Ideal gases are precisely what their name assumes them to be: ideal! And, just like most ideal things, they are non-existent! However, there are two gases that behave closely to what you expect from an ideal gas, although not in the most perfect way. Hydrogen (H2) and Helium (He) are examples of real gases that behave closely to the assumptions of ideal gas behavior. This is because they have weak intermolecular forces and occupy a very small volume. So, you might be thinking: when do we consider a gas ideal? Or, when does deviation from the ideal gas law happen?
In this article, we will look at the definition and application of the ideal gas law, and the deviation of real gases from this ideal behavior!
- This article is about the deviation from ideal gas law.
- First, we will see the ideal gas law.
- Then, we will analyse the density and deviations from ideal gas law.
- After that, we are going to explain the Boyle's law deviation from ideal gas law.
- To finish, the conditions and deviations from the ideal gas law.
Ideal Gas Law
Before diving into the definitions and ideal and real gases, let's review about the basic properties of gases and the kinetic molecular theory.
Gases are one of the three most common states of matter. Gases are commonly known for:
If you want to know more about the difference between the three most common states of matter, take a look at the article "Solids, Liquids, and Gases"
If a gas molecule behaves according to the "Kinetic Molecular Theory", then we consider them an ideal gas. When you are dealing with an ideal gas, the ideal gas law can be used to relate its volume, pressure, the number of moles, and temperature.
Pressure, Volume, and Temperature
Pressure is an intensive property, meaning that it does not depend on the amount of matter or substance present. The pressure of a gas is the force exerted by the gas on the surface of its container.
Pressure is the force exerted per unit area.
The SI unit of pressure is the pascal (1 Pa = 1 N/m2 or 1 kg m-s2) but it can be converted between different units. Some conversions that you might come across are:
Let's look at an example where you need to convert between different units of pressure!
Convert 700 mmHg to Pa and torr.
We can use the conversions above to answer this question.
a) Convert mmHg to Pa:
$$700mmHg\cdot \frac{133.322Pa}{1mmHg}=93325.4Pa$$
b) Convert Pa to torr:
$$93325.4Pa\cdot \frac{1atm}{1.013\cdot 10^{5}Pa}\cdot \frac{760torr}{1atm}=700.17torr$$
Did you know that although a pressure of 1 atm is considered the standard atmospheric pressure of the Earth, it can change at certain points depending on the weather? For example, if there is low atmospheric pressure in a certain area (also known as depression) compared to the surrounding pressure, you might notice a lot of clouds, high winds, warm air, and even tropical storms. On the other hand, if an area has high pressure (also called anticyclone), then you will see an absence of clouds and tranquil weather!
Gases also have partial pressure, which is the pressure exerted by an individual gas within a mixture. Partial pressure is a part of Dalton's Law of Partial pressures, which states that the sum of the partial pressures of each individual gas in a container is equal to the total pressure of the mixture of gases in the same container.
Partial pressure is defined as the pressure exerted by an individual gas within a mixture.
The equation Dalton's Law of Partial pressure is:
$$P_{total}=P_{A}+P_{B}+...$$
Fig. 1: Visualizing Partial Pressure, Isadora Santos - StudySmarter Originals.
If you are starting to feel confused, let's look at an example of how to calculate the total pressure of a container using Dalton's Law!
A sample of Nitrogen gas exerts a partial pressure of 1.25 atm inside a container. This container also has Neon gas exerting a partial pressure of 80 torr. Calculate the total pressure inside the container.
First, we need to convert the neon pressure from torr to atm. Then, we can just add up the partial pressures to get the total pressure inside the container.
$$80torr\cdot \frac{1atm}{760torr}=0.105atm$$
$$P_{total}=1.25atm+0.105atm=1.355atm$$
Feeling the need to review partial pressures? Check out the article "Ideal Gas Law"!
Volume is an extensive property that also affects the behavior of gases. Extensive properties are properties that depend on the amount of matter being measured. In gases, the volume is not fixed because gases take the shape of the container. Gases can also be compressed when pressure is applied, resulting in a change in volume.
Volume is the amount of space that matter occupies.
The SI base unit for volume is the liter (L). But, similar to pressure, it can be converted to other units!
