The Ideal Gas Law (College Board AP® Chemistry): Revision Note
The Ideal Gas Law
The physical properties of a gas are defined by four important variables:
Temperature, T
Pressure, P
Volume, V
Amount of gas, which is expressed as number of moles, n
An ideal gas is a hypothetical gas whose pressure, volume and temperature relationships are described completely by the ideal-gas equation which is given as:
PV = nRT
P is pressure; the SI unit is the pascal (Pa), but AP questions usually give pressure in atm, mm Hg or torr (1 atm = 760 mm Hg = 760 torr)
V is the volume with the SI unit of m3
n is the number of moles
R is the gas constant: 0.08206 L atm mol-1 K-1 (use with pressure in atm and volume in L) or 8.314 J mol-1 K-1 (use with Pa and m3, or for energy). Both values are on the equations and constants reference
T is temperature, expressed in kelvins (K)
The characteristics of an ideal gas are defined by two important assumptions:
The volume of the gas particles themselves is negligible compared with the volume of the container
This is why the volume of an ideal gas is taken as the same as the volume of its container
The particles have zero intermolecular force of attraction
Worked Example
Tennis balls are often filled with nitrogen gas, N2 (g), as this helps to keep the ball inflated for longer. To increase their bounce they can be filled with nitrogen to pressures above atmospheric pressure. If a tennis ball has a volume of 149 mL and contains 0.35 g of N2 gas, what is the pressure inside the ball at 24 ℃?
Analyze: The question asks for the pressure of nitrogen gas given the volume (149 mL), temperature (24 ℃) and mass (0.35 g) of nitrogen gas.
Plan: use the ideal gas equation to find the pressure; first convert the mass of nitrogen to moles, the temperature to K and the volume to L.
Answer:
Step 1: Convert the mass of nitrogen to moles
n = mass/molar mass
n = 0.35/28 = 0.0125 moles
Step 2: Convert temperature and volume into the correct units
T = 24 + 273 = 297 K
V = 149/1000 = 0.149L
R = 0.08206 L atm mol-1 K-1
Step 3: Rearrange the ideal gas equation to find the pressure
P = nRT/V
Step 4: Substitute values into the rearranged equation and determine the pressure
P = 0.0125 × 0.08206 × 297 / 0.149 = 2.0 atm (2 sig figs)
Examiner Tips and Tricks
Be careful about units…and significant figures
Always ensure that the unit and value of R used correspond with the units of pressure and volume
Use only the amounts given in the question: never assume 1 L or 1 mol, never use a coefficient from the balanced equation as n, and never use the molar mass as the mass of the sample
Exam questions usually give pressure in atm or mm Hg and volume in mL or L
The conversion factors for pressure are as follows:
1 atm = 760 mm Hg = 760 torr
Also, ensure your final answer is in the correct number of significant figures. Best practice involves doing all calculations until the final step before applying the correct number of significant figures
Unlock more, it's free!
Join the 100,000+ Students that ❤️ Save My Exams
the (exam) results speak for themselves:
Was this revision note helpful?
Build on this topic
