Molar volume calculations
The molar volumeThe volume occupied by one mole of any gas (24 dm鲁 or 24000 cm鲁 at room temperature and pressure). can be used in calculations involving the massThe amount of matter an object contains. Mass is measured in kilograms (kg) or grams (g). of solids, and volumes of gases, in reactions.
Calculating a volume from a mass
Worked example
4.6 g of sodium reacts completely with excessIn chemistry, a substance is in excess if there is more than enough of it to react with another reactant. water:
2Na(s) + 2H2O(l) 鈫 2NaOH(aq) + H2(g)
Calculate the volume of hydrogen produced. (Relative atomic mass of Na = 23.0, molar volume = 24 dm3)
Step 1 - Calculate the amount of sodium in moles
Number of moles = \(\frac{mass~(g)}{A_r}\)
Number of moles = \(\frac{4.6}{23}\)
Number of moleThe amount of substance that contains the same number of particles as there are atoms in 12 g of carbon-12 (contains the Avogadro's constant 6.0 脳10虏鲁 number of particles). of sodium = 0.20 mol
Step 2 - Find the amount of hydrogen in moles
From the balanced chemical equationA chemical equation written using the symbols and formulae of the reactants and products, so that the number of units of each element present is the same on both sides of the arrow., the mole ratioThe ratio of the amounts of two substances as shown in a balanced equation. Na:H2 is 2:1
2 mol of sodium produce 1 mol of hydrogen.
Therefore 0.20 mol of Na produces \(\frac{0.20}{2}\) = 0.10 mol of H2
Step 3 - Calculate the volume of hydrogen
volume (dm3) = number of moles x 24 dm3
volume = 0.10 x 24
= 2.4 dm3
Question
Calcium carbonate decomposeIf a substance decomposes, it breaks down into simpler compounds or elements. to form calcium oxide and carbon dioxide when it is heated:
CaCO3(s) \(\rightarrow\) CaO(s) + CO2(g)
Calculate the volume of carbon dioxide produced from 1.0 g of calcium carbonate. (Relative formula mass of CaCO3 = 100.1, molar volume = 24 dm3)
Number of moles of calcium carbonate = \(\frac{1.0}{100.1}\) = 0.010 mol
The mole ratio is 1:1 so 1 mol of calcium carbonate produces 1 mol of carbon dioxide.
This means that the number of moles of carbon dioxide = 0.010 mol
volume of carbon dioxide = 0.010 x 24
= 0.24 dm3
Calculating a mass from a volume
Worked example
Lithium hydroxide absorbs carbon dioxide from the air:
2LiOH(s) + CO2(g) \(\rightarrow\) Li2CO3(s) + H2O(l)
Calculate the mass of lithium hydroxide needed to absorb 12 dm3 of carbon dioxide. (Relative formula mass of LiOH = 23.9, molar volume = 24 dm3)
Step 1 - Calculate the amount of carbon dioxide
Number of moles = \(\frac{volume}{molar~volume}\)
Number of moles = \(\frac{12}{24}\)
= 0.50 mol
Step 2 - Find the amount of lithium hydroxide
From the balanced equation, the mole ratio LiOH:CO2 is 2:1
Therefore 0.50 mol of CO2 is absorbed by (0.50 x 2) = 1.0 mol of LiOH
Step 3 - Calculate the mass of lithium hydroxide
mass (g) = relative formula mass x number of moles
mass = 23.9 x 1.0
= 24 g (to 2 significant figures)
Question
Sodium reacts with chlorine to produce sodium chloride:
2Na(s) + Cl2(g) 鈫 2NaCl(s)
Calculate the mass of sodium chloride produced from 1.97 dm3 of chlorine and an excess of sodium. (Relative formula mass of NaCl = 58.5, molar volume = 24 dm3)
number of moles of chlorine = \(\frac{1.97}{24000}\) = 0.082 mol
The mole ratio is 1:1
number of moles of sodium chloride = 0.082 mol
mass of sodium chloride = 58.5 x 0.082
= 4.8 g