Problem 116 - Chemistry: An Atoms-Focused Approach

Question

Does the value of \(K_{\mathrm{p}}\) for the reaction \(\mathrm{CH}_{4}(g)+\mathrm{H}_{2} \mathrm{O}(g) \rightleftharpoons 3 \mathrm{H}_{2}(g)+\mathrm{CO}(g) \quad \Delta H^{\circ}=206 \mathrm{kJ}\) increase, decrease, or remain unchanged as the temperature increases?

Step-by-Step Solution

Answer

Answer: For the given reaction, the value of K_p will increase as the temperature increases.

Step 1: Determine the nature of the reaction from the heat of reaction (ΔH)

The heat of reaction given is ΔH° = 206 kJ. Since this value is positive, we can say that the reaction is endothermic.

Step 2: Use the Van't Hoff equation to understand the effect of temperature on K_p

The Van't Hoff equation relates the changes in equilibrium constant with changes in temperature and can be written as: \(\frac{d(\ln K_{p})}{dT} = \frac{\Delta H^{\circ}}{RT^{2}}\) Since the reaction is endothermic (ΔH > 0), the right side of the equation is positive. Therefore, the derivative of the natural logarithm of K_p with respect to temperature is also positive: \(\frac{d(\ln K_{p})}{dT} > 0\) This means that the value of K_p increases as the temperature increases.

Step 3: Final conclusion

For the given reaction, the value of K_p will increase as the temperature increases. This is because the reaction is endothermic, and increasing temperature will favor the forward reaction, which leads to a higher equilibrium constant value.

Key Concepts

Endothermic Reaction

In chemistry, reactions are classified based on how they interact with energy. An endothermic reaction is a type of chemical reaction that absorbs energy, usually in the form of heat, from its surroundings. This is key information you can gather from the enthalpy change (\( \Delta H \)).
When \( \Delta H \)is positive, it indicates that energy is required for the reaction to proceed. Hence, these reactions tend to absorb heat.

• In an endothermic reaction, the products are generally higher in energy than the reactants.
• Such processes might feel cold to the touch because they are taking in energy from their environment.

Understanding if a reaction is endothermic helps predict how it will behave under changing temperature conditions, such as whether increasing temperature will promote the forward reaction or not.

Van't Hoff Equation

The Van't Hoff equation is a vital tool in physical chemistry. It helps us understand how the equilibrium constant \( K \) changes with temperature. This equation essentially links the change in equilibrium constant to the change in temperature and the enthalpy change of the reaction.
The equation is expressed as:\[ \frac{d(\ln K_{p})}{dT} = \frac{\Delta H^{\circ}}{RT^2} \]where:

• \( \Delta H^{\circ} \)is the standard enthalpy change
• \( R \) is the universal gas constant
• \( T \) is the temperature in Kelvin

In this equation, a positive \( \Delta H^{\circ} \) (typical for endothermic reactions) results in the derivative being positive. Therefore, the natural logarithm of \( K_p \) increases with temperature. This indicates that for endothermic reactions, the equilibrium constant \( K_p \) increases as temperature rises.

Effect of Temperature on Equilibrium

Temperature changes can significantly impact the position of chemical equilibrium. For endothermic reactions, increasing the temperature generally causes the equilibrium to shift towards the products, favoring the forward reaction. This is because the absorption of excess heat helps the reaction to proceed.

• An increase in temperature supplies additional energy needed for endothermic reactions, driving them forward.
• This shift to products means a higher concentration of products at equilibrium, leading to an increase in the equilibrium constant \( K \).

Understanding the effect of temperature on equilibrium is crucial in processes like chemical reaction engineering, where controlling reaction conditions can optimize yields. For any reaction, noting whether it is endothermic or exothermic will provide insights into how temperature alterations will affect outcomes.