The molar heats of combustion of C2H2,(g), C(graphite) and H2(g), are 310.62, 94.05, and 68.32 kcal respectively. Calculate heat of formation of C2H2.

We have to calculate2Cgraphite +H2(g)→C2H2(g);ΔH=?Given,C2H2(g)+5/2O2(g)→2CO2(g)+H2O(g)ΔH=−310.62kcalCgraphite +O2(g)→CO2(g);ΔH=−94.05kcalH2(g)+1/2O2(g)→H2O(g); ΔH=−68.32kcalMultiply Eq. (2) by Z and add in Eq. (3)2Cgraphite +2O2(g)→CO2(g); ΔH=−188.10kcalH2(g)+1/2O2(g)→H2O(g); ΔH=−68.32kcal=2Cgraphite +5/2O2(g)+H2(g)→2CO2(g)+H2O(g)ΔH=−256.42kcal … (4)Subtract Eq. (1) from Eq. (4) C2-H2(g)+5/2O2-(g)→2CO2 -(g)+H 2O-(g);ΔH=−310.6+2kcal--------------------------------------------------------------------------------------2Cgraphite +H2(g)→C2H2(g); , ΔH=+54.2kcal

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The molar heats of combustion of C₂H₂,(g), C(graphite) and H₂(g), are 310.62, 94.05, and 68.32 kcal respectively. Calculate heat of formation of C₂H₂.

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answer is 54.2.

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Detailed Solution

We have to calculate

$2 C_{graphite} + H_{2} (g) \to C_{2} H_{2} (g); Δ H = ?$

Given,

$\begin{array}{l} C_{2} H_{2} (g) + 5 / 2 O_{2} (g) \to 2 {CO}_{2} (g) + H_{2} O (g) \\ Δ H = - 310.62 kcal \\ C_{graphite} + O_{2} (g) \to {CO}_{2} (g); Δ H = - 94.05 kcal \\ H_{2} (g) + 1 / 2 O_{2} (g) \to H_{2} O (g); Δ H = - 68.32 kcal \end{array}$

Multiply Eq. (2) by Z and add in Eq. (3)

$\begin{array}{l} 2 C_{graphite} + 2 O_{2} (g) \to {CO}_{2} (g); Δ H = - 188.10 kcal \\ \frac{H_{2} (g) + 1 / 2 O_{2} (g) \to H_{2} O (g); Δ H = - 68.32 kcal}{= 2 C_{graphite} + 5 / 2 O_{2} (g) + H_{2} (g) \to 2 {CO}_{2} (g) + H_{2} O (g)} \\ Δ H = - 256.42 kcal \dots (4) \end{array}$

Subtract Eq. (1) from Eq. (4)

$\underline{C_{2}} H_{2} (g) + 5 / 2 \underline{O_{2}} (g) \to 2 \underline{{CO}_{2}} (g) + H \underline{_{2} O} (g); Δ H = - 310 \underset{+}{.6} 2 kcal$