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

Перевод экспериментальных результатов из точек данных в визуальные представления, такие как графики, имеет важное значение для определения взаимосвязи между двумя или более свойствами. Эти свойства называются переменными. Когда переменных две, график, созданный на основе данных, называется двумерным. График имеет две оси. Независимая переменная отображается на оси x, а зависимая переменная — на оси y.
Возьмем, к примеру, этот образец данных о температуре и объеме газа. Объем газа зависит от температуры. Таким образом, мы построим график измеренной температуры по оси x и объема по оси y.
Когда есть несколько точек данных с одинаковым x-значением, например, если мы измеряем объем несколько раз при одной температуре, мы также вычисляем стандартное отклонение этих измерений. Стандартное отклонение — это статистическая величина, которая указывает на величину вариации, присутствующей в наборе значений.
Стандартное отклонение вычисляется по следующей формуле, где n — количество точек данных, x bar — среднее значение точек данных, а xi представляет каждую отдельную точку данных. Вы можете вычислить стандартное отклонение вручную, или программа для работы с электронными таблицами может вычислить его автоматически. Чем ближе стандартное отклонение к 0, тем ближе точки данных к среднему значению. Если стандартное отклонение равно 0, то все введенные точки данных имеют одинаковое значение.
Давайте рассмотрим средние значения и стандартные отклонения измерений объема при каждой температуре в нашем наборе данных. Мы можем суммировать каждый набор точек данных как среднее значение плюс-минус стандартное отклонение. Мы определяем значащие значения для каждого среднего значения из соответствующих измерений и округляем средние значения соответственно.
Стандартное отклонение каждой группы должно иметь такое же количество знаков после запятой, как и среднее, поэтому мы округляем каждое стандартное отклонение до сотых долей. Чтобы графически определить связь между двумя переменными, мы можем подогнать данные с помощью функции наилучшего соответствия.
Функция автоматически генерируется программным обеспечением для работы с электронными таблицами и может принимать форму линейной линии тренда, полиномиальной функции, экспоненциальной или логарифмической функции. В случае наших данных о температуре и объеме зависимость является линейной. Таким образом, точки данных подгоняются с помощью линейной регрессии по методу наименьших квадратов. Ваша программа для работы с электронными таблицами вернет уравнение для линии наилучшего соответствия и значения r-квадрат. Чем ближе значение r-квадрата к 1, тем лучше соответствие данных.
Затем вы можете использовать программное обеспечение для работы с электронными таблицами для поиска стандартных отклонений наклона, точки пересечения по оси y и вычисленного значения y. Чтобы определить значащие цифры для значений в уравнении, мы следуем простому правилу. Последняя значащая цифра каждого значения соответствует первому значащему знаку после запятой его стандартного отклонения.
Таким образом, мы округляем наклон до тысячных и y-пересечение до десятых долей, а стандартные отклонения округляем до соответствия. Наш уклон составляет 0,167 +/- 0,003 литра на Кельвина, а наш y-образный пересечение составляет -40,6 +/- 1,2 литра. Любое вычисленное y-значение будет округлено до десятых долей и составит +/- 0,8 литра. Это уравнение описывает взаимосвязь между температурой и объемом газа.
В этом лабораторном занятии вы создадите набор данных зависимых и независимых переменных, измерив диаметр и окружность стаканов различных размеров. Затем вы будете использовать эти данные для создания точечной диаграммы и выполнения линейной регрессии, учитывая важность значащих фигур. Вы также будете практиковать лабораторные навыки, такие как фильтрация и измерение объема с помощью пипеток, обращая внимание на неопределенность в измерениях и анализе.

