Question

Sulfur dioxide is produced in enormous amounts for sulfuric acid production. It melts at - 73˚C and boils at - 10˚C. Its ΔH˚fus is 8.619 kJ/mol and its ΔH˚vap is 25.73 kJ/mol. The specific heat capacities of the liquid and the gas are 0.995 J/g·K and 0.622 J/g·K, respectively. How much heat is required to convert 2.500 kg of solid SO₂ at the melting point to a gas at 60˚C?

Answer 1

Heat required to convert 2.500 kg of solid SO₂ at the melting point to a gas at 60˚C is 1,589.724 kilo joules.

Step-by-step explanation:

Heat required to melt sulfur dioxide solid -73˚C =
`q_1`

Latent heat melting of sulfur dioxide =
`\Delta H^o_(fus)=8.169 kJ/mol=8169 J/mol`

Mass of sulfur dioxide solid , m= 2.500 kg = 2500 g

Moles of sulfur dioxide solid ,n=
`(2500 g)/(64 g/mol)=39.062 mol`

`q_1=n* \Delta H^o_(fus)`

`q_1=39.062 mol* 8169 J/mol=319,097.48 J=319.097 kJ`

Heat required to raise the temperature of liquid sulfur dioxide from -73˚C to -10˚C =
`q_2`

-10˚C = 263.15 K, -73˚C = 200.15 K

Mass of sulfur dioxide liquid, m= 2.500 kg = 2500 g

Specific heat of liquid sulfur dioxide =
`C_1=0.995 J/g K`

Change in temperature =
`\Delta T_1=(263.15 K-200.15 K)=63 K`

`q_2=m* C_1* \Delta T_1`

`q_2=2500 g* 0.995 J/g K* 63 K=156,712.5 J=156.712 kJ`

Heat required to vaporize sulfur dioxide liquid at -10˚C=
`q_3`

Latent heat melting of sulfur dioxide =
`\Delta H^o_(vap)=25.73 kJ/mol=25730 J/mol`

Mass of sulfur dioxide liquid, m= 2.500 kg = 2500 g

Moles of sulfur dioxide solid ,n=
`(2500 g)/(64 g/mol)=39.062 mol`

`q_3=n* \Delta H^o_(vap)`

`q_3=39.062 mol* 25.73 kJ/mol=1,005.065 kJ`

Heat required to raise the temperature of liquid sulfur dioxide from -10˚C to 60˚C =
`q_4`

-10˚C = 263.15 K, 60˚C = 333.15 K

Mass of sulfur dioxide liquid, m= 2.500 kg = 2500 g

Specific heat of gas sulfur dioxide =
`C_2=0.622 J/g K`

Change in temperature =
`\Delta T_2=(333.15 K-263.15 K)=70 K`

`q_4=m* C_2* \Delta T_2`

`q_4=2500 g* 0.622 J/gK* 70 K=108,850 J=108.850 kJ`

Heat required to convert 2.500 kg of solid SO₂ at the melting point to a gas at 60˚C = Q

`Q=q_1+q_2+q_3+q_4`

`Q=319.097 kJ+156.712 kJ+1,005.065 kJ+108.850 kJ=1,589.724 kJ`