Question

Using the data provided, calculate the multiple bond energy $\left(\text{k}\text{J}\text{m}\text{o}{\left(\text{l}\right)}^{-1}\right)$ of a $\text{C}\equiv \text{C}$ bond in ${\text{C}}_2{\text{H}}_2$ . That energy is (take the bond energy of a $\text{C}-\text{H}$ bond as $350\text{k}\text{J}\text{m}\text{o}{\text{l}}^{-1}$ )
$2\text{C}\left(\text{s}\right)\to 2\text{C}\left(\text{g ; }\right)$ $\Delta \text{H}=1410\text{k}\text{J}\text{m}\text{o}{\text{l}}^{-1}$
${\left(\text{H}\right)}_2\left(\text{g}\right)\to 2\text{H}(\text{g}):$ $\Delta \text{H}=330\text{k}\text{J}\text{m}\text{o}{\text{l}}^{-1}$
$2\text{C}\left(\text{s}\right)+{\left(\text{H}\right)}_2\left(\text{q}\right)\to {\left(\text{C}\right)}_2{\left(\text{H}\right)}_2\text{;}\text{ΔH}=225{\left(\text{kJmol}\right)}^{-1}$

• A. 1165
• B. 837
• C. 865
• D. 815

Answer 1

Answer: (D)

(i) $2\text{C}\left(\text{s}\right)+{\left(\text{H}\right)}_2\left(\text{g}\right)\to \text{H}-\text{C}\equiv \text{C}-\text{H}(\text{g})$
$\Delta \text{H}=225\text{k}\text{J}\text{m}\text{o}{\text{l}}^{-1}$
(ii) $2\text{C}\left(\text{s}\right)\to 2\text{C}(\text{g})$

$\Delta {\text{H}}_1=1410\text{K}\text{J}\text{m}\text{o}{\text{l}}^{-1}$
$\left(\text{i}\text{i}\text{i}\right){\left(\text{H}\right)}_2(\text{g})\to 2\text{H}(\text{g})$
$\Delta {\text{H}}_2=330\text{K}\text{J}\text{m}\text{o}{\text{l}}^{-1}$
From equation (i) :
$225=\left(\Delta {\left(\text{H}\right)}_1+\Delta {\left(\text{H}\right)}_2\right)-[2\Delta {\left(\text{H}\right)}_{\text{C}-\text{H}}+\Delta {\left(\text{H}\right)}_{\text{C}\equiv \text{C}}]$
$225=\left[1410+330\right]+\left(2\times 350\right)+\Delta {\left(\text{H}\right)}_{\text{C}\equiv \text{C}}]$
$225=1040-\Delta {\text{H}}_{\text{C}\equiv \text{C}}$
$\Delta {\text{H}}_{\text{C}\equiv \text{C}}=1040-225=815\text{K}\text{J}\text{m}\text{o}{\text{l}}^{-1}$