IB DP Chemistry: SL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

1.2.4-Ideal-gas-finding-volume-formula-1Step 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

1.2.4-Ideal-gas-finding-volume-formula-worked-example2

= 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 10cm3So when you convert from m3 to cmyou MULTIPLY by 10and when you convert from cm3 to myou 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

1.2.4-Ideal-gas-finding-volume-pressureStep 2: Convert to the correct units and calculate the pressure

n = 0.20 mol

V = 10.1 dm3 = 0.0101 m= 10.1 x 10-3 m

R = 8.31 J K-1 mol-1

T = 25 oC = 298 K

1.2.4-Ideal-gas-finding-pressure-worked-example2P = 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

1.2.4-Ideal-gas-finding-temperature-formulaStep 2: Convert to the correct units and calculate the pressure

n = 0.047 mol

V = 1.2 dm3 = 0.0012 m= 1.2 x 10-3 m

R = 8.31 J K-1 mol-1

P = 100 kPa = 100 000 Pa

1.2.4-Ideal-gas-finding-temperature-worked-example2T = 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

Gases-Ideal-Gas-Law-Equation-Worked-Example-2-equation-1

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 m= 1.0 x 10-3 m3

R = 8.31 J K-1 mol-1

T = 23 oC = 296 K1.2.4-Ideal-gas-finding-the-moles-worked-example2

      n = 0.12 mol

Step 3: Calculate the molar mass using the number of moles of gas

1.2.4-Ideal-gas-finding-the-moles-worked-example-answer-1

Exam Tip

To calculate the temperature in Kelvin, add 273 to the Celsius temperature, eg. 100 oC is 373 Kelvin.

 

 

 

 

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