Question

For the following reaction at 300 K: \[ \text{A}_2(g) + 3\text{B}_2(g) \rightarrow 2\text{AB}_3(g) \] The enthalpy change is \(+15 \, \text{kJ}\), then the internal energy change is:

• A. 19988.4 J
• B. 200 J
• C. 1999 J
• D. 1.9988 kJ

Answer 1

The Correct Option is A

The equation relating enthalpy change ($\Delta H$) and internal energy change ($\Delta U$) is:
\[ \Delta H = \Delta U + \Delta n_g RT \]
In this equation:
$\Delta n_g$ denotes the change in the number of moles of gas.
R represents the gas constant (8.314 J K$^{-1}$ mol$^{-1}$).
T signifies the temperature in Kelvin.
For the specified reaction:
$\Delta n_g$ is calculated as: moles of gaseous products minus moles of gaseous reactants.
$\Delta n_g = 2 - 4 = -2$.
Given values are:
$\Delta H = +15$ kJ, which is equivalent to $15 \times 10^3$ J.
T = 300 K.
The internal energy change ($\Delta U$) is derived using the rearranged formula: $\Delta U = \Delta H - \Delta n_g RT$.
\(\Delta U = 15000 J - (-2 mol)(8.314 J K^{-1}mol^{-1})(300 K)\)
\(\Delta U = 15000 + 4988.4 = 19988.4 J\)