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Δ Hf∘ of a hy...

Question

$Δ H_{f}^{\circ}$ of a hypothetical salt, $M X$ is $150 {kJmol}^{- 1}$ and for $M X_{2}$ it is $- 600 {kJmol}^{- 1}$ . The enthalpy of disproportionation of $M X$ is $- 100 {x kJmol}^{- 1}$ . The value of $x$ is

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Solution

Disproportionation reaction of MX
$2 M X \to M + M X_{2}$
$M + \frac{1}{2} X_{2} \to M X Δ_{f} H_{1} = - 150 k J m o l^{- 1}$
$M + X_{2} \to M X_{2} Δ_{f} H_{2} = - 600 k J m o l^{- 1}$
$Δ H = Δ_{f} H_{2} - 2 Δ_{f} H_{1}$
$= - 600 - (2 \times (- 150)$
$= - 300 k J m o l^{- 1}$
x=3

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