In what mass of water must 67.2 liters of HCl be dissolved in order to obtain a nine percent HCl solution?

Given:

V (HCl) = 67.2 L;

W (HCl) = 9%.

Find:

m (H2O) =?

Solution:

1) In order to find the mass of HCl, we use the formula: m: M = V: Vm, hence m = (M x V): Vm.

2) M (HCl) = 1 + 35.5 = 36.5 g / mol.

Vm (HCl) = 22.4 L / mol.

3) Find the mass of HCl.

m (HCl) = (36.5 x 67.2): 22.4 = 109.5 g.

4) Find the mass of the solution.

W = (m substance: m solution) x 100%;

9% = (109.5 g: m solution) x 100%, hence 0.09 = 109.5 g: m solution.

m solution = 109.5: 0.09 = 1217 g.

5) Find the mass of water.

m solvent = m solution – m solute;

m (H2O) = 1217 g – 109.5 g = 1107.5 g.

Answer: m (H2O) = 1107.5 g.




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