Question

What is the value of $\Delta$H - $\Delta$U for the formation of one mole of methyl alcohol from elements in standard state?

• A. -RT
• B. -2.5 RT
• C. -3 RT
• D. -1.5 RT

Answer 1

Answer: (B)

-2.5 RT

Answer 2

For the formation of methyl alcohol, the reaction is:

$$\text{C(graphite)} + 2\,\text{H}_2(g) + \tfrac{1}{2}\,\text{O}_2(g) \rightarrow \text{CH}_3\text{OH}(l)$$

Only gases contribute to the $RT$ term. Count moles of gas:

• Reactants: $2$ moles of $\text{H}_2$ and $0.5$ moles of $\text{O}_2$; total $2.5$ moles.
• Products: $0$ (since methyl alcohol is liquid).

Thus,

$$\Delta n_{\text{gas}} = 0 - 2.5 = -2.5$$

Using the relation:

$$\Delta H = \Delta U + \Delta n_{\text{gas}} \cdot RT$$

we have:

$$\Delta H - \Delta U = -2.5\,RT$$