1.7.1 Reacting Volume Calculations

• Reacting volume calculations are commonly associated with the reactions of gases
• All gases occupy the same volume under the same conditions
  • At room temperature and pressure (r.t.p.), the molar gas volume of any gas is 24.0 dm³
    • Room temperature and pressure are 293 K / 20 ^oC and 101.3 kPa respectively
  • At standard temperature and pressure (s.t.p.), the molar gas volume of any gas is 22.4 dm³  
    • Standard temperature and pressure are 273 K / 0 ^oC and 101.3 kPa respectively
• The equation to calculate the number of moles for any volume of gas is:

Number of moles = 

Worked Example

Answers

1. 1. Number of moles 0.1875 moles
   2. Number of moles 0.201 moles (to 3 s.f.)

• Volumes of gas can also be calculated using
  • Number of moles calculations
  • Volume calculations
• This can help determine the size of the equipment that you use in an experiment

Worked Example

Answer

Step 1: Write the balanced equation for the reaction

• • 2Na (s) + H₂O (l) → 2NaOH (aq) + H₂ (g)

Step 2: Calculate the number of moles of sodium

• • Number of moles 0.0652 moles (to 3s.f.)

Step 3: Use the stoichiometry of the equation to calculate the number of moles of hydrogen

• • The stoichiometric ratio of Na : H₂ is 2 : 1
  • Therefore, the number of moles of hydrogen is 0.0326 moles

Step 4: Calculate the volume of hydrogen gas evolved

• • Volume of gas = number of moles x molar gas volume
  • Volume of gas = 0.0326 x 22.4 = 0.730 dm³ (to 3s.f.)

Worked Example

Answer

Step 1: Write the balanced equation for the reaction

• • C₃H₈ (g) + 5O₂ (g) → 3CO₂ (g) + 4H₂O (g)

Step 2: Determine the number of moles of gas produced

• • One mole of propane produces 3 moles of carbon dioxide and 4 moles of water
  • Therefore, one mole of propane produces a total of 7 moles of gas

Step 3: Calculate the volume of gas that is produced

• •  6.50 dm³ of propane will produce 7 x 6.50 dm³ of gas = 45.5 dm³ gas

Kinetic theory of gases

• The kinetic theory of gases states that molecules in gases are constantly moving
• The theory makes the following assumptions:
  • That gas molecules are moving very fast and randomly
  • That molecules hardly have any volume
  • That 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 related 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

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)

Worked Example

Answer

Step 1: Rearrange the ideal gas equation to find volume of gas

V = 

Step 2: 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

V

Worked Example

Answer

Step 1: Rearrange the ideal gas equation to find the number of moles of gas

n = 

Step 2: Calculate the number of moles of gas

• • P = 300 kPa = 300 000 Pa
  • V = 1000 cm³ = 1 dm³ = 0.001 m³
  • R = 8.31 J K^-1 mol^-1
  • T = 23 ^oC = 296 K

n

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

n = 

molar mass

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