- 1 L = 10-3 m3.
- 1 L = 1 dm3.
- 1 L = 103 cm3.
- 1 L = 1.0567 qt.
- 1 gallon = 4 qt.
- 1 gal = 3.7854 L.
- 1 cm3 = 1 mL.
- 1 in3 = 16.39 cm3.
So, if you understand how to use these different conversions, you can apply them to various examples like the one below!
A certain gas is found inside a 3.00 in3 container. Convert the volume of the container to liters (L).
By using the volume conversions, we can quickly find the volume of the container in liters.
$$3.00in^{3}\cdot \frac{16.39cm^{3}}{1in^{3}}\cdot \frac{1L}{10^{3}cm^{3}}=0.0492L$$
Temperature is an intensive property, so it does not depend on the amount of substance. Changing temperature causes phase changes.
Temperature is defined as the measurement of the average kinetic energy
You might be asked to convert between other temperature units in your exam, so these are the conversions you should know:
- Temperature from Celsius to Kelvin:
$$T_{K}=T_{Celsius}+273.15$$
$$T_{Celsius}=T_{K}-273.15$$
$$T_{Celsius}=\frac{T_{Fahrenheit}-32}{1.8}$$
$$T_{Fahrenheit}=(1.8\cdot T_{Celsius})+32$$
Convert a temperature of 23 °C to Kelvin and Fahrenheit.
$$T_{K}=23^{o}C+273.15=296.15K$$
$$T_{Fahrenheit}=(1.8\cdot 23^{o}C)+32=73.4F$$
There are three laws that, when combined, create the Ideal Gas law Formula. These three laws are Boyle's Law, Charles's Law, and Avogadro's Law:
- Boyle's Law states that a confined gas's volume (V) is inversely proportional to the pressure (P) exerted on the gas.
- Charles' Law states that the temperature of a gas is directly proportional to the volume of a gas.
- Avogadro's Law states that the quantity of gas is directly proportional to the volume of a gas, as long as the pressure and temperature of the gas stay the same.
Fig. 2: Graphical representation of Boyle's law, Charles's Law, and Avogadro's Law, Isadora Santos - StudySmarter Originals.
If you want to know more about these three laws, check out the article "Ideal Gas Law"!
The formula for the Ideal Gas Law is:
$$P\cdot V=n\cdot R\cdot T$$
Where:
- P = pressure in Pa.
- V = volume of gas in liters.
- n = amount of gas in moles.
- R = universal gas constant = 0.082057 L·atm / (mol·K).
- T = temperature of the gas in Kelvin (K).
Now, let's work through an example and apply the ideal gas law equation!
You have a container with 2 moles of oxygen gas at 298 K. The container has a pressure of 1.40 atm. Find the volume (in L) of the container?
Now, we can rearrange the ideal gas law formula to solve for the volume!
$$V=\frac{n\cdot R\cdot T}{P}=\frac{(2.0mol\ O_{2})(0.08206)(298K)}{1.4atm}=34.9L$$
Density and Deviation from Ideal Gas Law
We can also use the ideal gas law to find the density of gases. Density is also an intensive property and can be calculated by dividing mass over volume. When dealing with density, we say that gases deviate from the ideal gas law at moderate and higher densities.
Density is defined as the amount of mass per volume.
The ideal gas law formula relating density is:
$$d=\frac{m}{V}=\frac{PM}{RT}$$
Where:
- d = density (g/L).
- P = pressure (atm).
- M = molar mass (g).
- R = ideal gas constant (R = 0.08206 J/mol·K).
- T = temperature (K).
Let's utilize the ideal gas/density formula and solve an example!
Calculate the density of carbon monoxide at 0.89 atm and a temperature of 335 K.
First, we need to find the molar mass of carbon monoxide. So:
Now, we can plug with are the variables into the ideal gas law-density equation!
$$d=\frac{PM}{RT}=\frac{(0.89atm)\cdot (28.01g)}{(0.08206\frac{J}{mol\cdot K})\cdot (335K)}=0.907\frac{g}{L}$$
Deviations from the Ideal Gas Law
So far, we have only looked at ideal gases and how they behave. Now, we have to consider what happens when gases do not behave ideally! If a gas molecule deviates from ideal behavior (according to the kinetic molecular theory), then we call them real gases. Compared to ideal gases, real gases do have volume and forces of attraction/repulsion present, so particles do interact with one another.
