Given are the following data at 298 K. ΔcH∘C2H4,g=−1410.9kJmol−1; ΔcH∘C2H6,g=−1559.8kJmol−1; ΔcH∘H2,g=−285.8kJmol−1 The value of ΔrH∘  of the reaction C2H4(g)+H2(g)⟶C2H6(g) will be

# Given are the following data at 298 K.  The value of ${\mathrm{\Delta }}_{\mathfrak{r}}{H}^{\circ }$  of the reaction ${\mathrm{C}}_{2}{\mathrm{H}}_{4}\left(\mathrm{g}\right)+{\mathrm{H}}_{2}\left(\mathrm{g}\right)⟶{\mathrm{C}}_{2}{\mathrm{H}}_{6}\left(\mathrm{g}\right)$ will be

1. A

434.7 kJ mol-1

2. B

-434.7 kJ mol-1

3. C

136.9 kJ mol-1

4. D

-136.9 kJ mol-1

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### Solution:

${\mathrm{\Delta }}_{\mathrm{c}}{H}^{\circ }=-285.8\mathrm{kJ}{\mathrm{mol}}^{-1}$

The required chemical equation for which ${\mathrm{\Delta }}_{1}{H}^{\circ }$ ° is required is${\mathrm{C}}_{2}{\mathrm{H}}_{4}\left(\mathrm{g}\right)+{\mathrm{H}}_{2}\left(\mathrm{g}\right)⟶{\mathrm{C}}_{2}{\mathrm{H}}_{6}\left(\mathrm{g}\right)$  This equation is obtained by the manipulations Eq.(i) + Eq. (iii) - Eq. (ii) Hence,${\mathrm{\Delta }}_{\mathrm{r}}{H}^{\circ }=\left[-1410.9-285.8-\left(-1559.8\right)\right]\mathrm{kJ}{\mathrm{mol}}^{-1}=-136.9\mathrm{kJ}{\mathrm{mol}}^{-1}$