a common way to separate and isolate a target compound in organic chemistry. In this process, a solute moves from one phase to another so it can be separated from unreacted starting materials or impurities. Extraction is also useful when a product is dissolved in a reaction solvent that is hard to remove by evaporation, such as a solvent with a high boiling point. There are three main types of extraction. In solid-liquid extraction, the solute moves from a solid phase...

simple distillation

Separating Liquids by Boiling Point

Separating liquids by boiling point is the goal of distillation. A miscible mixture contains liquids that mix evenly, and it can be heated so that the more volatile liquid evaporates first. Volatility is a liquid’s tendency to vaporize, and boiling begins when bubbles form in the liquid phase. In a closed container, liquid and vapor can reach equilibrium, which means the rate of vaporization equals the rate of condensation. The pressure from the vapor above the liquid is called vapor pressure.

steam distillation

Steam Distillation and Low-Boiling Separation

Steam distillation is a separation method for temperature-sensitive organic compounds. It works best when the organic compound is immiscible in water, meaning the two liquids do not mix. The method helps remove the organic molecule from a non-volatile contaminant without using the higher temperatures needed for many other separations. In steam distillation, the immiscible mixture is heated until both water and the volatile organic compound distill together. The vapor rises to a condenser,...

thin-layer chromatography

TLC Separation by Polarity

Thin-layer chromatography (TLC) separates compounds in a mixture by polarity. It uses the same basic parts as other chromatography methods: a stationary phase, a mobile phase, and the solute. In TLC, the stationary phase is a thin coating on a plate instead of material packed into a column. The stationary phase in most TLC systems is polar silica gel, a form of silicon dioxide. Its surface has OH groups that can form hydrogen bonds. The sample is first spotted on a pencil start line with a...

column chromatography

Separating Mixtures by Polarity

Column chromatography separates compounds in an organic chemistry lab by using differences in physical properties. It is especially useful for microscale separations when less than 10 grams of material is available for analysis. The method can separate a mixture based on solubility, polarity, hydrophobicity, size, and charge. Any chromatography system has three main parts: the stationary phase, the mobile phase, and the sample mixture. In column chromatography, the stationary phase is usually...

hydrolysis of an ester

Soap Formation from Triglycerides

Triglycerides are lipids made of a glycerol backbone linked to three fatty acids. They are common in vegetable oils and animal fats. Plant lipids are the basis of vegetable oils, while animal lipids are used as lard or general sources of fats. A fatty acid has a long carbon chain, usually between 12 and 20 carbons, with a weak organic acid at one end. Some fatty acids contain double bonds. These are unsaturated fats. The double bond usually gives the chain a bent, cis shape. As a result,...

synthesis of luminol

Luminol Chemiluminescence in Forensics

Luminol chemiluminescence shows how a chemical reaction can produce light and help with blood detection. Chemical reactions may be endothermic or exothermic, depending on whether they absorb or release heat as reactants become products. The enthalpy of a reaction is the energy difference between reactants and products, or ΔH. A positive ΔH means the reaction is endothermic. A negative ΔH means it is exothermic. Many reactions do not happen in a single step. They can pass through intermediates...

esterification

Ester Formation and Everyday Fragrances

Esters are organic compounds with a carbonyl group attached to an oxygen that connects to another alkyl or aryl group. Their general formula is RCOOR'. They are often made by reacting a carboxylic acid with an alcohol in an esterification reaction. In this process, the hydroxyl group of the acid is replaced by an alkyl or aryl group. Many simple esters have familiar fruit and flower smells because their structures are small and less complex. Formic acid and methanol can combine to form methyl...

