Most of the sulfur used in the United States is chemically synthesized from hydrogen sulfide gas recovered from natural gas wells. In the first step of this synthesis, called the Claus process, hydrogen sulfide gas is reacted with dioxygen gas to produce gaseous sulfur dioxide and water. Suppose a chemical engineer studying a new catalyst for the Claus reaction finds that 994 liters per second of dioxygen are consumed when the reaction is run at 170 ⁰C and 0.77 atm. Calculate the rate at which sulfur dioxide is being produced. Give your answer in kilograms per second. Round your answer to 2 significant digits.

1.4 kg/s

Explanation:

The reaction of the production of sulfur dioxide is:

H₂S (g) + O₂ (g) → SO₂ (g) + H₂ (g)

By the ideal gas law, the number of moles of oxygen per second is:

PV = nRT

Where P is the pressure, V is the volume, n is the number of moles, R is the gas constant (0.082 atm. L/mol. K), and T is the temperature (170°C + 273 = 443 K).

n = PV/RT

n = (0.77*994) / (0.082*443)

n = 21.07 mol/s

The stoichiometry reaction is 1 mol of O₂:1 mol of SO₂, so the rate of SO₂ is also 21.07 mol/s. The molar mass of SO₂ is:

32 g/mol of S + 2*16 g/mol of O = 64 g/mol

So, the mass rate is the molar mass multiplied by the molar rate:

m = 64 g/mol * 21.07 mol/s

m = 1348.5 g/s

m = 1.4 kg/s