For the reaction CO(g)+3 H2(g) ⇌CH4(g)+H2 O(g) K=2.2 ×10^ll at 473 K and 4.6 ×10^8 at 533 K. C

step 1 Thermodynamics is the branch of physics that deals with the relationships between heat and other

For the reaction CO(g)+3 H2(g) ⇌CH4(g)+H2 O(g) K=2.2 ×10^ll...

For the reaction $$\mathrm{CO}(g)+3 \mathrm{H}_{2}(g) \rightleftharpoons \mathrm{CH}_{4}(g)+\mathrm{H}_{2} \mathrm{O}(g)$$ $K=2.2 \times 10^{\mathrm{ll}}$ at $473 \mathrm{~K}$ and $4.6 \times 10^{8}$ at $533 \mathrm{~K}$. Calculate $\Delta G^{\circ}$ at both temperatures. 66. For the reaction $$\begin{array}{l}\mathrm{H}_{2}(g)+\mathrm{I}_{2}(g) \rightleftharpoons 2 \mathrm{HI}(g) \\K=50.0 \text { at } 721 \mathrm{~K}\end{array}$$ (a) What is $\Delta G^{\circ}$ at $721 \mathrm{~K} ?$ (b) What is $K$ at $25^{\circ} \mathrm{C} ?\left(\Delta G_{i}^{\circ} \mathrm{I}_{2}(g)=+19.4 \mathrm{~kJ} / \mathrm{mol}\right)$

For the reaction
$$\mathrm{CO}(g)+3 \mathrm{H}_{2}(g) \rightleftharpoons \mathrm{CH}_{4}(g)+\mathrm{H}_{2} \mathrm{O}(g)$$
$K=2.2 \times 10^{\mathrm{ll}}$ at $473 \mathrm{~K}$ and $4.6 \times 10^{8}$ at $533 \mathrm{~K}$. Calculate $\Delta G^{\circ}$ at both
temperatures.
66. For the reaction
$$\begin{array}{l}\mathrm{H}_{2}(g)+\mathrm{I}_{2}(g) \rightleftharpoons 2 \mathrm{HI}(g) \\K=50.0 \text { at } 721 \mathrm{~K}\end{array}$$
(a) What is $\Delta G^{\circ}$ at $721 \mathrm{~K} ?$
(b) What is $K$ at $25^{\circ} \mathrm{C} ?\left(\Delta G_{i}^{\circ} \mathrm{I}_{2}(g)=+19.4 \mathrm{~kJ} / \mathrm{mol}\right)$

Key Concepts

van't Hoff Equation

The van't Hoff equation quantifies the relationship between the equilibrium constant (K) and temperature. It expresses how ln K changes with the reciprocal of the temperature (1/T) and is related to the reaction’s standard enthalpy change (?H°). This equation is essential for analyzing the effect of temperature on the position of equilibrium and for determining the enthalpic contributions to the reaction process.

Temperature Dependence of Equilibrium

The temperature dependence of equilibrium refers to how the equilibrium constant (K) and, consequently, the standard Gibbs free energy change (?G°) vary with temperature. As temperature changes, the balance between reactants and products shifts according to the reaction’s enthalpy change. This concept is crucial for understanding and predicting the behavior of chemical reactions under different thermal conditions.

Equilibrium Constant (K)

The equilibrium constant (K) is a ratio that expresses the concentrations or pressures of products to reactants at chemical equilibrium, with each species raised to the power of its stoichiometric coefficient. It provides insight into the position of equilibrium; a larger K signifies that the products are favored, whereas a smaller K indicates that the reactants are favored. K is a central concept in chemical thermodynamics and directly influences the calculation of ?G°.

Standard Gibbs Free Energy Change

Standard Gibbs free energy change (?G°) is a thermodynamic quantity that indicates the spontaneity of a chemical reaction under standard conditions. It is related to the equilibrium constant by the equation ?G° = -RT ln K, thereby connecting the concepts of free energy and equilibrium. A negative ?G° implies that the reaction is spontaneous in the forward direction under standard conditions, while a positive value indicates non-spontaneity.

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