Question

When two moles of hydrogen atoms join together to forms mole of hydrogen molecules in a rigid vessel $H(g) + H(g) \longrightarrow H_2(g)$ then :

• A. $w < 0$
• B. $\Delta U = negative$
• C. $q_{system} = positive$
• D. $q_{surrounding} = negative$

Answer 1

Answer: (B)

$\Delta U = negative$

Answer 2

The reaction given is the formation of hydrogen molecules from hydrogen atoms:

$2H(g) \longrightarrow H_2(g)$

Let's analyze each option:

1. Work (w): The reaction occurs in a rigid vessel. This means the volume of the system remains constant throughout the process. For a process occurring at constant volume, the change in volume ($\Delta V$) is zero. The work done ($w$) by or on the system is given by the formula: $w = -P\Delta V$. Since $\Delta V = 0$, the work done $w = -P(0) = 0$. Therefore, the statement $w < 0$ is incorrect.

2. Change in Internal Energy ($\Delta U$): The formation of a chemical bond (like the H-H bond in $H_2$) is an exothermic process. This means that energy is released from the system to the surroundings during bond formation. According to the First Law of Thermodynamics, the change in internal energy ($\Delta U$) is given by: $\Delta U = q + w$, where $q$ is the heat exchanged and $w$ is the work done. As established in point 1, for a rigid vessel, $w = 0$. Therefore, the First Law simplifies to: $\Delta U = q_{system}$. Since the reaction is exothermic, heat is released by the system, which means $q_{system}$ is negative ($q_{system} < 0$). Consequently, $\Delta U$ must also be negative. Therefore, the statement $\Delta U = negative$ is correct.

3. Heat of the system ($q_{system}$): As explained in point 2, the formation of chemical bonds releases energy. This is an exothermic process. For an exothermic process, the heat exchanged by the system ($q_{system}$) is negative, as the system loses heat. Therefore, the statement $q_{system} = positive$ is incorrect.

4. Heat of the surrounding ($q_{surrounding}$): Since the system releases heat (exothermic process, $q_{system} < 0$), this heat is absorbed by the surroundings. When the surroundings absorb heat, the heat exchanged by the surroundings ($q_{surrounding}$) is positive. Therefore, the statement $q_{surrounding} = negative$ is incorrect.

Based on the analysis, only the statement $\Delta U = negative$ is correct.