What is the density of 53.4 wt aqueous naoh?

Missing question: what is the density of 53.4 wt% aqueous NaOH if 16.7 mL of the solution diluted to 2.00L gives 0.169 M NaOH?

Answer is: density is 1.52 g/mL.

c₁(NaOH) = ?; molarity of concentrated sodium hydroxide.

V₁(NaOH) = 16.7 mL; volume of concentrated sodium hydroxide.

c₂(NaOH) = 0.169 M; molarity of diluted sodium hydroxide.

V₂(NaOH) = 2.00 L · 1000 mL/L = 2000 mL; volume of diluted sodium hydroxide.  

Use equation: c₁V₁  = c₂V₂.

c₁ = c₂V₂ / V₁.

c₁ = 0.169 M · 2000 mL / 16.7 mL.

c₁(NaOH) = 20.23 M.

m(NaOH) = 20.23 mol · 40 g/ml.

m(NaOH) = 809.53 g.

The mass fraction is the ratio of one substance (in this example sodium hydroxide) with mass to the mass of the total mixture (solution).

Make proportion: m(NaOH) : m(solution) = 53.4 g : 100 g.

m(solution) = 1516 g in one liter of solution.

d(solution) = 1516 g/L = 1.52 g/mL.

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