Gases for the DAT
/Learn key DAT concepts about gases, plus practice questions and answers
everything you need to know about gases for the dat
Table of Contents
Part 1: Introduction to gases
Part 2: Gas law equations
a) Kinetic molecular theory of gases
b) Ideal gas law
c) Ideal gas law derivatives
d) Dalton’s law
e) Henry’s law
Part 3: High yield terms
Part 4: Questions and answers
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Part 1: Introduction to gases
Gas laws are a cornerstone of general chemistry. They elucidate the behavior of gases under varying conditions and provide crucial insights into their properties and interactions. These laws, including Boyle's Law, Charles's Law, Avogadro's Law, and more, establish relationships between key variables such as pressure, volume, temperature, and quantity of gas molecules. Combined in the Ideal Gas Law, these principles offer a comprehensive framework for predicting and understanding the behavior of gases in different situations, from everyday applications to industrial processes and environmental considerations. This guide will teach you all the gas laws you need to know for the DAT. As you study this topic, pay attention to the bolded high-yield terms.
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Part 2: Gas law equations
a) Kinetic molecular theory of gases
What is gas? You might have been taught that gas is a state of matter that fills the entire space available to it and takes on the shape of its container.
One way to examine gases is with the kinetic molecular theory. According to the kinetic molecular theory, gases are made of molecules that are always in motion. Gas molecules travel in a straight line and collide with other gas molecules or the walls of their container. These collisions are elastic, meaning that no energy is lost. Pressure is a result of gas molecules colliding with the sides of the gas’ container. Increasing the temperature of the gas will proportionally increase the kinetic energy of the gas. The gas laws explored later in this guide were derived from assumptions of this theory.
An ideal gas is one that exactly follows the gas laws. Ideal gases are only theoretical, have no volume, and exhibit no intermolecular forces. These theoretical assumptions are closely approached under specific conditions, such as high temperatures and low pressures (leading to large volumes). However, when pressures are moderately high or volumes are low, intermolecular attractions become noticeable.
Similarly, at moderately low temperatures, gas molecules slow down due to decreased kinetic energy. Consequently, in both cases, the actual volume occupied by the gas is less than what the ideal gas law predicts.
When pressures exceed 300 atmospheres, volumes or temperatures are low, and the volume of individual gas particles cannot be ignored. Consequently, the gas occupies more volume than predicted by the ideal gas law.
b) Ideal gas law
The ideal gas law allows us to describe the properties of a gas sample. It is expressed as:
P: Pressure
V: Volume
n: number of moles
T: Temperature
R: ideal gas constant
In the context of gas law problems, R will likely be expressed as 0.0821 L*atm / mol*K. However, on test day, you may see R expressed as 8.314 J/K*mol. Always be mindful of the units!
The ideal gas law is a numerical representation of the kinetic molecular theory. Looking at the figure below, we can see how changes in temperature, pressure, volume, and number of moles affect gas molecules.
FIGURE 1: GAS MOLECULES SHOWN IN RED. ENERGY SHOWN BY LENGTH OF BLACK LINE. ENERGY IS THE SAME FOR 1 AND 3 BUT HIGHER FOR 2.
The left image is the baseline that images 1, 2, and 3 will be compared to. In image 1, the volume of the container is decreased. This gives the gas molecules less room to move and causes more collisions between molecules and walls of the container. The collisions with the container create more pressure than when there is more volume, so the pressure for image 1 is higher than the baseline.
For image 2, the temperature is increased, while volume remains the same. The increase of temperature results in an increase in energy that makes the molecules move faster. This leads to more impactful collisions with the walls of the container, so the pressure is higher than the baseline image.
Image 3 depicts an increase in the number of molecules that are added, shown in this image as the number of moles. Adding gas molecules prompts the volume to increase in order to make space for the extra molecules.
Let’s walk through an example of how you might need to use the ideal gas equation.
Suppose we have a sealed container with a volume of 5.0 liters that contains helium gas at a pressure of 2.0 atmospheres and a temperature of 300 Kelvin. If we want to know how many moles of helium are present in the container, we can use the ideal gas law equation. Start by determining what variables we are already given, and algebraically rearrange the equation to solve for moles of gas.
Given: Pressure (P) = 2.0 atm Volume (V) = 5.0 L Temperature (T) = 300 K Ideal gas constant (R) = 0.0821 L·atm/(K·mol)
PV=nRT
n = PV / RT
n = (2.0 atm) * (5.0 L) / (0.0821 L·atm/(K·mol) * 300 K)
n ≈ (10.0 atm*L) / (24.63 L·atm/mol) n ≈ 0.406 moles
So, there are approximately 0.406 moles of helium gas present in the container. This calculation demonstrates how we can use the ideal gas law to determine the number of moles of a gas when given its pressure, volume, and temperature.
When making gas-related calculations, scenarios frequently involve Standard Temperature and Pressure (STP). In STP conditions, the temperature is 273 K (0°C), and the pressure is 1 atm. At STP, one mole of an ideal gas fills a volume of 22.4 liters.
c) Ideal gas law derivatives
The ideal gas law gives rise to numerous derivative formulas centering on specific variables, all of which can be derived by considering identical samples of an ideal gas undergoing two sets of slightly distinct conditions.
Boyle’s law articulates that the volume and pressure of a gas exhibit an inverse relationship. This means that when the pressure increases, the sample volume must decrease, and vice versa. This principle is formulated as:
k = PV
k: Proportionality constant P: Pressure
V: Volume
Here is a practice problem walking you through how Boyle’s law is used in making calculations.
Suppose we have a sealed container of fixed volume containing a sample of helium gas at a pressure of 4.0 atmospheres. If we compress the gas, reducing its volume to half of its original volume while keeping the temperature constant, what will be the new pressure?
We can rearrange this equation to solve for the final pressure (P2): P2 = (P1 * V1) / V2
Now, plug in the given values and solve for final pressure.
P2 = 8.0 atm
The new pressure of the helium gas after compressing it to half of its original volume while keeping the temperature constant will be 8.0 atmospheres. This pressure is double the original pressure. The volume was multiplied by ½, so the pressure was multiplied by the inverse, which is 2. Our calculations agree with Boyle’s law, so the final pressure is 8 atm.
Charles's law is another derivative of the ideal gas law. This law declares that the volume and temperature of a gas are directly proportional. In simpler terms, an increase in volume corresponds to an increase in temperature. This law is articulated as:
k = V/T
k: Proportionality constantV: Volume
T: Temperature
Charles’s law can be used as follows:
Suppose we have a sealed container filled with a sample of oxygen gas at a constant pressure of 2.0 atmospheres. If we heat the gas, causing its temperature to increase from 273 Kelvin to 373 Kelvin while keeping the pressure constant, what will be the new volume of the gas?
Given: Initial temperature (T1) = 273 K Final temperature (T2) = 373 K Initial volume (V1) = 1.0 L (for instance) Pressure (P) = 2.0 atm
Charles's Law states that the volume of a gas is directly proportional to its temperature when the pressure is kept constant. Mathematically, it can be expressed as V1 / T1 = V2 / T2, where V1 and T1 are the initial volume and temperature, and V2 and T2 are the final volume and temperature, respectively.
As with the previous gaw laws, we can rearrange Charles's Law to solve for the variable we are looking for. In this case, it’s final volume (V2): V2 = (V1 * T2) / T1
Plug the given values into the equation and solve.
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