Question

How much heat energy is required to convert 66.3 g of liquid sulfur dioxide, SO2, at 201.2 K to gaseous SO2 at 263.1 K if the molar heat of vaporization of SO2 is 24.9kJ/mol, and the specific heat capacity (C) of liquid SO2 is 1.36J

Answer 1

The heat energy required to convert 66.3 g of liquid sulfur dioxide,
`SO_2`, at 201.2 K to gaseous
`SO_2` at 263.1 K is 31.477 KJ

How to calculate the heat energy required?

First, we shall calculate the heat needed to vaporize the liquid sulfur dioxide,
`SO_2`, at 201.2 K to gaseous
`SO_2`

• Mass of sulfur dioxide (m) = 66.3 g
• Molar mass of sulfur dioxide (M) = 64 g/mol
• Mole of sulfur dioxide (n) = m / M = 66.3 / 64 = 1.04 mole
• Heat of Vaporization (ΔHv) = 24.9 KJ/mol
• Heat (H) =?

H = n × ΔHv

= 1.04 × 24.9

= 25.896 KJ

Next, we shall determine the heat required to change the temperature from 201.2 K to 263.1 K. Details below:

• Mass of sulfur dioxide (M) = 66.3 g
• Initial temperature of sulfur dioxide (T₁) = 201.2 K
• Final temperature of sulfur dioxide (T₂) = 263.1
• Change in temperature of sulfur dioxide (ΔT) = 263.1 - 201.2 = 61.9 K
• Specific heat capacity of sulfur dioxide (C) = 1.36 J/gºC
• Heat (Q) =?

Q = MCΔT

= 66.3 × 1.36 × 61.9

= 5581.3992 J

Divide by 1000 to express in KJ

= 5581.3992 / 1000

= 5.581 KJ

Finally, we shall determine the heat required to convert liquid sulfur dioxide to gaseous sulfur dioxide. Details below:

• Heat required to vaporize sulfur dioxide (H) = 25.896 KJ
• Heat required to change the temperature from 201.2 K to 263.1 K (Q) = 5.581 KJ
• Total heat required =?

Total heat required = H + Q

= 25.896 + 5.581

= 31.477 KJ