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Q6.28(b)(ii):
Dihydrogen gas is obtained from natural gas by partial oxidation with steam as per following endothermic reaction: $CH_4 (g) + H_2O (g) \rightleftharpoons CO (g) + 3H_2 (g)$ (b) How will the values of $K_p$ and composition of equilibrium mixture be affected by (ii) increasing the temperature

Solution :

Given Variables & Initial Setup

The chemical reaction under consideration is:

$CH_4(g) + H_2O(g) \rightleftharpoons CO(g) + 3H_2(g)$

The standard enthalpy change ($\Delta H^\circ$) for this reaction is positive ($\Delta H^\circ > 0$), signifying that the reaction is endothermic [Per the First Law of Thermodynamics and the definition of enthalpy in chemical systems].

Step 1: Effect on Equilibrium Constant ($K_p$)

The temperature dependence of the equilibrium constant is described by the van 't Hoff equation:

$\ln\left(\frac{K_{p2}}{K_{p1}}\right) = \frac{-\Delta H^\circ}{R} \left(\frac{1}{T_2} - \frac{1}{T_1}\right)$

  • For an endothermic reaction, $\Delta H^\circ > 0$.
  • When temperature increases ($T_2 > T_1$), the term $(\frac{1}{T_2} - \frac{1}{T_1})$ is negative.
  • The negative sign in the equation multiplied by the negative value of the parenthesis results in a positive value for $\ln(\frac{K_{p2}}{K_{p1}})$.
  • Therefore, $\frac{K_{p2}}{K_{p1}} > 1$, which implies $K_{p2} > K_{p1}$.

[By the van 't Hoff Equation, the equilibrium constant of an endothermic reaction increases with an increase in temperature].

Step 2: Effect on Composition of Equilibrium Mixture

According to Le Chatelier's Principle, if a system at equilibrium is subjected to a change in temperature, the equilibrium will shift in a direction that tends to counteract the imposed change [Per Le Chatelier's Principle regarding thermal stress].

  • Since the reaction is endothermic, the system absorbs heat: $Reactants + Heat \rightleftharpoons Products$.
  • Increasing the temperature adds heat to the system.
  • To minimize this stress, the system consumes the added heat by proceeding in the forward direction.
  • Consequently, the concentration of products ($CO$ and $H_2$) will increase, and the concentration of reactants ($CH_4$ and $H_2O$) will decrease.

Visual Representation of Thermal Shift

Temperature Increase Shift towards Products (Right) Reactants Products

Summary of Analysis

Parameter Effect of Increasing Temperature
Equilibrium Constant ($K_p$) Increases
Concentration of $CH_4, H_2O$ Decreases
Concentration of $CO, H_2$ Increases

Final Solution: Upon increasing the temperature, the value of $K_p$ will increase, and the equilibrium position will shift to the right, resulting in an increased yield of the products ($CO$ and $H_2$) and a decreased amount of reactants ($CH_4$ and $H_2O$).


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