Q12.27P - Chemistry: Molecular Nature Of Matter And Change

Question

Sulfur dioxide is produced in enormous amounts for sulfuric acid production. It melts at  $\mathbf{-}{\mathbf{73}}^o\mathbf{C}$and boils at$\mathbf{-}{\mathbf{10}}^o\mathbf{C}$  . Its ${\mathbf{\Delta H}}^o\mathbf{fus}$ is 8.619 kJ/mol and its is 25.73 kJ/mol. The specific heat capacities of the liquid and gas are 0.995 J/gK and 0.622 J/gK, respectively. How much heat is required to convert 2.500 kg of solid ${\mathbf{SO}}_2$ at the melting point to a gas at ${\mathbf{60}}^o\mathbf{C}$ ?      

Step-by-Step Solution

Answer

The total heat required to convert 2500gram of solid  ${\mathbf{SO}}_2$to vapour phase  ${\mathbf{SO}}_2$ at the melting point of the gas at ${\mathbf{60}}^o\mathbf{C}$ is 1605812.5Joule. 

Step 1: Enthalpy of Vaporization

The phase diagram is the diagram which shows the change in phase. It tells about the change into all phases – Solid, Liquid and Gaseous.

It represents all the phases and transition are shown by the lines and the area between lines show the whole phase of the molecule.

 

Step 2: Numerical Explanation

Molar Mass of  =64g/mole

Boiling Point =  $\mathbf{-}{\mathbf{10}}^o\mathbf{C}$

Melting Point =  $\mathbf{-}{\mathbf{73}}^o\mathbf{C}$

$\begin{array}{l}\Delta H^{o}fus=8.619kJ/mole\\ ChangeJ/moletoJ/g\\ \Rightarrow \Delta H^{o}fus=\frac{8.619kJ/mole\times 1mole}{64g\times 1000J/kJ}\\ \Rightarrow \Delta H^{o}fus=134.5J/g\\ \Delta {H^o}_{vap}=25.73kJ/mole\\ \Rightarrow \Delta {H^o}_{vap}=\frac{25.73kJ/mole\times 1mole}{64g\times 1000J/kJ}\\ \Rightarrow \Delta {H^o}_{vap}=401.6J/g\end{array}$

Specific Heat Capacity of liquid, $\mathbf{Cliq}$=0.995kJ/mole

Specific Heat Capacity of Gas,$\mathbf{Cgas}$ =0.622kJ/mole

Mass of  ${\mathbf{SO}}_2$= 2.5kg = 2500g

$\begin{array}{l}Convert2.5kgSolidSO2toliquidSO2\\ SpecificHeatCpacity,q=m\Delta H^{o}fus\\ \Rightarrow q=\left(2500g\right)\times (134.5J/g)\\ \Rightarrow q=336250J\end{array}$

$\begin{array}{l}Convert2.5kgliquidSO2from-{73}^{o}Cto-{10}^{o}C\\ SpecificHeatCpacity,q=mCliq\Delta T\\ \Delta T=(-{10}^{o}C)-(-{73}^{o}C)={63}^{o}C\\ \Rightarrow q=2500g\times 0.995\times {63}^{o}C\\ \Rightarrow q=156712.5J\end{array}$

 

$\begin{array}{l}Convert2.5kgliquidSO2intoVapoursfrom-{10}^{o}Cto-{10}^{o}C\\ SpecificHeatCapacity,q=m\Delta {H^o}_{vap}\\ \Rightarrow q=2500g\times 401.6J/g\\ \Rightarrow q=1004000J\end{array}$

$\begin{array}{l}Convert2.5kgGaseousSO2from-{10}^{o}Cto{60}^{o}C\\ SpecificHeatCapacity,q=MCgas\Delta T\\ \Delta T=\left({60}^{o}C\right)-(-{10}^{o}C)={70}^{o}C\\ \Rightarrow q=2500g\times 0.622j/gk\times {70}^{o}C\\ \Rightarrow q=108850J\end{array}$

The total heat energy required to convert solid into vapours.

$\begin{array}{l}TotalEnergy=(336250+156712.5+1004000+108850)\\ qTotal=1605812.5J\end{array}$