Use of amount of substance in relation to volumes of gases

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Apuntes de la lección

Avogadro's Law and Molar Gas Volume

  • Avogadro's Law: equal amounts in moles of any gas occupy the same volume under the same conditions of temperature and pressure.
  • At room temperature and pressure (RTP), one mole of any gas occupies 24 dm³ (or 24,000 cm³).
  • RTP conditions are 20 °C and 1 atmosphere (atm) pressure.
  • This volume is called the molar gas volume.
  • The molar gas volume applies only at RTP; at other conditions the volume per mole is different.

Calculating Moles from Gas Volume

  • To find moles from volume in dm³: moles = volume (dm³) ÷ 24.
  • To find moles from volume in cm³: moles = volume (cm³) ÷ 24,000.
  • Example: 225.6 dm³ of methane contains 225.6 ÷ 24 = 9.4 moles.
  • Example: 960 cm³ of sulfur dioxide contains 960 ÷ 24,000 = 0.04 moles.
  • Always check whether the volume is given in dm³ or cm³ before dividing.

Calculating Gas Volume from Moles

  • To find volume from moles: volume (dm³) = moles × 24.
  • To find volume in cm³: volume (cm³) = moles × 24,000.
  • Example: 3 moles of hydrogen occupy 3 × 24 = 72 dm³ at RTP.
  • Example: 0.25 moles of carbon dioxide occupy 0.25 × 24 = 6 dm³ at RTP.
  • Example: 5.4 moles of oxygen occupy 5.4 × 24 = 129.6 dm³ at RTP.

Converting Mass to Gas Volume

  • If a mass is given, first convert it to moles using moles = mass ÷ Mr (or Ar for atoms).
  • Then convert moles to volume using volume = moles × 24 (for dm³) or × 24,000 (for cm³).
  • Example: 154 g of N₂ (Mr = 28) gives 154 ÷ 28 = 5.5 moles, which occupy 5.5 × 24 = 132 dm³ at RTP.
  • Make sure the relative formula mass matches the formula of the gas (e.g., N₂ uses 2 × 14 = 28).

Using Equations to Compare Gas Volumes

  • In a balanced equation, the coefficients give the mole ratio, which is also the volume ratio for gases at the same conditions.
  • Example: C₃H₈(g) + 5O₂(g) → 3CO₂(g) + 4H₂O(g) means 1 volume of propane reacts with 5 volumes of oxygen.
  • 150 cm³ of propane needs 5 × 150 = 750 cm³ of oxygen.
  • The total volume of gaseous products is (3 + 4) × 150 = 1050 cm³.
  • Always use the mole ratio from the equation when comparing volumes of gaseous reactants and products.

Common Mistakes to Avoid

  • Do not use 24 dm³ per mole unless the conditions are RTP.
  • Do not mix cm³ and dm³ in the same calculation without converting first.
  • Do not ignore the mole ratio when comparing gas volumes.
  • Do not assume equal masses of different gases occupy equal volumes; it is equal moles that occupy equal volumes.

Exam Tips

  • Check the units the question asks for (cm³ or dm³) and give your answer in those units.
  • Show your working clearly, especially when converting between mass, moles and volume.
  • For reacting gas volume questions, write down the mole ratio from the balanced equation first.
  • Remember that 1 dm³ = 1000 cm³, so 24 dm³ = 24,000 cm³.

Diapositivas

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Preguntas de práctica

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  1. 1.What volume does one mole of any gas occupy at room temperature and pressure?

    Easy
    • A22.4 dm3
    • B24 dm3
    • C24 cm3
    • D24000 dm3

  2. 2.Which of the following statements about gases at room temperature and pressure are correct? (select all that apply)

    Easy
    • AEqual amounts in moles of any gas occupy the same volume.
    • BOne mole of any gas occupies 24 dm3.
    • COne mole of any gas occupies 22.4 dm3.
    • DThe molar gas volume at RTP is 24000 cm3.

  3. 3.At the same temperature and pressure, equal masses of different gases occupy the same volume.

    Easy

    True or false?

  4. 4.A gas cylinder contains 0.25 moles of carbon dioxide at RTP. What volume does this gas occupy?

    Medium
    • A6 dm3
    • B96 dm3
    • C0.0104 dm3
    • D6000 dm3

  5. 5.What is the volume of 154 g of nitrogen gas at RTP? (Ar: N = 14)

    Medium
    • A132 dm3
    • B5.5 dm3
    • C3696 dm3
    • D672 dm3

  6. 6.Place the steps in the correct order to calculate the volume of gas produced from a given mass of reactant.

    Medium
    • Write the balanced equation.
    • Calculate moles of the given substance.
    • Use the mole ratio from the equation.
    • Multiply moles of gas by 24 dm3.

  7. 7.Match each quantity with its correct value or unit.

    Medium
    • Molar gas volume at RTP
    • Temperature at RTP
    • Pressure at RTP
    • 24 dm3
    • 20 °C
    • 1 atm

  8. 8.In the reaction N2(g) + 3H2(g) → 2NH3(g), what volume of ammonia is produced from 565 cm3 of hydrogen?

    Medium
    • A1130 cm3
    • B377 cm3
    • C283 cm3
    • D847 cm3

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