IB DP Chemistry: HL复习笔记1.2.4 The Ideal Gas Equation
Ideal Gas Equation
Kinetic theory of gases
- The kinetic theory of gases?states that molecules in gases are constantly moving
- The theory makes the following assumptions:
- The gas molecules are moving very fast and randomly
- The molecules hardly have any volume
- The gas molecules do not attract or repel each other (no?intermolecular forces)
- No kinetic energy is lost when the gas molecules collide with each other (elastic collisions)
- The temperature of the gas is directly proportional to the average kinetic energy of the molecules
- Gases that follow the kinetic theory of gases are called?ideal gases
- However, in reality gases do not fit this description exactly?but?may come very close and are called?real gases
- The volume that a gas occupies depends on:
- Its pressure
- Its temperature
Ideal gas equation
- The?ideal gas equation?shows the relationship between pressure, volume, temperature and number of moles of gas of an ideal gas:
PV = nRT
P = pressure (pascals, Pa)
V = volume (m3)
n = number of moles of gas (mol)
R = gas constant (8.31 J K-1?mol-1)
T = temperature (Kelvin, K)
- The ideal gas equation can also be used to calculate the?molar?mass?(M) of a gas
Worked Example
Calculate the volume, in dm3, occupied by 0.781 mol of oxygen at a pressure of 220 kPa and a temperature of 21 °C.
Answer:
Step 1:?Rearrange the ideal gas equation to find volume of the gas
Step 2:?Convert into the correct units and calculate the volume the oxygen gas occupies
p = 220 kPa = 220 000 Pa
n = 0.781 mol
R = 8.31 J K-1?mol-1
T = 21?oC = 294 K
= 0.00867 m3
=?8.67 dm3
Exam Tip
A word about units...Students often mess up gas calculations by getting their unit conversions wrong, particularly from cm3?to m3. Think about what a cubic metre actually is - a cube with sides 1 m or 100 cm long.The volume of this cube is 100 x 100 x 100 = 1 000 000 or?106?cm3So when you convert from?m3?to cm3?you?MULTIPLY?by 106?and when you convert from?cm3?to m3?you?DIVIDE by 106? (or multiply by 10-6?which is the same thing)
Worked Example
Calculate the pressure of a gas, in kPa, given that 0.20 moles of the gas occupy 10.1 dm3?at a temperature of 25?oC.
Answer:
Step 1:?Rearrange the ideal gas equation to find the pressure of the gas
Step 2:?Convert to the correct units and calculate the pressure
n = 0.20 mol
V = 10.1 dm3?= 0.0101 m3?= 10.1 x 10-3?m3?
R = 8.31 J K-1?mol-1
T = 25?oC = 298 K
P = 49 037 Pa =?49 kPa?(2 sig figs)
Worked Example
Calculate the temperature of a gas, in?oC, if 0.047 moles of the gas occupy 1.2 dm3 at a pressure of 100 kPa.
Answer:
Step 1:?Rearrange the ideal gas equation to find the temperature of the gas
Step 2:?Convert to the correct units and calculate the pressure
n = 0.047 mol
V = 1.2 dm3?= 0.0012 m3?= 1.2 x 10-3?m3?
R = 8.31 J K-1?mol-1
P = 100 kPa = 100 000 Pa
T = 307.24 K = 34.24?oC=?34?oC??(2 sig figs)
Worked Example
A flask of volume 1000 cm3 contains 6.39 g of a gas. The pressure in the flask was 300 kPa and the temperature was 23 °C.Calculate the molar mass of the gas.
Answer:
Step 1:?Rearrange the ideal gas equation to find the number of moles of gas
Step 2:?Convert to the correct units and calculate the number of moles of gas
P = 300 kPa = 300 000 Pa
V = 1000 cm3?= 0.001 m3?=?1.0 x 10-3?m3
R = 8.31 J K-1?mol-1
T = 23?oC = 296 K
? ? ? n = 0.12 mol
Step 3:?Calculate the molar mass using the number of moles of gas
Exam Tip
To calculate the temperature in?Kelvin, add 273 to the Celsius temperature, eg. 100?oC is 373 Kelvin.
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