What is the Ideal Gas Law?
The Ideal Gas Law describes the relationship between pressure,
volume, temperature, and the amount of gas present in a system.
It combines several gas laws into one useful equation.
The Ideal Gas Law is:
\[
PV=nRT
\]
This equation is used extensively in chemistry, physics,
engineering, and atmospheric science.
Variables in the Equation
| Symbol |
Description |
Common Units |
| \(P\) |
Pressure |
atm, kPa, mmHg |
| \(V\) |
Volume |
L |
| \(n\) |
Number of Moles |
mol |
| \(R\) |
Gas Constant |
0.0821 L·atm/mol·K |
| \(T\) |
Temperature |
K |
Important Temperature Conversion
Temperature must always be expressed in Kelvin.
\[
K = ^\circ C + 273.15
\]
Example:
\[
25^\circ C + 273.15 = 298.15K
\]
Rearranging the Ideal Gas Law
Depending on the unknown variable, the equation can be rearranged:
Pressure:
\[
P=\frac{nRT}{V}
\]
Volume:
\[
V=\frac{nRT}{P}
\]
Moles:
\[
n=\frac{PV}{RT}
\]
Temperature:
\[
T=\frac{PV}{nR}
\]
Example Problem
Calculate the pressure of 2.0 moles of gas occupying
10.0 L at 300 K.
Use:
\[
P=\frac{nRT}{V}
\]
Substitute values:
\[
P=\frac{(2.0)(0.0821)(300)}{10.0}
\]
\[
P=4.93\ atm
\]
Practice Problems
Problem 1:
Convert 50°C to Kelvin.
323.15 K
Problem 2:
Find the volume of 1.5 mol of gas at 300 K and 1 atm.
36.9 L
Problem 3:
A gas occupies 5.0 L at 2 atm and 273 K.
Calculate the number of moles.
Approximately 0.45 mol
Problem 4:
What pressure is exerted by 1 mol of gas in a
22.4 L container at 273 K?
Approximately 1 atm
Problem 5:
Convert 100°C to Kelvin.
373.15 K
Challenge Problems
-
Calculate the volume of 3.5 mol of gas at
400 K and 2 atm.
-
A gas occupies 15 L at 350 K and 1.2 atm.
Determine the number of moles present.
-
Calculate the pressure exerted by 0.75 mol
of gas in an 8.0 L container at 290 K.
-
Determine the temperature of 2 mol of gas
occupying 12 L at 4 atm.