Question

Calculate the enthalpy change when infinitely dilute solution of $Ca{Cl}_2$ and ${Na}_2{CO}_3$ mixed $\Delta H_r^o$ for ${Ca}^{2+}\left(aq\right)$, ${CO}_3^{2-}\left(aq\right)$ and $Ca{CO}_3\left(s\right)$ are $-129.80,-161.65,-288.5kcal$ ${mol}^{-1}$ respectively (nearest number in kcal).

Answer 1

Dilute solution of $CaC{l}_2$ contains $C{a}^{+2}$ and $C{l}^{-}$ ions
Dilute solution of $N{a}_{2}C{O}_3$ contains $N{a}^{+}$ and $C{O}_3^{-2}$ ions
When both are mixed
$C{a}^{+2}(aq.)+C{l}^{-}(aq.)+N{a}^{+}(aq.)+C{O}_3^{-2}(aq.)\to CaC{O}_3\left(s\right)+N{a}^{+}(aq.)+C{l}^{-}(aq.);\Delta H$
$\Delta H=\Sigma \Delta H_f^o\left(products\right)-\Sigma \Delta H_f^o\left(reactants\right)$
$\Rightarrow \Delta H=\Delta H_{f,CaC{O}_3\left(s\right)}^o+\Delta H_{f,N{a}^{+}(aq.)}^o+\Delta H_{f,C{l}^{-}(aq.)}^o-[\Delta H_{f,C{a}^{+2}(aq.)}^o+H_{f,C{l}^{-}(aq.)}^o+H_{f,N{a}^{+}}^o+H_{f,C{a}^{+2}(aq.)}^o]$
on simplification
$\Delta H=\Delta H_{f,CaC{O}_3\left(s\right)}^o-\Delta H_{f,C{a}^{+2}(aq.)}^o-\Delta H_{f,C{O}_3^{-2}(aq.)}^o$
$\Rightarrow \Delta H=-288.5+129.8+161.65=2.95kcal/mol$
Answer = 3