identification of unknown aldehydes and ketones

identification-of-unknown-aldehydes-and-ketones

Carbonyl Tests for Aldehydes and Ketones

Aldehydes and ketones are carbonyl compounds, which means they contain a C=O functional group. A ketone has two alkyl or aryl groups attached to the carbonyl carbon. Acetone is the simplest ketone, with two methyl groups. An aldehyde is similar, but it has at least one hydrogen attached to the carbonyl carbon. Formaldehyde is the simplest aldehyde, and acetaldehyde has one hydrogen and one methyl group. The carbonyl carbon in both aldehydes and ketones is electrophilic because the oxygen atom...

uv-vis spectroscopy of dyes

How Dyes Absorb Visible Light

Dyes absorb visible light because their molecular structure lets them interact with specific wavelengths. When light hits a substance, some light is absorbed and the rest is reflected or transmitted. The color we see depends on the wavelength that is reflected. A blue substance reflects blue light, around 430 to 480 nm, and absorbs the complementary orange region, around 590 to 630 nm. Compounds that do not absorb in the visible range appear colorless to the human eye. Light also has energy and...

identifying alcohols

Alcohol Tests for Primary, Secondary, and Tertiary

Alcohol tests can help sort alcohols by structure and reactivity. Alcohols are organic molecules with a hydroxyl group attached to an alkyl or aryl group, written as ROH. If the carbon with the hydroxyl group has one R group, the alcohol is primary. If it has two R groups, it is secondary. If it has three R groups, it is tertiary. Alcohols can also be aromatic when they contain a benzene ring. Phenol is the simplest aromatic alcohol. To identify an alcohol, chemists can use its chemical...

chemistry

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Scientific Laws and Theories

Scientific Laws

In science, a law is defined as a concise, verbal or mathematical, statement that summarizes a vast number of experimental observations. ...

The Scientific Method

Chemistry is an empirical science. Scientists often pose questions to understand the chemistry in everyday life and seek answers to these questions. To ...

CHEM.1.A

What is an Experiment?

An experiment is a planned activity carried out under controlled conditions. The purpose of an experiment is to investigate the relationship between two ...

Study Design in Statistics

A study design is a set of techniques that allow a researcher to collect and analyze data from different variables defined for a specific research ...

Observational Studies

Observational studies are a type of analytical study where researchers observe events without any interventions. In other words, the researcher does not ...

Experimental Designs

An experimental design is a systematic process that allows researchers to evaluate the relationship between dependent and independent variables. There are ...

Randomized Experiments

The randomization process involves assigning study participants randomly to experimental or control groups based on their probability of being equally ...

Crossover Experiments

Crossover experiments, also called the repeated-measurements design, is a study design in which all experimental units are exposed to all treatments in ...

Controls in Experiments

When conducting an experiment, it is crucial to have control to reduce bias and accurately measure the dependent variables. It also marks the results more ...

Bias

Bias refers to any tendency that prevents a question from being considered unprejudiced. In research, bias occurs when one outcome or answer is selected ...

Blinding

Blinding is a commonly used method of not telling participants which treatment a subject is receiving. Blinding is a critical part of a randomized control ...

CHEM.1.B

Proper Personal Protective Equipment

Robert M. Rioux &#38; William A Elliott, Pennsylvania State University, University Park, PA
Hazards are many and varied in the laboratory, but the right ...

Emergency Eyewash and Shower Stations

Robert M. Rioux, Pennsylvania State University, University Park, PA
The Occupational Safety and Health Administration (OSHA) mandates that an emergency ...

Electrical Safety

Robert M. Rioux &amp; Suprita Jharimune, Pennsylvania State University, University Park, PA
Among the many hazards present in the laboratory, electrical ...

Working with Centrifuges

Source: Robert M. Rioux &amp; Suprita Jharimune, Pennsylvania State University, University Park, PA
Earth's gravitational force is capable of separating ...

