Questions: Calculate the temperature at which the following reaction becomes feasible: 4 HCl + O2 -> 2 Cl2 + 2 H2O Enthalpy: +280 kJ / mol Entropy: +235 J / Kmol A. 1191.49 K B. 515.0 K C. 65.80 K D. 45.0 K

Calculate the temperature at which the following reaction becomes feasible:
4 HCl + O2 -> 2 Cl2 + 2 H2O

Enthalpy: +280 kJ / mol
Entropy: +235 J / Kmol
A. 1191.49 K
B. 515.0 K
C. 65.80 K
D. 45.0 K

Transcript text: Calculate the temperature at which the following reaction becomes feasible: \[ 4 \mathrm{HCl}+\mathrm{O}_{2} \rightarrow 2 \mathrm{Cl}_{2}+2 \mathrm{H}_{2} \mathrm{O} \] Enthalpy: $+280 \mathrm{~kJ} / \mathrm{mol}$ Entropy: $+235 \mathrm{~J} / \mathrm{Kmol}$ A. 1191.49 K B. 515.0 K C. 65.80 K D. 45.0 K

Solution

Solution Steps

Step 1: Identify the Given Data

We are given the following data for the reaction:

Enthalpy change, $\Delta H = +280 \, \text{kJ/mol}$
Entropy change, $\Delta S = +235 \, \text{J/Kmol}$

Step 2: Convert Units

Convert the enthalpy change from kJ to J to match the units of entropy: \[ \Delta H = 280 \, \text{kJ/mol} \times 1000 \, \text{J/kJ} = 280000 \, \text{J/mol} \]

Step 3: Use the Gibbs Free Energy Equation

The reaction becomes feasible when the Gibbs free energy change, $\Delta G$, is zero: \[ \Delta G = \Delta H - T \Delta S \] Set $\Delta G = 0$ and solve for $T$: \[ 0 = \Delta H - T \Delta S \] \[ T = \frac{\Delta H}{\Delta S} \]

Step 4: Substitute the Values

Substitute the values of $\Delta H$ and $\Delta S$ into the equation: \[ T = \frac{280000 \, \text{J/mol}}{235 \, \text{J/Kmol}} \] \[ T = 1191.4894 \, \text{K} \]

Step 5: Round to Four Significant Digits

Round the temperature to four significant digits: \[ T = 1191.49 \, \text{K} \]