The problem is solved by balancing the reaction equation as shown below. The stoichiometry of the reaction is now applied in solving the question.
The balanced reaction equation is:
SiO2 + 6HF → H2[SiF6] + 2H2O
Using stoichiometry
The amount of silicon dioxide reacted = 12.5 g/60.08 g/mol = 0.21 mole
1 mole SiO2 yields 2 moles of H2O
0.21 mole of SiO2 yields 0.21 * 2/1 = 0.42 moles of H2O
The amount of HF reacted = 24.6 g/20.01 g/mol = 1.23 moles of HF
6 moles of HF yield 2 mole of H2O
1.23 moles of HF yields 2 * 1.23/6 = 0.41 moles of H2O
Hence HF is the limiting reactant.
Theoretical yield of H2O = 0.41 moles of H2O * 18 g/mol = 7.38 g
The percentage yield of the water is = actual yield/theoretical yield * 100
Hence;
% yield = 2.50 g/7.38 g * 100 = 33.9%
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