Sulfur dioxide is produced in enormous amounts for sulfuric acid production. It melts at −73.0°C and boils at −10.0°C.

Question

Sulfur dioxide is produced in enormous amounts for sulfuric acid production. It melts at −73.0°C and boils at −10.0°C. ΔH^0 fus is 8.619 kJ/mol, and its  ΔH^0 vap is 25.73 kJ/mol. The specific heat capacities of the liquid and gas are 0.995 J/g ·K and 0.622 J/g ·K, respectively. How much heat is required to convert 3.000 kg of solid SO₂ at the melting point to a gas at 60.0° C?

 Answer in : _ x 10 ^_ J

Answer 1

SO₂:

molar mass = 64.07 g/mol

melting pt: -73.0º

boiling point: -10.0º

∆H_fusion = 8.619 kJ/mol x 1 mol/64.07 g x 1000 J/kJ = 134.5 J/g

∆H_vap = 25.73 kJ/mol x 1 mol/64.07 g x 1000 J/kJ = 401.6 J/g

C_liq = 0.995 J/g/º

C_gas = 0.622 J/g/º

mass (m) = 3.000 kg SO₂ = 3,000 g SO₂

Step 1: convert 3 kg solid SO2 @ -73º to liquid SO2 @ -73º (phase change)

q = m∆Hfusion = (3000 g)(134.5 J/g) = 403,500 J

Step 2: convert 3 kg liquid SO2 @ -73º to -10º

q = mC_liq∆T = (3000 g)(0.995 J/g/º)(63º) = 188,055 J

Step 3: convert 3 kg liquid SO2 @ -10º to vapor @ -10º (phase change)

q = m∆H_vap = 3000 g x 401.6 J/g = 1,204,800 J

Step 4: convert 3 kg gaseous SO2 @-10º to 60º

q = mC_gas∆T = (3000 g)(0.622 J/g/º)(70º) = 130,620 J

Add up joules from all steps:

403,500 + 188,055, + 1,204,800 + 130,620 = 1,926,975 J

Putting into scientific notation (with 3 sig. figs.): 1.93x10⁶ J