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 with a value of 1 atm (SI unit)
- Other values and units include 760 mm Hg and 760 torr
- V is the volume with the SI unit of m3
- n is the number of moles
- R is the molar gas constant with a value of 9.314 J mol-1 K-1 (SI unit)
- Other values and units include 0.08206 L atm mol-1 K-1 and 62.36 L torr mol-1 K-1
- T is temperature which is expressed in Kelvin
- The characteristics of an ideal gas are defined by two important assumptions:
- The volume of an ideal gas is negligible compared to the volume of its 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
- The volume of an ideal gas is negligible compared to the volume of its container
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: We are asked to calculate the pressure of nitrogen gas given the volume (149mL), temperature (24℃) and mass (0.35 g) of nitrogen gas.
Plan: Using the ideal gas equation, we can determine the pressure. However, we must convert the given mass of nitrogen gas to moles and ensure the appropriate units of temperature and volume before substituting these values into the ideal gas equation.
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-1K-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 × 294 / 0.149 = 2.0 atm (2 sig figs)
Exam Tip
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
- Usually, your examiner typically reports pressure in atm or mmHg and volume in mL or L
- The conversion factors for pressure are as follows:
- 1 atm = 760 mmHg or 760 torrs
- 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
