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Reacting Volume Calculations (Edexcel A Level Chemistry): Revision Note

Richard Boole

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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 = fraction numerator Volume space of space gas space left parenthesis dm cubed right parenthesis over denominator Molar space gas space volume space left parenthesis dm cubed right parenthesis end fraction

Worked Example

Molar gas volume calculations

Calculate the number of moles present in 4.5 dm3 of carbon dioxide at:

  1. Room temperature and pressure

  2. Standard temperature and pressure

Answers

  1. Number of moles equals fraction numerator Volume space of space gas space left parenthesis dm cubed right parenthesis over denominator Molar space gas space volume space left parenthesis dm cubed right parenthesis end fraction space equals fraction numerator 4.5 over denominator 24 end fraction equals0.1875 moles

    • Number of moles equals fraction numerator Volume space of space gas space left parenthesis dm cubed right parenthesis over denominator Molar space gas space volume space left parenthesis dm cubed right parenthesis end fraction space equals fraction numerator 4.5 over denominator 22.4 end fraction equals0.201 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

Calculating gas volumes from moles

Calculate the volume of gas produced when 1.50 g of sodium reacts with water at standard temperature and pressure.

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 equals fraction numerator mass space left parenthesis straight g right parenthesis over denominator molar space mass space left parenthesis straight g space mol to the power of negative 1 end exponent right parenthesis end fraction equals fraction numerator 1.5 over denominator 23.0 end fraction equals0.0652 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 fraction numerator 0.0652 over denominator 2 end fraction equals0.0326 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

Calculating gas volumes from other volumes

Calculate the total volume of gas produced when 6.50 dm3 of propane combusts completely 

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

Ideal Gases

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

Calculating the volume of a gas

Calculate the volume 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 gas

V = fraction numerator n R T over denominator P end fraction

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 equals fraction numerator 0.781 space cross times 8.31 cross times 294 over denominator 220000 end fraction equals space 0.00867 space straight m cubed space equals space 8.67 space dm cubed

Worked Example

Calculating the molar mass of a gas

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 relative molecular mass of the gas.

Answer

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

n = fraction numerator P V over denominator R T end fraction

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

nequals fraction numerator 300000 cross times 0.001 over denominator 8.31 cross times 296 end fraction equals 0.12 space mol

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

n = fraction numerator m a s s over denominator m o l a r space m a s s end fraction

molar massequals fraction numerator 6.39 over denominator 0.12 end fraction equals 53.25 space straight g space mol to the power of negative 1 end exponent

Examiner Tips and Tricks

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

You must be able to rearrange the ideal gas equation to work out all parts of it.

The units are incredibly important in this equation - make sure you know what units you should use, and do the necessary conversions when doing your calculations! 

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    Richard Boole

    Author: Richard Boole

    Expertise: Chemistry

    Richard has taught Chemistry for over 15 years as well as working as a science tutor, examiner, content creator and author. He wasn’t the greatest at exams and only discovered how to revise in his final year at university. That knowledge made him want to help students learn how to revise, challenge them to think about what they actually know and hopefully succeed; so here he is, happily, at SME.