Working with Hot and Cold Sources

Source: Robert M. Rioux &amp; Suprita Jharimune, Pennsylvania State University, University Park, PA
Working with extreme temperatures, both high and low, ...

guidelines-in-case-of-a-laboratory-emergency

Guidelines in Case of a Laboratory Emergency

Robert M. Rioux &amp; Zhifeng Chen, Pennsylvania State University, University Park, PA
The most common laboratory emergencies include chemical spills, ...

chemical-storage-categories-hazards-and-compatibilities

Chemical Storage: Categories, Hazards And Compatibilities

Source: Robert M. Rioux &amp; Taslima A. Zaman, Pennsylvania State University, University Park, PA
While the use of various chemicals in experimental ...

Safe Handling of Mineral Acids

Source: Robert M. Rioux &#38; Taslima A. Zaman, Pennsylvania State University, University Park, PA
A mineral acid (or inorganic acid) is defined as a ...

Handling Chemical Spills

Source: Robert M. Rioux &#38; Taslima Zaman, Pennsylvania State University, University Park, PA
Since chemicals are commonly used for laboratory research ...

Proper Use of Autoclaves

Robert M. Rioux &amp; Zhifeng Chen, Pennsylvania State University, University Park, PA
Autoclaving is one of the most commonly used methods in the ...

Fume Hoods and Laminar Flow Cabinets

Robert M. Rioux &amp; William A. Elliott, Pennsylvania State University, University Park, PA
Fume hoods and laminar flow cabinets are engineering controls ...

handling-air-and-water-sensitive-chemicals-using-a-schlenk-line

Handling Air- and Water-Sensitive Chemicals Using a Schlenk Line

Robert M Rioux, Ajay Sathe, Zhifeng Chen, Pennsylvania State University, University Park, PA
The use of reagents sensitive to oxidation or moisture ...

proper-operation-of-vacuum-based-equipment

Proper Operation of Vacuum Based Equipment

Source: Robert M. Rioux, Ajay Sathe &#38; Zhifeng Chen, Pennsylvania State University, University Park, PA
Vacuum is required for a number of laboratory ...

Operating the Glovebox

Robert M Rioux, Ajay Sathe, Zhifeng Chen, Pennsylvania State University, University Park, PA 
A glovebox is an isolated enclosure that is designed to ...

operation-of-high-pressure-reactor-vessels

Operation of High-pressure Reactor Vessels

Robert M Rioux, Pennsylvania State University, University Park, PA
The use of gases in a synthetic chemistry laboratory is essential for carrying out a ...

CHEM.1.C

Lab Techniques

Measurement Accuracy
The ability to repeat an experiment and get the same results, or reproducibility, is essential in scientific research. However, ...

Two-Dimensional Graphs
Some chemistry experiments take the form of directly changing one property of the system that you are studying otherwise known as ...

Proper Lab Notebook Keeping

Organic Lab Notebook Keeping
Record keeping is a vital skill in science and organic chemistry labs. Without proper notes, descriptions, quantities, or ...

Basic Organic Chemistry Techniques

Glassware in Organic Chemistry
There are standard pieces of glassware that are used in the organic chemistry lab. Beakers and Erlenmeyer flasks are ...

Measurement: Standard Units

Every measurement provides three kinds of information: the size or magnitude of the measurement (a number), a standard of comparison for the measurement ...

Measurement: Derived Units

The International System of Units or SI system, by international agreement, has fixed measurement units for seven fundamental properties: length, mass, ...

uncertainty-in-measurement-accuracy-and-precision

Uncertainty in Measurement: Accuracy and Precision

Scientists typically make repeated measurements of a quantity to ensure the quality of their findings and to evaluate both the precision and the accuracy ...

uncertainty-in-measurement-reading-instruments

Uncertainty in Measurement: Reading Instruments

Counting is the type of measurement that is free from uncertainty, provided the number of objects being counted does not change during the process. Such ...

CHEM.1.E

Scientific and engineering practices. The student, for at least 40% of instructional time, asks questions, identifies problems, and plans and safely conducts classroom, laboratory, and field investigations to answer questions, explain phenomena, or design solutions using appropriate tools and models. The student is expected to:

Graphs, Curve Fit, and Standard Deviation

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