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Heat of Reaction

Methanol can ...

Question

Methanol can be prepared synthetically by heating carbon monoxide and hydrogen gases under pressure in the presence of a catalyst. The reaction is
$C O (g) + 2 H_{2} (g) \to {C H}_{3}) H (l)$
Determine the enthalpy of this reaction by an appropriate combination of the following data:
$C_{(g r a p h i t e)} + \frac{1}{2} {2 O}_{2} (g) ⟶ C O (g) (Δ H = - 110.5 k J {m o l}^{- 1}) . . . (i)$
$C_{(g r a p h i t e)} + {2 O}_{2} (g) ⟶ C O (g) (Δ H = - 393.5 k J {m o l}^{- 1}) . . . . (i i)$
$H_{2} (g) + {2 O}_{2} (g) ⟶ H_{2} O (l) (Δ H = - 285.9 k J {m o l}^{- 1}) . . . . (i i i)$
${C H}_{3} O H (l) \frac{3}{2} {2 O}_{2} (g) ⟶ {C O}_{2} (g) + 2 H_{2} O (l) (Δ H = - 726.6 k J {m o l}^{- 1}) . . . . (i v)$

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Solution

The required equation can be obtained in the following manner
-eq $(i)$ +2 eq. $(i i i)$ +eq. $(i i)$ -eq. $(i v)$
$= {C O}_{2} (g) + 2 H_{2} (g) \to {C H}_{3} O H (g)$
So, $Δ H = 110.5 - 571.8 - 393.5 + 726.6 = - 128.2 k J {m o l}^{- 1}$

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Similar questions

Δ U^{o}

300 K

4 C O (g) + 8 H_{2} (g) ⟶ 3 {C H}_{4} (g) + {C O}_{2} (g) + 2 H_{2} O (l)

C_{(g r a p h i t e)} + 1 / 2 O_{2} (g) ⟶ C O (g); Δ {H_{1}}^{o} = - 110.5 k J

C O (g) + 1 / 2 O_{2} (g) ⟶ {C O}_{2} (g); Δ {H_{2}}^{o} = - 282.9 k J

H_{2} (g) + 1 / 2 O_{2} (g) ⟶ H_{2} O (l); Δ {H_{3}}^{o} = - 285.8 k J

C_{(g r a p h i t e)} + 2 H_{2} (g) ⟶ {C H}_{4} (g); Δ {H_{4}}^{o} = - 74.8 k J

Determine $Δ U^{\circ}$ at 300 K for the following reaction using the listed enthalpies of reaction.

$4 C O (g) + 8 H_{2} (g) \to 3 C H_{4} (g) + C O_{2} (g) + 2 H_{2} O (l)$

$C (g r a p h i t e) + \frac{1}{2} O_{2} (g) \to C O (g); Δ {H_{1}}^{\circ} = - 110.5 k J$

$C O (g) + \frac{1}{2} O_{2} (g) \to C O_{2} (g); Δ {H_{2}}^{\circ} = - 282.9 k J$

$H_{2} (g) + \frac{1}{2} O_{2} (g) \to H_{2} O (l); Δ H_{3}^{0} = - 285.8 k J$

$C (g r a p h i t e) + 2 H_{2} (g) \to C H_{4} (g); Δ H_{4}^{0} = - 74.8 k J$

C_{(g r a p h i t e)} + O_{2} (g) \to C O_{2} (g); Δ_{r} H^{o} = - 393.5 k J m o l^{- 1}

H_{2} (g) + \frac{1}{2} O_{2} (g) \to H_{2} O (l); Δ_{r} H^{o} = - 285.8 k J m o l^{- 1}

C O_{2} (g) + 2 H_{2} O (l) \to C H_{4} (g) + 2 O_{2} (g); Δ_{r} H^{o} = + 890.3 k J m o l^{- 1}

Δ_{r} H^{o}

298 K

C_{(g r a p h i t e)} + 2 H_{2} (g) \to C H_{4} (g)

C_{(g r a p h i t e} + O_{2} (g) \to C O_{2} (g); Δ_{r} H^{o} = - 393.5 k J m o l^{- 1}

H_{2} (g) + \frac{1}{2} O_{2} (g) \to H_{2} O (l); Δ_{r} H^{o} = - 285.8 k J m o l^{- 1}

C O_{2} (g) + 2 H_{2} O (l) \to C H_{4} (g) + 2 O_{2} (g); Δ^{r} H 6 o = + 890.3 k J m o l^{- 1}

D e l t a_{r} H^{o}

298 K

C_{(g r a p h i t e)} + 2 H_{2} (g) \to C H_{4} (g)

C H_{3} O H (I)

C H_{3} O H (I) + \frac{3}{2} O_{2} (g) \to C O_{2} (g) + 2 H_{2} O (l); △_{r} H^{θ} = - 726 k J m p l^{- 1}

C_{(g r a p h i t e)} + O_{2} (g) \to C O_{2} (g); △_{c} H^{θ} = - 393 k J m o l^{- 1}

H_{2} (g) + \frac{1}{2} O_{2} (g) \to H_{2} O (l); △_{f} H^{θ} = - 286 k J m o l^{- 1}

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