Answer to Question #101153 in Chemistry for Melanson

Question

Using the overall reaction for making synthetic gypsum by means of recycling sulfur dioxide gas:

SO2(g) + CaSO3(s) + 1⁄2O2(g) + 2 H2O(l) ˇ CaSO4 . 2H2O(s) + CO2(g)

(a) determine the mass of synthetic gypsum produced for every kilogram of sulfur dioxide recycled.

(b) determine both the mass and the volume of water required to recycle a kilogram of sulfur dioxide.

Answer 1

(a) According to the reaction, one kilogram of SO₂ equeals:

n (SO₂) = m(SO₂)/M(SO₂) = 1,000 g / 64 g/mol = 15.625 mol,

where n - number of moles, m - mass, M - molecular weight.

As a result, the same the same number of moles of CaSO₄ · 2H₂O(s) (synthetic gypsum) was produced (n (CaSO₄ · 2H₂O) = 15.625 mol), its mass equals:

m (CaSO₄ · 2H₂O) = n (CaSO₄ · 2H₂O) × M (CaSO₄ · 2H₂O) = 15.625 mol × 172 g/mol = 2,687.5 g = 2.7 kg.

Answer: 2.7 kg of CaSO₄ · 2H₂O

(b) According to the reaction, equal amounts of SO₂ and H₂O are used in the reaction. As a result, 15.625 mol of water were used in the reaction. The mass of water equals:

m (H₂O) = n (H₂O) × M (H₂O) = 15.625 mol × 2 × 18 g/mol = 562.5 g

As the density of water equals 1,000 g/l, the volume of water is:

V = 562.5 g / 1,000 g/l = 0.5625 l

Answer: 562.5 g and 0.5625 l of water