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

実験結果をデータポイントからグラフなどの視覚的表現に変換することは、2つ以上のプロパティ間の関係を決定するために不可欠です。これらのプロパティは変数と呼ばれます。変数が 2 つある場合、データから作成されたグラフは 2 次元と呼ばれます。グラフには 2 つの軸があります。独立変数は X 軸にプロットされ、従属変数は Y 軸にプロットされます。
たとえば、ガスの温度と体積に関するこのサンプルデータを考えてみましょう。ガスの量は温度によって異なります。したがって、測定された温度をx軸にプロットし、体積をy軸にプロットします。
同じ x 値を持つデータポイントが複数ある場合、たとえば 1 つの温度で体積を複数回測定した場合など、それらの測定値の標準偏差も計算します。標準偏差は統計値であり、一連の値に存在する変動の量を示します。
標準偏差は、n がデータ ポイントの数、x bar がデータ ポイントの平均値、xi が個々のデータ ポイントを表す次の式を使用して計算されます。標準偏差は手動で計算することも、スプレッドシートプログラムで自動的に計算することもできます。標準偏差が 0 に近いほど、データ ポイントは平均値に近くなります。標準偏差が0に等しい場合、入力されたすべてのデータポイントは同じ値を持ちます。
データセットの各温度での体積測定値の平均値と標準偏差を見てみましょう。データポイントの各セットは、平均プラスまたは標準偏差として要約できます。対応する測定値から各平均の有効数字を決定し、それに応じて平均値を丸めます。
各グループの標準偏差は平均と同じ小数点以下の桁数を持つ必要があるため、各標準偏差を100分の1に丸めます。2つの変数間の関係をグラフィカルに決定するために、データをベストフィット関数で適合させることができます。
この関数は、スプレッドシートソフトウェアによって自動的に生成され、線形トレンドライン、多項式関数、指数関数または対数関数の形式をとることができます。温度と体積のデータの場合、関係は線形です。したがって、データポイントは線形最小二乗回帰によって適合されます。スプレッドシート プログラムは、最適適合線と r-squared 値の方程式を返します。r二乗値が 1 に近いほど、データの適合度が高くなります。
次に、スプレッドシート ソフトウェアを使用して、傾きの標準偏差、Y 切片、および計算された Y 値を見つけることができます。方程式の値の有効数字を決定するために、単純なルールに従います。各値の最後の有効数字は、その標準偏差の小数点以下の最初の有効桁数に対応します。
したがって、傾きを1000分の1の位に丸め、y切片を10分の1の位に丸め、標準偏差を一致するように丸めます。傾きはケルビンあたり0.167 +/- 0.003リットルで、y切片は-40.6 +/- 1.2リットルです。計算されたy値は10分の1に丸められ、+/- 0.8リットルになります。この方程式は、温度とガスの体積の関係を表しています。
このラボでは、さまざまなサイズのビーカーの直径と円周を測定することにより、従属変数と独立変数のデータセットを作成します。次に、このデータを使用して散布図を作成し、有効数字の重要性を念頭に置いて線形回帰を実行します。また、ピペットを使用したろ過や容量の測定など、測定と分析の不確実性に注意を払いながら、ラボのスキルを練習します。

