16 Ideal Gas Law
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The Ideal Gas Equation
The ideal gas equation is given as [latex]PV = nRT[/latex].
LEARNING OBJECTIVES
Apply the ideal gas law to solve problems in chemistry.
KEY TAKEAWAYS
Key Points
- An ideal gas exhibits no attractive forces between particles.
- In the ideal gas equation, both pressure and volume are directly proportional to temperature.
Key Terms
- ideal gas constant: R = 8.3145 J·mol-1·K-1
- ideal gas: A gas whose particles exhibit no attractive interactions whatsoever; at high temperatures and low pressures, gases behave close to ideally.
- kinetic energy: The energy possessed by an object because of its motion; in kinetic gas theory, the kinetic energy of gas particles is dependent upon temperature only.
Kinetic Theory and Ideal Gases
All gases are modeled on the assumptions put forth by the kinetic theory of matter, which assumes that all matter is made up of particles (i.e., atoms or molecules). There are spaces between these particles, and attractive forces become stronger as the particles converge. Particles are in constant, random motion, and they collide with one another and the walls of the container in which they are enclosed. Each particle has an inherent kinetic energy that is dependent upon temperature only.
A gas is considered ideal if its particles are so far apart that they do not exert any attractive forces upon one another. In real life, there is no such thing as a truly ideal gas, but at high temperatures and low pressures (conditions in which individual particles will be moving very quickly and be very far apart from one another so that their interaction is almost zero), gases behave close to ideally; this is why the ideal gas law is such a useful approximation.
“Ideal Gas Law Introduction”: This video discusses the ideal gas law PV = nRT and how you use the different values for R: 0.0821, 8.31, and 62.4.
Ideal Gas Law Equation
The ideal gas equation is given as:
[latex]PV = nRT[/latex]
The four variables represent four different properties of a gas:
- Pressure (P), often measured in atmospheres (atm), kilopascals (kPa), or millimeters mercury/torr (mm Hg, torr)
- Volume (V), given in liters
- Number of moles of gas (n)
- Temperature of the gas (T) measured in degrees Kelvin (K)
R is the ideal gas constant, which takes on different forms depending on which units are in use. The three most common formulations of R are given as:
[latex]8.3145 \frac{\text{L } \cdot \text{ kPa}}{\text{K } \cdot \text{ mol}} = 0.0821 \frac{\text{L } \cdot \text{ atm}}{\text{K } \cdot \text{ mol}} = 62.4 \frac{\text{L } \cdot \text{ mm Hg}}{\text{K } \cdot \text{ mol}}[/latex]
EXAMPLE 1
A 20 L box contains a fixed amount of gas at a temperature of 300 K and 101 kPa of pressure. How many moles of gas are contained in the box?
[latex]PV = nRT[/latex]
[latex]n = \frac{PV}{RT} = \frac{\text{(101 kPa)(20 L)}}{\text{(8.3145 L } \cdot \text{ kPa } \cdot \text{ K}^\text{-1 } \cdot \text{ mol}^\text{-1} \text{) } \cdot \t