Calculate the standard heat of formation of carbon disulphide $(l)$ . Given that the standard heats of combustion of carbon (s), sulphur (s) and carbon disulphide $(l)$ are $- 393.3, - 293.7$ and $- 1108.76 k J {m o l}^{- 1}$ respectively.

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Solution

Required equation is
$C (s) + 2 S (s) \to {C S}_{2} (l); Δ H_{f} = ?$
Given
$C (s) + O_{2} (g) ⟶ {C O}_{2} (g); (Δ H = - 393.3 k J) . . . (i)$
$S (s) + O_{2} (g) ⟶ {S O}_{2} (g); (Δ H = - 293.72 k J) . . . (i i)$
${C S}_{2} (l) + 3 O_{2} (g) ⟶ {C O}_{2} (g) + {S O}_{2} (g); (Δ H = - 1108.76 k J) . . . (i i i)$
Mulltiply eq $(i i)$ by $2$
$S (s) + {2 O}_{2} (g) ⟶ {2 S O}_{2} (g); (Δ H = - 587.44 k J) . . . (i v)$
Adding eqs. $(i)$ and $(i v)$ and subtracting eq. $(i i i)$
$[C (s) + 2 S (s) + 3 O_{2} (g) - {C S}_{2} (l) - 3 O_{2} (g) \to {C O}_{2} (g) + 2 {S O}_{2} (g) - {C O}_{2} - 2 {S O}_{2}]$
$C (s) + 2 S (s) \to {C S}_{2} (l)$
This is the required equation
Thus $Δ H_{f} = - 393.3 - 587.4 + 1108.76 = 128.02 k J$
Standard Heat of formation of ${C S}_{2} (l) = 128.02 k J$

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