科学的な測定とラボスキル

2次元グラフ
一部の化学実験は、温度などの独立変数とも呼ばれる、研究対象のシステムの1つのプロパティを直接変更し、体積などの従属変数と呼ばれる別のプロパティへの影響を測定するという形をとります。データが収集されたら、2つのパラメータ間の相互作用を定量化するか、評価可能な形式に変換して、他の関係と比較する必要があります。
2次元グラフは、2つのプロパティ間の特定の種類の数学的関係を導き出したり、それらの間にそのような関係が存在しないことを立証したりするために使用できます。この分析では、最終的に、従属変数が独立変数に応答してどのように変化するかが決定されます。液体または気体の温度を調整し、その体積の変化を監視する例では、温度が独立変数であり、体積が従属変数です。
2 次元グラフを作成するには、各データ ポイントに、従属変数と独立変数の両方の座標と呼ばれる値が必要です。独立変数は X 軸にプロットされ、従属変数は Y 軸にプロットされます。これらのプロットはスプレッドシートソフトウェアで簡単に作成でき、プロットされたデータの分析にも使用できます。
カーブフィッティング
データセットを2次元グラフにプロットすると、カーブフィッティングを使用して、独立変数の観点から従属変数の方程式または関数を生成できます。関数は、派生元のデータを最適にモデル化する数学的モデルを表します。カーブフィッティングは、データポイントのパターンに適した線を生成する関数を見つける手法です。スプレッドシートソフトウェアには、「ベストフィット」と呼ばれるさまざまなカーブフィッティングツールがあります。これは通常、線形最小二乗回帰分析ですが、ほとんどのソフトウェアでは非線形最小二乗回帰も提供されています。
最適な線形方程式の精度は、データポイントのx値をプラグインし、方程式の「理論」結果をデータポイントの実際のy値と比較することで確認できます。スプレッドシートソフトウェアは通常、関数の決定係数(R2)値を計算し、関数がデータポイントにどの程度一致しているかを示します。R2 の値が 1 に近いほど、線形回帰の適合度が高くなります。他の関数には、関数がデータにどの程度適合しているかを判断するための、より専門的な方法があります。
最適関数から計算された従属値の不確実性を決定するには、複雑な "誤差伝播" 手法が必要になります。ただし、方程式内の不確かさを、最適関数の傾きとy切片の両方の標準偏差の形で計算することは可能です。これは通常、2次元プロットの生成に使用されるツールとは異なるツールで実行されます。
標準偏差
標準偏差は、一連の値に存在する変動の量を表します。母集団標準偏差 (σ) は、ビー玉の袋に入った各ビー玉の質量など、有限母集団の各メンバーからのデータがある場合に使用されます。サンプル標準偏差(s)は他のすべてのケースに使用され、スプレッドシートソフトウェアのデフォルトの標準偏差計算です。1 「標準偏差」はサンプル標準偏差を指していると想定できます。
ランダム測定誤差は、値のセットの約68%が平均の両側の1標準偏差の範囲内にある、値の95%が平均の両側の2標準偏差内にある、値の99.7%が平均の両側の3標準偏差内にある、ほぼ「正規」分布に従うと仮定されます。したがって、標準偏差は、エラーと不確実性を説明するのに便利な方法です。
サンプル標準偏差の式は次のとおりです。
<img src="/CDNSource/lm/labs/42/42_Concepts_1.jpg">
この式では、Nは値の数です。<img src="/CDNSource/lm/labs/42/30034eq02.jpg"> は値の平均値で、xi は個々の値を表します。したがって、標準偏差を手動で計算するには、値のセットの平均を計算し、各値から平均を減算し、各差を二乗し、二乗差を加算し、合計を値の数より1つ少ない値で除算し、商の平方根を取ります。s が 0 に近いほど、値間の変動は少なくなります。表計算ソフトに値を入力すると、ソフトウェア内から標準偏差を計算できます。
標準偏差の有効数字の数は、それがどの値のためのものかによって異なります。同じ条件下で取得されたデータポイントのグループの標準偏差を報告する場合、まず平均値の有効数字の適切な数を決定する必要があります。その後、標準偏差は平均と同じ小数点以下の桁数に丸められます。有効数字が 4 つの数値、平均が 15.361 mL、標準偏差が 0.2313 のボリュームのセットの場合、平均と標準偏差は 0.23 mL ± 15.36 mL と報告されます。
スプレッドシート ソフトウェアの通常の方法である、最小二乗解析によって決定される最適関数の平均と y 切片の標準偏差を報告する場合、標準偏差の小数点第 1 位は、平均値または y 切片の最後の有効数字です。したがって、標準偏差は小数点以下 1 桁に丸め、傾きまたは y 切片は対応する小数点以下の桁数に丸める必要があります。たとえば、傾きが 0.1691 L·K-1 で、標準偏差が 0.00512 の場合、傾きは 0.169 L·K-1 ± 0.005 L·K-1 として報告されます。
傾きまたは y 切片の標準偏差が対応する値よりもはるかに小さいため、このルールに従うと、元の計測データで許容されるよりも多くの有効数字が傾きまたは y 切片に与えられる場合は、代わりに x 値と y 値から傾きまたは y 切片の有効数字を決定し、標準偏差を 1 つの有効数字に丸めます。したがって、傾きが 0.1691 L·K-1、標準偏差が 0.0000512、x 値と y 値に有効数字が 4 桁ある場合、傾きは 0.1691 L·K-1 ± 0.00005 L·K- 1 として報告する必要があります。この場合、計算された値とその標準偏差の小数点以下の桁数が異なる場合でも問題ありません。最小二乗法では、x 値と y 値の両方を使用して傾斜角と y 切片が計算されることに注意してください。
標準偏差を不確かさの範囲として報告する場合は、不確かさが 1 つの標準偏差を表すことに特に注意してください。これにより、正規分布を仮定すると、測定値の真の値が平均のその範囲内に収まる可能性が約 68% あることが読者に伝わります。不確実性を平均から2標準偏差として報告する方が、確率が約95%に増加するため、多くの場合、より適切な場合があります。これを行うには、標準偏差に 2 を掛けてから、適切な有効数字の数に丸めます。
参照
<ol style="font-size:17px">
	<li style="font-size:17px">ハリス、ワシントンD.C.(2015年)。定量的化学分析。ニューヨーク州ニューヨーク:WHフリーマンアンドカンパニー。</li>
</ol>

2次元グラフ
一部の化学実験は、研究しているシステムの1つの特性を直接変更する形をとります。これは...

