Question

Identify the equation in which change in enthalpy is equal to change in internal energy

• A. $2H_{2}O_{2} (I) \to 2H_{2}O(I) +O_{2}(g)$
• B. $C(s) +O_{2}(g) \to CO_{2}(g)$
• C. $PCl_{5}(g) \to PCl_{3}(g) +Cl_{2}(g)$
• D. $N_{2}(g) + 3\,H_{2}(g) \to 2NH_{3}(g)$

Answer 1

Answer: (B)

Key Idea Relationship between change in enthalpy and change in intemal energy is given as:

$\Delta H=\Delta U+\Delta n_{g} RT$

In the given options,

(a) $2 H _{2} O _{2}(l) \to 2H _{2} O (l)+ O _{2}(g)$ $\Delta n_{g} = 1$

$\therefore \Delta H=\Delta U+RT$

(b) $C ( s )+ O _{2}(g) \to CO _{2}(g)$

$ \Delta n_{ g }=1-1=0$

$\therefore \Delta H=\Delta U$

(c) $PCl _{5}(g) \to PCl _{3}(g)+ Cl _{2}(g)$

$\Delta \,n_{g}=2-1=1$

$\therefore \Delta H=\Delta U+RT$

(d) $N _{2}(g)+3 H _{2}(g) \to 2 NH _{3}(g)$

$\Delta\, n_{g}RT=2-3=-1$

$\therefore \Delta H=\Delta U-RT$

Equation given in option (b) has enthalpy change equal to internal change