Question

For a reaction A + B $\rightarrow$ products $\Delta\text{H}$ is $-$84.2 kJ and $\Delta\text{S}$ is $-$200 J K$^{-1}$. Calculate the highest value of temperature so that the reaction will proceed in forward direction.

• A. 421 K
• B. 237 K
• C.
• D.

Hint:

For a reaction to be spontaneous, $\Delta G<0$. Use the Gibbs-Helmholtz equation, $\Delta G = \Delta H - T\Delta S$. Convert all energy units to be consistent (e.g., J for both $\Delta H$ and $T\Delta S$). Remember to flip the inequality sign when dividing or multiplying by a negative number. The temperature at which $\Delta G = 0$ is the equilibrium temperature, which serves as a boundary for spontaneity.

Answer 1

The Correct Option is A

Step 1: State the condition for a reaction to proceed in the forward direction.\ A reaction proceeds spontaneously in the forward direction if the change in Gibbs free energy ($\Delta G$) is negative ($\Delta G<0$).\
Step 2: Recall the Gibbs-Helmholtz equation.\ The Gibbs free energy change is related to enthalpy change ($\Delta H$), temperature ($T$), and entropy change ($\Delta S$) by the equation:\ \[\Delta G = \Delta H - T\Delta S\]\
Step 3: Substitute the given values and set up the inequality for spontaneity.\ Given:\ $\Delta H = -84.2 \text{ kJ} = -84200 \text{ J}$ (convert kJ to J)\ $\Delta S = -200 \text{ J K}^{-1}$\ For spontaneity, $\Delta G<0$:\ \[\Delta H - T\Delta S<0\]\ \[ -84200 \text{ J} - T(-200 \text{ J K}^{-1})<0 \]\ \[ -84200 + 200T<0 \]\
Step 4: Solve the inequality for temperature ($T$).\ \[200T<84200\]\ \[T<\frac{84200}{200}\]\ \[T<421 \text{ K}\]\
Step 5: Determine the highest temperature for forward reaction.\ The reaction will proceed in the forward direction for any temperature $T$ less than $421 \text{ K}$. At $T = 421 \text{ K}$, $\Delta G = 0$, meaning the reaction is at equilibrium.\ The question asks for the "highest value of temperature so that the reaction will proceed in forward direction". This implies the limiting temperature at which spontaneity ceases or is just about to cease. In the context of multiple-choice questions, when a boundary value is calculated, it is often the intended answer for "highest value" or "lowest value" for a process to occur, including equilibrium. Therefore, the highest temperature for spontaneity is considered up to, but not including, 421 K. However, as per common MCQ interpretation where the boundary is an option, 421 K is usually the desired answer.\ Comparing with options, $421 \text{ K}$ is the calculated equilibrium temperature, which is the upper limit for spontaneity.