Education

JoVE Lab Manual

化学

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

Oxidation states help identify redox reactions. In a redox reaction, oxidation is the loss of one or more electrons, and reduction is the gain of one or more electrons. These reactions are often tracked by changes in oxidation state, also called oxidation number. Each atom in a molecule has an oxidation state. This number shows how oxidized an atom is compared with its free elemental form. It is written as the charge an atom would have if every bond were purely ionic. In that model, bonding...

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

Reaction heat is explained through enthalpy, Hess’s law, and calorimetry. These ideas show how heat moves during chemical reactions and how scientists measure it. Thermodynamics is the study of heat energy and other forms of energy, such as work. Its laws are used across science, from biology to physics. The first law says energy is conserved in an isolated system. Energy can change form, such as thermal energy becoming work, but it cannot be created or destroyed. The second law of...

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

Flame testing uses a metal sample and a flame to identify a substance by its color. Each element gives off a characteristic light emission in the flame, so the color can help distinguish one element from another. This same idea appears in fireworks, where different metal components create different colors. The color comes from energy absorbed by the metallic component. When a species absorbs energy, that energy can go into translation, vibration, rotation, or electron excitement. Electron...

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

Chemical kinetics describes the speed of a chemical reaction. The rate depends on the reaction mechanism, the complexity of the reaction, and the number of reactants involved. Reactant concentration also affects how fast a reaction happens. The rate law is the experimental relationship that connects these factors to reaction rate. In the rate law, each reactant contributes through a reaction order. The general form is r = k[A]^m[B]^n for aA + bB + ... → cC. Here, r is the reaction rate, k is...

temperature dependence

Reaction Rate, Arrhenius, and Catalysts

Chemical kinetics explains how fast a reaction happens and why that speed changes. The reaction rate is the speed of a chemical reaction. It is defined as the change in concentration of a reactant or product over time. Reaction speed depends on several factors, including the concentration of the reactants and the temperature of the reaction. Each reactant affects the rate in a specific way. That relationship is described by the rate law. The rate law is an equation that connects the...

galvanic cells

Battery Power from Redox Reactions

Electrochemistry studies how chemical change and electrical energy are linked. In this branch of chemistry, electrons move from one species to another. That movement can either produce current or be driven by an applied current. The main reaction in electrochemistry is the oxidation-reduction, or redox, reaction. A redox reaction has two half-reactions. Oxidation is the loss of electrons, and reduction is the gain of electrons. These changes also shift the oxidation state of each substance. The...

electrolytic cells

Electroplating with Electrolytic Cells

Electrochemistry links electrical energy with chemical change, and electrolytic cells show how electricity can drive a nonspontaneous reaction. In these reactions, electrons move from one species to another. The key chemistry is a redox reaction, or oxidation-reduction reaction, which happens in two half-reactions. Oxidation is the loss of electrons, and reduction is the gain of electrons. The substance that loses electrons is the reducing agent, and the substance that gains electrons is the...

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

Organic chemistry labs use specific glassware, careful weighing steps, and controlled heating to keep reactions safe and accurate. Beakers and Erlenmeyer flasks are often used for mixing or holding solvents, but they are not meant for measuring volume unless only an approximate amount is needed. Volumetric glassware is used when a precise volume matters. This group includes graduated cylinders, volumetric pipettes, and volumetric flasks. A graduated cylinder is commonly used in the organic lab...

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

入門化学ラボコースの指導者と学生のための、包括的でカリキュラムに焦点を当てたビデオ。

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Learn how to plot independent and dependent variables, use best-fit lines, and report standard deviation to describe uncertainty in science data.

Graphs, Curve Fit, and Standard Deviation | JoVE K12

科学的な測定とラボスキル を教える準備を、この 3 分間の教員向けガイドで行いましょう。JoVE Lab Manual の Chemistry ラボの主要な準備手順を解説します。

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この 15 分間の学生プロトコル動画で、科学的な測定とラボスキル の手順をステップごとに学びましょう。JoVE Lab Manual の Chemistry コレクションの一部です。

Chemistry の 科学的な測定とラボスキル 学生プロトコル - 20K+ 回の視聴 | JoVE Lab Manual

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 ...

uncertainty-in-measurement-significant-figures

Uncertainty in Measurement: Significant Figures

All the digits in a measurement, including the uncertain last digit, are called significant figures or significant digits. Note that zero may be a ...

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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