# Question 55c1b

Jul 18, 2017

The heat energy required is 45.1 kJ.

#### Explanation:

A typical heating curve for a compound like ${\text{SO}}_{2}$ is shown below. (From SlideShare)

The melting point of ${\text{SO}}_{2}$ is -73.15 °C (200.00 K), and the boiling point is -10.0 °C (263.1 K).

In this problem, we are starting with the liquid at point B , warming it to its boiling point C, and then evaporating it to point D.

Thus, there are two separate heat transfers involved:

• ${q}_{1}$ = heat required to warm the liquid from from 200.5 K to 263.1 K (Point B to C in the diagram)
• ${q}_{2}$ = heat required to evaporate the liquid at 263.1 K (Point C to D)

q = q_1 + q_2 = mCΔT + nΔ_text(vap)H

where

${q}_{1}$ and ${q}_{2}$ are the heats involved in each step

$m \textcolor{w h i t e}{m l} = \text{the mass of the sample}$

$C \textcolor{w h i t e}{m l} = \text{the specific heat capacity of SO"_2 = "1.36 J·°K"^"-1""g"^"-1}$

ΔTcolor(white)(l) = T_"f" -T_"i"

Δ_text(fus)H = "the molar enthalpy of evaporation of SO"_2 = "24.9 kJ·mol"^"-1"

${\boldsymbol{q}}_{1}$

ΔT = "263.1 K - 200.5 K" = "62.6 K"

q_1 = mCΔT = 95.1 color(red)(cancel(color(black)("g"))) × 1.36 color(white)(l)"J"·color(red)(cancel(color(black)( "K"^"-1""g"^"-1"))) × 62.6 color(red)(cancel(color(black)("K"))) = "8096 J" = "8.096 kJ"

${\boldsymbol{q}}_{2}$

n = 95.1 color(red)(cancel(color(black)("g SO"_2))) × "1 mol SO"_2/(64.06 color(red)(cancel(color(black)("g SO"_2)))) = "1.485 mol SO"_2

q_2 = 1.485 color(red)(cancel(color(black)("mol"))) × "24.9 kJ"·color(red)(cancel(color(black)("mol"^"-1"))) = "36.97 J"#

$q = {q}_{1} + {q}_{2} = \text{(8.096 + 36.97) kJ" = "45.1 kJ}$

The process requires 45.1 kJ of heat energy.