Real gases are defined as gases that do not have ideal behavior and therefore are not considered ideal gases.
Deviations from the ideal gas law are less at low pressure and high temperature, and greater at high pressure and low temperature. Also, heavier gases tend to deviate most from the ideal gas behavior.
This deviation at high pressure and low temperature happens because, at low temperatures, the attractive forces can interact with the gas molecules because they have low speeds. When gases are at a low temperature, then they will have low kinetic energies.
- Temperature and kinetic energy are directly proportional to one another.
Since real gases deviate from the ideal gas law, what can we do if we needed to calculate the pressure, volume, amount of gas, or temperature of real gases? Easy. We can use van der Waal's equation for real gases!
$$[P+a(\frac{n}{V})^{2}]\cdot [V-bn]=nRT$$
- P = pressure of the gas
- V = volume of gas
- n = amount of gas in moles
- R = universal gas constant = 0.082057 L·atm / (mol·K)
- T = temperature of the gas in Kelvin (K)
- Constant a and Constant b = depend on the type of gas we are dealing with.
The van der Waal's equation was actually derived from the ideal gas law formula, and some corrections were made to consider the volume occupied by the gas and the intermolecular forces that are present. This is what the constants a and b are: correction factors! The values for these constants are specific for each gas. If you come across a question asking to use the real gas formula, you will be given these values, so you worry about memorizing them!
So, try not to feel overwhelmed when you see this equation! It's not as complicated as it looks and can be easily applied in calculations.
You have 0.990 moles of O2 in 1.00 L at 298 K. Using the Van der Waals formula, calculate the pressure for O2.
a = 1.36 atm·L2/mol2
b = 0.0318 atm/mol
R = 0.0821 atm/mol·K
$$P=\frac{nRT}{V-nb}-\frac{n^{2}a}{V^{2}}$$
$$P=\frac{(0.990)(0.0821)(298)}{1.00-(0.990\cdot 0.0318)}-\frac{(0.990)^{2}(1.36)}{(1.00)^{2}}$$
$$P=23.68atm$$
Boyle's Law Deviation from Ideal Gas
Let's talk about Boyle's law! This law states that, at a constant temperature and number of moles, the volume (V) of a confined gas is inversely proportional to the pressure (P) exerted on the gas In other words, when volume increases, pressure decreases (and vice versa).
When we say that real gases deviate from the ideal gas law, it means that real gases do not follow Boyle's law, Charles's law, or Avogadro's law perfectly!
Conditions and Deviations from the Ideal Gas Law
To make things simple, let's summarize the conditions for deviation from the ideal gas law!:
- Gases only obey the ideal gas law at high temperature and low pressure. So, gases will deviate from the ideal gas law at high pressure and low temperatures.
- Ideal gases are assumed to occupy a negligible volume. But, in reality, gas molecules do occupy volume, especially at low temperatures and high pressures!
- Ideal gases are said to have perfect elastic collisions. Now we know that at low temperature and high pressure, gas pressures are lower than predicted and do possess some intermolecular interactions.
Now, you should have an understanding of ideal and real gases, and also the different equations that are used to analyze their behavior!
Deviation From Ideal Gas Law - Key takeaways
- The kinetic molecular theory is used to explain the behavior of gas molecules. If a gas molecule behaves according to the kinetic molecular theory, then we consider them an ideal gas.
- If a gas molecule deviates from ideal behavior (according to the kinetic molecular theory), then we call them real gases.
- Deviations from the ideal gas law are less at low pressure and high temperature, and greater at high pressure and low temperature.
References
- Moore, J. T., & Langley, R. (2021). AP Chemistry, 2022. New York: McGraw-Hill.
- Thorpe, G. S. (2008). Cliff's AP chemistry (3rd ed.). Hoboken, NJ: Wiley Pub.
- Zumdahl, S. S., Zumdahl, S. A., & DeCoste, D. J. (2017). Chemistry. Boston, MA: Cengage.
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