The standard reaction Gibbs energy for a chemical reaction at an absolute temperature T is given by,

Q: Why do we compare $A$ with $\Delta H^\circ$ and not $\Delta S^\circ$?

In the Gibbs-Helmholtz equation $\Delta G^\circ = \Delta H^\circ - T\Delta S^\circ$, the term without the temperature variable $T$ is $\Delta H^\circ$. In the given equation $A - BT$, $A$ is the constant term. Hence, $A$ corresponds to $\Delta H^\circ$.

Q: What does the constant $B$ represent physically?

By comparing the equations, $B$ corresponds to $\Delta S^\circ$, which is the standard entropy change of the reaction. It represents the change in randomness or disorder of the system.

Q: Can a reaction be spontaneous if it is endothermic?

Yes! Spontaneity depends on $\Delta G^\circ$, not just $\Delta H^\circ$. Even if $\Delta H^\circ > 0$ (endothermic), if the temperature $T$ is high enough and $\Delta S^\circ > 0$, the term $-T\Delta S^\circ$ can make $\Delta G^\circ$ negative, driving the reaction forward.

Q: Why is the temperature $T$ taken as absolute?

Absolute temperature (in Kelvin) is used because thermodynamic equations are derived based on the absolute zero scale, where molecular motion theoretically stops. Using Celsius would result in negative temperatures, which would break the mathematical relationships like $-T\Delta S^\circ$.

Q: Does the value of $B$ affect whether the reaction is endothermic or exothermic?

No. The terms endothermic and exothermic refer strictly to the heat exchange at constant pressure, which is governed solely by the enthalpy change $\Delta H^\circ$ (or $A$ in this case). $B$ (entropy) affects spontaneity, not the heat nature of the reaction.

Question

The standard reaction Gibbs energy for a chemical reaction at an absolute temperature $T$ is given by, $\Delta_r G^\circ = A - BT$ Where $A$ and $B$ are non-zero constants. Which of the following is true about this reaction? Options: (A) Endothermic if, $A < 0$ and $B > 0$ (B) Exothermic if, $B < 0$ (C) Exothermic if, $A > 0$ and $B < 0$ (D) Endothermic if, $A > 0$

Sigma Percentile · Accepted Answer

### The Power of the Gibbs-Helmholtz Equation Imagine you are trying to predict the future of a chemical reaction. Will it happen on its own? Will it release heat or absorb it? To answer these profound questions, thermodynamics gives us a master key: the **Gibbs-Helmholtz equation**. In this problem, we are given a simple linear equation for the standard Gibbs free energy: $$ \Delta_r G^\circ = A - BT $$ At first glance, $A$ and $B$ are just abstract mathematical constants. But in physical chemistry, every variable tells a story. Let's decode what $A$ and $B$ actually represent. ### Decoding the Constants To find the physical meaning of $A$ and $B$, we need to bring in our standard thermodynamic equation. The Gibbs free energy change is defined as: $$ \Delta_r G^\circ = \Delta_r H^\circ - T\Delta_r S^\circ $$ Here, $\Delta_r H^\circ$ is the standard enthalpy change, and $\Delta_r S^\circ$ is the standard entropy change. Now, let's place our two equations side by side and compare them term by term. The constant term that does not depend on temperature $T$ is $A$ in our given equation, and $\Delta_r H^\circ$ in the standard equation. Therefore, we can confidently say: $$ A = \Delta_r H^\circ $$ Similarly, the coefficient of the temperature $T$ is $B$ in the given equation, and $\Delta_r S^\circ$ in the standard equation. This means: $$ B = \Delta_r S^\circ $$ ### Endothermic vs Exothermic The question asks us to determine the conditions under which the reaction is endothermic or exothermic. What makes a reaction endothermic? An **endothermic** reaction is one that absorbs heat from its surroundings. In thermodynamic terms, the system gains enthalpy, meaning the enthalpy change $\Delta_r H^\circ$ must be strictly positive (greater than zero). Since we just established that $A = \Delta_r H^\circ$, it naturally follows that for an endothermic reaction, the constant $A$ must be positive: $$ A > 0 $$ Conversely, an **exothermic** reaction releases heat, meaning its enthalpy decreases ($\Delta_r H^\circ < 0$). This would correspond to $A < 0$. ### The Final Verdict Let's look at the options provided. We are looking for a statement that correctly links the sign of $A$ or $B$ to the nature of the reaction. Option (d) states: "Endothermic if, $A > 0$". This perfectly matches our logical deduction! If $A$ is positive, the enthalpy change is positive, and the system absorbs heat, making it endothermic. The constant $B$ (which represents entropy) has absolutely no say in whether a reaction is endothermic or exothermic; it only influences the overall spontaneity. Therefore, option (d) is the flawlessly correct answer.

Animated Solution for Chemistry - Chemical Thermodynamics: The standard reaction Gibbs energy for a chemical reaction at an absolute temperature $T$ is given by, $Δ_{r} G^{\circ} = A - B T$ Where $A$ and $B$ are non-zero constants. Which of the following is true about this reaction?

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Visualized Solution

$Gibbs-Helmholtz Equation$

$Comparing Coefficients$

$Enthalpy and Reaction Type$

$Conclusion$

The Sigma Insight: Entropy and Free Energy

The Power of the Gibbs-Helmholtz Equation

Decoding the Constants

Endothermic vs Exothermic

The Final Verdict

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