Question

Sulfuric acid is essential to dozens of important industries from steelmaking to plastics and pharmaceuticals. More sulfuric acid is made than any other industrial chemical, and world production exceeds 2.0 x 10 kg per year. The first step in the synthesis of sulfuric acid is usually burning solid sulfur to make sulfur dioxide gas. Suppose an engineer studying this reaction introduces 4.4 kg of solid sulfur and 6.90 atm of oxygen gas at 950. °C into an evacuated 50.0 L tank. The engineer believes K-0.71 for the reaction at this temperature. Calculate the mass of solid sulfur he expects to be consumed when the reaction reaches equilibrium. Round your answer to 2 significant digits. Note for advanced students: the engineer may be mistaken in his belief about the value of Kp, and the consumption of sulfur you calculate may not be what he actually observes.

Answer 1

Given:

K = 0.71 = Kp

The reaction of sulphur with oxygen is

                            S(s)   + O2(g)  ---> SO2(g)

initial Pressure                   6.90         0

Change                                -x            +x

Equilibrium                     6.90-x          x

Kp = pSO2 / pO2 = 0.71 = x / (6.90-x)

4.899 - 0.71x  = x

4.899 = 1.71x

x = 2.86 atm = pressure of SO2 formed

temperature = 950 C = 950 + 273.15 K = 1223.15 K

Volume = 50 L

Let us calculate moles of SO2 formed using ideal gas equation as

PV = nRT

R = gas constant = 0.0821 L atm / mol K

putting other values

n = PV / RT = 2.86 X 50 / 1223.15 X 0.0821 = 1.42 moles

Moles of Sulphur required = 1.42 moles

Mass of sulphur required or consumed = moles X atomic mass of sulphur

mass of S = 1.42 X 32 = 45.57 grams or 0.04557 Kg  of sulphur