Научные измерения и лабораторные навыки

Двумерные графы
Некоторые химические эксперименты принимают форму прямого изменения одного свойства изучаемой системы, известного как независимая переменная, например, температура, и измерения влияния на другое свойство, также известное как зависимая переменная, например, объем. После того, как данные собраны, взаимодействие между двумя параметрами должно быть количественно оценено — или преобразовано в форму, которую можно оценить, — и сравнено с другими отношениями.
Двумерные графы могут быть использованы для вывода определенных типов математических отношений между двумя свойствами или для установления того, что между ними не существует такой связи. Анализ в конечном итоге определит, как зависимая переменная изменяется в ответ на независимую переменную. В примере с регулировкой температуры жидкости или газа и мониторингом изменений его объема температура является независимой переменной, а объем — зависимой переменной.
Чтобы построить двумерный график, каждая точка данных должна иметь значение, известное как координата как зависимых, так и независимых переменных. Независимая переменная отображается на оси x, а зависимая переменная — на оси y. Эти графики легко создаются в программном обеспечении для работы с электронными таблицами, которое также можно использовать для анализа построенных данных.
аппроксимация кривой
После того, как набор данных был нанесен на двумерный график, можно использовать аппроксимацию кривой для создания уравнения или функции для зависимой переменной в терминах независимой переменной. Функции представляют собой математическую модель, которая наилучшим образом моделирует данные, из которых она получена. Аппроксимация кривой — это метод нахождения функции, которая создает линию, хорошо соответствующую шаблону точек данных. Программное обеспечение для работы с электронными таблицами имеет различные инструменты подгонки кривых, которые называются «наилучшим соответствием». Обычно это линейный регрессионный анализ по методу наименьших квадратов, хотя большинство программ также предлагает нелинейную регрессию по методу наименьших квадратов.
Точность наиболее подходящего линейного уравнения может быть проверена путем подстановки значений x для точек данных и сравнения «теоретических» результатов уравнения с фактическими значениями y точек данных. Программное обеспечение для работы с электронными таблицами обычно вычисляет значение коэффициента детерминации (R2) для функции, которое показывает, насколько хорошо функция соответствует точкам данных. Чем ближе значение R2 к 1, тем лучше подходит для линейной регрессии. Другие функции имеют более специализированные методы для определения того, насколько хорошо функция соответствует данным.
Определение неопределенности зависимых значений, вычисленных из функции наилучшего соответствия, потребовало бы сложных методов «распространения ошибок». Тем не менее, можно вычислить неопределенность в уравнении в виде стандартного отклонения как для наклона, так и для точки пересечения с осью y функции наилучшего соответствия. Обычно это выполняется с помощью инструмента, отличного от того, который используется для создания двумерного графика.
стандартное отклонение
Стандартное отклонение описывает величину вариации, присутствующей в наборе значений. Стандартное отклонение популяции (σ) используется, когда есть данные от каждого члена конечной популяции, такие как масса каждого шарика в мешке с шариками. Образец стандартного отклонения (ов) используется для всех остальных случаев и является расчетом стандартного отклонения по умолчанию в программном обеспечении для работы с электронными таблицами. 1 Можно предположить, что «стандартное отклонение» относится к выборочному стандартному отклонению.
Предполагается, что случайная ошибка измерения следует примерно «нормальному» распределению, где около 68% набора значений лежат в диапазоне одного стандартного отклонения по обе стороны от среднего, 95% значений лежат в пределах двух стандартных отклонений по обе стороны от среднего и 99,7% значений лежат в пределах трех стандартных отклонений по обе стороны от среднего. Таким образом, стандартное отклонение является полезным способом описания ошибок и неопределенностей.
Уравнение для стандартного отклонения выборки выглядит следующим образом:
<img src="/CDNSource/lm/labs/42/42_Concepts_1.jpg">
В этом уравнении N — количество значений; <img src="/CDNSource/lm/labs/42/30034eq02.jpg"> — среднее (или среднее) значений; а xi представляет каждое отдельное значение. Таким образом, чтобы вычислить стандартное отклонение вручную, вычислите среднее значение набора значений, вычтите среднее из каждого значения, возведите в квадрат каждую разницу, сложите квадраты разностей, разделите общую сумму на единицу меньше, чем количество значений, и возьмите квадратный корень из частного. Чем ближе s к нулю, тем меньше разброс между значениями. Если значения введены в программное обеспечение для работы с электронными таблицами, стандартное отклонение может быть рассчитано в программном обеспечении.
Количество значащих цифр в стандартном отклонении зависит от того, для каких значений оно предназначено. При сообщении стандартного отклонения для группы точек данных, полученных в одинаковых условиях, сначала необходимо определить соответствующее количество значащих цифр в среднем значении. Затем стандартное отклонение округляется до того же количества знаков после запятой, что и среднее. Для набора объемов с четырьмя значащими цифрами, средним значением 15,361 мл и стандартным отклонением 0,2313, среднее значение и стандартное отклонение будут представлены как 15,36 мл ± 0,23 мл.
При сообщении о стандартном отклонении среднего значения и y-точки для функции наилучшего соответствия, определенной с помощью анализа по методу наименьших квадратов, который является обычным методом для работы с электронными таблицами, первый десятичный знак стандартного отклонения является последней значащей цифрой среднего значения или y-точки. Таким образом, стандартное отклонение должно быть округлено до одного значащего знака после запятой, а наклон или y-точка пересечения должна быть округлена до соответствующего знака после запятой. Например, если наклон равен 0,1691 Л·К-1 и имеет стандартное отклонение 0,00512, то наклон должен быть указан как 0,169 Л·К-1 ± 0,005 Л·К-1.
Если стандартное отклонение наклона или точки пересечения с осью y настолько меньше соответствующего значения, что следование этому правилу дает более значащие значения наклона или точки пересечения, чем это позволяют исходные данные измерения, то вместо этого определите значащие значения наклона или точки пересечения по осям x и y и округлите стандартное отклонение до одной значащей величины. Таким образом, для наклона 0,1691 L·K-1, стандартного отклонения 0,0000512 и значений x и y с четырьмя значащими цифрами наклон должен быть указан как 0,1691 L·K-1 ± 0,00005 L·K-1. В этом случае вычисленное значение и его стандартное отклонение могут иметь разное количество знаков после запятой. Имейте в виду, что метод наименьших квадратов использует значения x и y для вычисления наклона и y-пересечения.
При указании стандартного отклонения как диапазона неопределенности обязательно обратите особое внимание, что неопределенность представляет собой одно стандартное отклонение. Это говорит читателю о том, что существует около 68% вероятности того, что истинное значение измерения находится в пределах этого диапазона среднего значения, предполагая нормальное распределение. Часто может быть более целесообразным сообщать о неопределенности в виде двух стандартных отклонений от среднего, так как это увеличивает вероятность примерно до 95%. Для этого просто умножьте стандартное отклонение на два, прежде чем округлить его до соответствующего числа значащих цифр.
Ссылки
<ol style="font-size:17px">
	<li style="font-size:17px">Harris, D.C. (2015). Количественный химический анализ. Нью-Йорк, Нью-Йорк: W.H. Freeman and Company.</li>
</ol>

Двумерные графы
Некоторые химические эксперименты принимают форму прямого изменения одного свойства системы, которую вы изучаете, иначе известного как ...

Education

JoVE Lab Manual

Химия

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

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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

Comprehensive, curriculum-focused videos for both instructors and students in introductory chemistry lab courses.

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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 ...

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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