Answer:
The balanced chemical equation for the reaction between hydrochloric acid (HCl) and sodium sulfate (Na2SO4) is:
2 HCl + Na2SO4 → 2 NaCl + H2SO4
This equation shows that two moles of hydrochloric acid react with one mole of sodium sulfate to produce one mole of sulfuric acid. Therefore, we need to first calculate the number of moles of sodium sulfate that react with the given mass of hydrochloric acid, and then use the mole ratio to find the number of moles (and mass) of sulfuric acid produced.
Calculate the number of moles of sodium sulfate:
molar mass of Na2SO4 = 2(23.0 g/mol) + 1(32.1 g/mol) + 4(16.0 g/mol) = 142.1 g/mol
moles of Na2SO4 = mass/molar mass = 13.7 g/142.1 g/mol = 0.0965 mol
Use the mole ratio to find the number of moles of sulfuric acid produced:
From the balanced equation, we see that 2 moles of HCl react with 1 mole of Na2SO4 to produce 1 mole of H2SO4.
So, the number of moles of H2SO4 produced = (0.0965 mol Na2SO4) x (1 mol H2SO4 / 1 mol Na2SO4) = 0.0965 mol H2SO4
Calculate the mass of sulfuric acid produced:
molar mass of H2SO4 = 1(2.0 g/mol) + 1(32.1 g/mol) + 4(16.0 g/mol) = 98.1 g/mol
mass of H2SO4 = moles x molar mass = 0.0965 mol x 98.1 g/mol = 9.50 g
Therefore, 9.50 grams of sulfuric acid are produced when hydrochloric acid reacts with 13.7 grams of sodium sulfate.