Sulfuric acid is carefully poured into distilled water. The resulting solution has a density ρp = 1200 kg / m3

Sulfuric acid is carefully poured into distilled water. The resulting solution has a density ρp = 1200 kg / m3 and a mass m = 120 g. Determine the mass of acid poured into the water? Note. Water density ρw = 1000 kg / m3, acid density ρк = 1800 kg / m3. The volume of the solution is equal to the sum of the volumes of water and acid

To find the value of the mass of sulfuric acid poured into water, we will use the equality: mр / ρр = V (volume of the resulting solution) = mw / ρw + mk / ρk = (mr – mk) / ρw + mk / ρk = ((mr – mk) * ρk + mk * ρw) / (ρw * ρk) = (mr * ρk – mk * ρk + mk * ρw) / (ρw * ρk) = (mr * ρk – mk * (ρk – ρw)) / (ρв * ρк), whence we express: mр * ρк – mк * (ρк – ρв) = mр * ρв * ρк / ρр; mк * (ρк – ρв) = mр * ρк – mр * ρв * ρк / ρр and mк = (mр * ρк – mр * ρв * ρк / ρр) / (ρк – ρв) = mр * ρк * (1 – ρв / ρр) / (ρк – ρв).

Constants and variables: mр – the mass of the resulting solution (mр = 120 g = 0.12 kg); ρк – density of sulfuric acid (according to the condition ρк = 1800 kg / m3); ρw is the density of water (according to the condition ρw = 1000 kg / m3); ρр is the density of the resulting solution (ρр = 1200 kg / m3).

Calculation: mк = mр * ρк * (1 – ρв / ρв) / (ρк – ρв) = 0.12 * 1800 * (1 – 1000/1200) / (1800 – 1000) = 0.045 kg or 45 g.

Answer: 45 g of sulfuric acid was poured into the water.