Volumes of gases

• In 1811 the Italian scientist Amedeo?Avogadro?developed a theory about the volume of gases
• Avogadro’s law?(also called?Avogadro’s hypothesis)?enables the mole ratio of reacting gases to be determined from volumes of the gases
• Avogadro?deduced that equal volumes of gases must contain the same number of molecules
• At standard temperature and pressure(STP)?one mole?of any gas has a volume of?22.7 dm³
• The units are normally written as?dm^3?mol^-1(since it is 'per mole')
• The conditions of?STP?are
  • a temperature of?0^o?C?(273 K)
  • pressure of?100 kPa

Stoichiometric relationships

• The stoichiometry of a reaction and?Avogadro's Law?can be used to deduce the?exact?volumes?of gaseous reactants and products
  • Eg. in the?combustion?of 50 cm^3?of propane, the volume of oxygen needed is (5 x 50) 250 cm³, and (3 x 50) 150 cm^3?of carbon dioxide is formed, using the ratio of propane: oxygen: carbon dioxide, which is 1: 5: 3 respectively, as seen in the equation

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

• Remember that if the gas volumes are not in the same ratio as the coefficients then the amount of product is determined by the limiting reactant so it is essential to identify it first

Answer:

Step 1: From the equation deduce the molar ratio of the gases, which is NH_3?:O₂?:NO or 4:5:4 (water is not included as it is in the liquid state)

Step 2: We can see that oxygen will run out first (the?limiting reactant) and so 50 cm³?of O_2?requires 4/5 x 50 cm³?of NH_3?to react?= 40 cm^3?

Step 3: Using Avogadro's Law, we can say 40 cm^3?of NO will be produced

Step 4: There will be of 70-40 = 30 cm^3?of NH_3?left over

Therefore?the total remaining volume will be 40 + 30 =?70 cm^3?of gases

• The?molar gas volume?of 22.7 dm^3?mol^-1?can be used to find:
  • The volume of a given number of moles of gas:

volume of gas (dm³) = amount of gas (mol) x 22.7 dm^3?mol^-1

• • The number of moles of a given volume of gas:

• The relationships can be expressed using a formula triangle

To use the gas formula triangle cover the one you want to find out about with your finger and follow the instructions

Answer:

volume of gas (dm³) = amount of gas (mol) x 22.7 dm^3?mol^-1

3.0 mol x 22.7 dm^3?mol^-1=?68 dm³

Answer 1:

Use the formula:

Answer 2:

Step 1:?Convert the volume from cm³?to dm³

960/1000 = 0.960 dm³

Step 2:?Use the formula