Questions: In which reaction would you expect ΔH to be substantially greater than ΔU (i.e., ΔH> ΔU) ? A) H2O(s) → H2O(t) B) H2(g) + Br2(g) → 2 HBr(g) C) HCl(aq) + NaOH(aq) → NaCl(aq) + H2O(l) D) CO2(s) → CO2(g) E) C2H2(g) + H2(g) → C2H4(g)

In which reaction would you expect ΔH to be substantially greater than ΔU (i.e., ΔH> ΔU) ?
A) H2O(s) → H2O(t)
B) H2(g) + Br2(g) → 2 HBr(g)
C) HCl(aq) + NaOH(aq) → NaCl(aq) + H2O(l)
D) CO2(s) → CO2(g)
E) C2H2(g) + H2(g) → C2H4(g)

Transcript text: In which reaction would you expect $\Delta H$ to be substantially greater than $\Delta U$ (i.e., $\Delta H>$ $\Delta U)$ ? A) $\mathrm{H}_{2} \mathrm{O}(s) \rightarrow \mathrm{H}_{2} \mathrm{O}(t)$ B) $\mathrm{H}_{2}(\mathrm{~g})+\mathrm{Br}_{2}(\mathrm{~g}) \rightarrow 2 \mathrm{HBr}(\mathrm{g})$ C) $\mathrm{HCl}(a q)+\mathrm{NaOH}(a q) \rightarrow \mathrm{NaCl}(a q)+\mathrm{H}_{2} \mathrm{O}(l)$ D) $\mathrm{CO}_{2}(\mathrm{~s}) \rightarrow \mathrm{CO}_{2}(\mathrm{~g})$ E) $\mathrm{C}_{2} \mathrm{H}_{2}(\mathrm{~g})+\mathrm{H}_{2}(\mathrm{~g}) \rightarrow \mathrm{C}_{2} \mathrm{H}_{4}(\mathrm{~g})$

Solution

Solution Steps

Step 1: Understanding the Relationship Between $\Delta H$ and $\Delta U$

The relationship between the change in enthalpy ($\Delta H$) and the change in internal energy ($\Delta U$) is given by the equation:

\[ \Delta H = \Delta U + \Delta n \cdot R \cdot T \]

where $\Delta n$ is the change in the number of moles of gas, $R$ is the ideal gas constant, and $T$ is the temperature in Kelvin. If $\Delta n$ is positive, $\Delta H$ will be greater than $\Delta U$.

Step 2: Analyzing Each Reaction

Option A: $\mathrm{H}_{2} \mathrm{O}(s) \rightarrow \mathrm{H}_{2} \mathrm{O}(l)$
- This is a phase change from solid to liquid, with no change in the number of moles of gas ($\Delta n = 0$).
Option B: $\mathrm{H}_{2}(\mathrm{~g})+\mathrm{Br}_{2}(\mathrm{~g}) \rightarrow 2 \mathrm{HBr}(\mathrm{g})$
- The number of moles of gas remains the same ($\Delta n = 0$).
Option C: $\mathrm{HCl}(a q)+\mathrm{NaOH}(a q) \rightarrow \mathrm{NaCl}(a q)+\mathrm{H}_{2} \mathrm{O}(l)$
- This is a reaction in aqueous solution with no change in the number of moles of gas ($\Delta n = 0$).
Option D: $\mathrm{CO}_{2}(\mathrm{~s}) \rightarrow \mathrm{CO}_{2}(\mathrm{~g})$
- This is a sublimation process where solid $\mathrm{CO}_{2}$ becomes gaseous $\mathrm{CO}_{2}$. The change in moles of gas is positive ($\Delta n > 0$).
Option E: $\mathrm{C}_{2} \mathrm{H}_{2}(\mathrm{~g})+\mathrm{H}_{2}(\mathrm{~g}) \rightarrow \mathrm{C}_{2} \mathrm{H}_{4}(\mathrm{~g})$
- The number of moles of gas remains the same ($\Delta n = 0$).

Step 3: Identifying the Reaction with $\Delta H > \Delta U$

From the analysis, only option D involves a positive change in the number of moles of gas, which means $\Delta H$ will be substantially greater than $\Delta U$.

Final Answer

$\boxed{\text{D}}$

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