IB DP Chemistry: HL复习笔记1.2.3 Avogadro's Law & Molar Gas Volume

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 dm³ 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 cm³ of propane, the volume of oxygen needed is (5 x 50) 250 cm³, and (3 x 50) 150 cm³ 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 NH₃ :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 O₂ requires 4/5 x 50 cm³ of NH₃ to react = 40 cm³ 

Step 3: Using Avogadro's Law, we can say 40 cm³ of NO will be produced

Step 4: There will be of 70-40 = 30 cm³ of NH₃ left over

Therefore the total remaining volume will be 40 + 30 = 70 cm³ of gases

• The molar gas volume of 22.7 dm³ 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 dm³ 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 dm³ mol^-1

3.0 mol x 22.7 dm³ 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