Given: C( graphite )+2H2(g)→CH4(g); ΔH1C(g)+4H(g)→CH4(g); ΔH2which one of the following is true?

Given: $\begin{aligned} C (graphite) + 2 H_{2} (g) \to {CH}_{4} (g); Δ H_{1} \\ C (g) + 4 H (g) \to {CH}_{4} (g); Δ H_{2} \end{aligned}$
which one of the following is true?

A
$Δ H_{1} = Δ H_{2}$
B
$Δ H_{1} > Δ H_{2}$
C
$Δ H_{1} < Δ H_{2}$
D
$Δ H_{1} = 2 Δ H_{2}$

Solution:

The equation $C (graphite) + 2 H_{2} (g) \to {CH}_{4} (g)$ may be considered as the sum of the following three equations.

$\begin{array}{l} C (graphite) \to C (g) Δ H_{a} \\ 2 H_{2} (g) \to 4 H (g) Δ H_{b} \\ C (g) + 4 H (g) \to {CH}_{4} (g) Δ H_{2} \end{array}$

Hence $Δ H_{1} = Δ H_{a} + Δ H_{b} + Δ H_{2}$

Since $Δ H_{a}$ and $Δ H_{b}$ are positive, $Δ H_{1} > Δ H_{2}$

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