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Question 4.4: The enthalpy of solution for the reaction Na2SO4(s)→2 Na^+(a...

The enthalpy of solution for the reaction

Na_{2}SO_{4}\left( s \right)\overset{H_{2}O\left( l \right)}{\longrightarrow } 2 Na^{+}\left( aq \right)+SO^{2-}_{4}\left( aq \right)

 

is determined in a constant pressure calorimeter. The calorimeter constant was determined to be 342.5  J  K^{-1}.When 1.423 g of Na_{2}SO_{4} is dissolved in 100.34 g of H_{2}O\left( l \right),\Delta T=0.031  K. Calculate \Delta H°_{solution} for Na_{2}SO_{4} from these data. Compare your result with that calculated using the standard enthalpies of formation in Table 4.1 (Appendix A, Data Tables) and in Chapter 10 in Table 10.1.

 

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\Delta H°_{solution}=-\frac{M_{salt}}{m_{salt}}\left( \frac{m_{H_{2}O}}{M_{H_{2}O}}C_{P, m}\left( H_{2} O\right)\Delta T+C_{calorimeter}\Delta T \right)

 

=-\frac{142.04  g  mol^{-1}}{1.423 g}×\left( ^{\frac{100.34 g}{18.02  g  mol^{-1}}×75.3  J  K^{-1} mol^{-1}×0.031  K} _{+342.5  J  K^{-1}×0.031  K}\right)

 

=-2.4 ×10^{3}  J  mol^{-1}

We next calculate \Delta H°_{solution} using the data tables.

\Delta H°_{solution}=2\Delta H°_{f}\left( Na^{+},aq \right)+\Delta H°_{f}\left( SO^{2-}_{4},aq \right)-\Delta H°_{f}\left( Na_{2}SO_{4},s \right)

 

=2×\left( -240.1  kJ mol^{-1} \right)-909.3  kJ mol^{-1}+1387.1  kJ mol^{-1}

 

=-2.4  kJ mol^{-1}

The agreement between the calculated and experimental results is good.

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