Observe the following reactions $\begin{aligned} & \mathrm{AB}(g)+25 \mathrm{H}_2 \mathrm{O}(l) \rightarrow…

Observe the following reactions $\begin{aligned} & \mathrm{AB}(g)+25 \mathrm{H}_2 \mathrm{O}(l) \rightarrow \mathrm{AB}_{\left(50 \mathrm{H}_2 \mathrm{O}\right)} ; \Delta \mathrm{H}=x \mathrm{~kJ} \mathrm{~mol}^{-1} \\ & \mathrm{AB}(\mathrm{~g})+50 \mathrm{H}_2 \mathrm{O}(l) \rightarrow \mathrm{AB}_{\left(50 \mathrm{H}_2 \mathrm{O}\right)} ; \Delta \mathrm{H}=y \mathrm{~kJ} \mathrm{~mol}^{-1} \end{aligned}$
The enthalpy of dilution $\left(\Delta \mathrm{H}_{\mathrm{dil}}\right)$ in $\mathrm{kJ} \mathrm{mol}^{-1}$ is
  1. $(y-x)$
  2. $(y+x)$
  3. $\frac{y}{x}$
  4. $\frac{x}{y}$

Solution

Enthalpy of Dilution: Dilution of a solution from one concentration to another is accompanied by enthalpy change called enthalpy of dilution. $\begin{gathered} \mathrm{AB}(\mathrm{~g})+50 \mathrm{H}_2 \mathrm{O}(\ell) \rightarrow \mathrm{AB}_{\left(50 \mathrm{H}_2 \mathrm{O}\right)} \Delta \mathrm{H}=\mathrm{ykJ} \mathrm{~mol}^{-1} \\ \mathrm{AB}_{\left(25 \mathrm{H}_2 \mathrm{O}\right)} \rightarrow \mathrm{AB}(\mathrm{~g})+25 \mathrm{H}_2 \mathrm{O}(\ell) \Delta \mathrm{H}=-\mathrm{xkJ} \mathrm{~mol}^{-1} \\ \mathrm{AB}_{\left(25 \mathrm{H}_2 \mathrm{O}\right)}+25 \mathrm{H}_2 \mathrm{O}(\ell) \rightarrow \mathrm{AB}_{\left(50 \mathrm{H}_2 \mathrm{O}\right)} ; \Delta \mathrm{H}=(\mathrm{y}-\mathrm{x}) \mathrm{kJ} \mathrm{~mol}^{-1} \end{gathered}$

Asked in: AP EAMCET 2024 (21 May Shift 1)

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