Question
Consider the following reaction :
$$C{O_{\left( g \right)}} + \frac{1}{2}{O_{2\left( g \right)}} \to C{O_{2\left( g \right)}}$$
How are $$\Delta U$$ and $$\Delta H$$ related for the reaction ?
A.
$$\Delta H = \Delta U - 0.5RT$$
B.
$$\Delta H = \Delta U - RT$$
C.
$$\Delta H = \Delta U + 0.5RT$$
D.
$$\Delta H = \Delta U - 1.5RT$$
Answer :
$$\Delta H = \Delta U - 0.5RT$$
Solution :
$$\Delta H = \Delta U + \Delta {n_g}RT$$
$$\Delta {n_g} = 1 - \frac{3}{2} = - \frac{1}{2}\,\,{\text{or}}\,\, - 0.5\,;$$ $${\text{Hence,}}\,\Delta H = \Delta U - 0.5RT$$