Question

Aqueous sulfuric acid solutions containing 15.0 wt% H2SO4 and 80.0 wt% H2SO4 are mixed to form a 60.0 wt% product solution. The 15 wt% solution was in a laboratory in which the temperature was 25 °C. The 80% solution had just been taken from a storage cabinet in an air-conditioned stockroom and was at a temperature of 15 °C when the mixing occurred. All solutions are at 1 atm pressure.

(a) The mass of the 15 wt% solution is 3 kg. What is the mass of 60 wt% solution (kg)?

Answer 1

To obtain a 60% sulfuric acid solution, 6.75 kg of the 80% solution must be mixed with 3 kg of the 15% solution, resulting in a total mass of 9.75 kg for the 60% solution.

Step-by-step explanation:

To find the mass of the 60 wt% solution, we will use a mass balance based on the sulfuric acid content in the solutions before and after mixing. We have a 15.0 wt% H₂SO₄ solution and an 80.0 wt% H₂SO₄ solution that need to be combined to form a 60.0 wt% H₂SO₄ solution. Considering that we have 3 kg of the 15 wt% solution, the mass of H₂SO₄ in that solution is 0.15 × 3 kg = 0.45 kg.

Let m be the mass of the 80 wt% solution needed. The mass of H₂SO₄ in this solution is 0.80 × m. After mixing, the total mass of the mixture is 3 kg + m, and it contains (0.45 kg + 0.80m) kg of H₂SO₄. The weight percent of H₂SO₄ in the final solution must be 60%, so the mass of H₂SO₄ must be 0.60 × (3 kg + m).

Setting up the mass balance:

0.45 kg + 0.80m = 0.60 × (3 kg + m)

Solving for m:

0.45 kg + 0.80m = 1.80 kg + 0.60m

0.20m = 1.35 kg

m = 1.35 kg / 0.20 = 6.75 kg

Therefore, the mass of the 80 wt% solution needed is 6.75 kg, and the total mass of the 60 wt% solution is 3 kg + 6.75 kg = 9.75 kg.