Problem 77 - Introductory Chemistry Atoms First

Question

The equilibrium constant for the synthesis of methanol, $$ \mathrm{CO}(g)+2 \mathrm{H}_{2}(g) \rightleftarrows \mathrm{CH}_{3} \mathrm{OH}(g) $$ Methanol is \(4.3\) at \(250{ }^{\circ} \mathrm{C}\) and \(1.8\) at \(275^{\circ} \mathrm{C}\). (a) Does this reaction shift to the left or to the right when the reaction mixture is heated? Explain how you know. (b) Is this reaction endothermic or exothermic? Explain how you know. (c) Rewrite the equation for the reaction, including heat on the appropriate side.

Step-by-Step Solution

Answer

(a) The reaction shifts to the left when heated. (b) The reaction is endothermic. (c) The rewritten equation including heat is: \( \mathrm{CO}(g)+2 \mathrm{H}_{2}(g) + heat \rightleftarrows \mathrm{CH}_{3} \mathrm{OH}(g) \)

Step 1: 1. Temperature effect on the reaction

When the reaction mixture is heated, the temperature of the system increases. In this case, we're given that increasing the temperature from 250°C to 275°C results in the equilibrium constant decreasing from 4.3 to 1.8.

Step 2: 2. Determining the direction of shift

Since the equilibrium constant decreases (from 4.3 to 1.8) when the temperature increases, we can conclude that the reaction shifts in the direction that absorbs heat. In other words, upon heating, the reaction will favor the reverse reaction, which is exothermic and releases heat. Therefore, the reaction shifts to the left.

Step 3: 3. Endothermic vs Exothermic

Given that the reaction shifts to the left when heated, this indicates that the forward reaction is endothermic, meaning it absorbs heat, and the reverse reaction is exothermic, meaning it releases heat.

Step 4: 4. Rewriting the equation with heat

As the forward reaction is endothermic, we can add heat to the left side of the reaction equation. The rewritten equation for the synthesis of methanol, including heat, is: \( \mathrm{CO}(g)+2 \mathrm{H}_{2}(g) + heat \rightleftarrows \mathrm{CH}_{3} \mathrm{OH}(g) \) To summarize: (a) The reaction shifts to the left when the reaction mixture is heated. (b) The reaction is endothermic. (c) The rewritten equation including heat is: \( \mathrm{CO}(g)+2 \mathrm{H}_{2}(g) + heat \rightleftarrows \mathrm{CH}_{3} \mathrm{OH}(g) \)

Key Concepts

Chemical Equilibrium

In chemical reactions, chemical equilibrium is a state where the rate of the forward reaction equals the rate of the reverse reaction. As a result, the concentrations of the reactants and products remain constant over time, but not necessarily equal. A dynamic equilibrium exists because reactions continue to occur, but there is no net change in concentration.

For the synthesis of methanol:
\[\begin{equation} \mathrm{CO}(g) + 2 \mathrm{H}_2(g) \rightleftarrows \mathrm{CH}_3\mathrm{OH}(g) \end{equation}\], there is an equilibrium state reached where the formation rate of methanol and its decomposition occur at the same pace.

Le Chatelier's Principle

Le Chatelier's principle predicts how a system at equilibrium responds to changes in concentration, temperature, or pressure. If an external change is applied to a system at equilibrium, the system adjusts in such a way as to minimize that change. When the methanol reaction is heated, Le Chatelier's principle indicates that the system will respond by favoring the reaction that cools the system down. This is because increasing the temperature provides more energy to the reactants, shifting the equilibrium to favor the endothermic reaction that absorbs this excess heat.

Endothermic and Exothermic Reactions

The terms endothermic and exothermic describe the energy changes in a chemical reaction. Endothermic reactions absorb energy or heat from their surroundings, making the environment cooler. On the other hand, exothermic reactions release energy or heat, warming up their surroundings.

In the context of the methanol reaction:
\[\begin{equation} \mathrm{CO}(g) + 2 \mathrm{H}_2(g) + heat \rightleftarrows \mathrm{CH}_3\mathrm{OH}(g) \end{equation}\], the forward reaction is endothermic (absorbing heat), and the reverse reaction is exothermic (releasing heat). This understanding clarifies why the system shifts towards the reactants when the temperature is increased; it is a natural response to absorb excess thermal energy.

Temperature Effect on Reactions

The impact of temperature on chemical reactions is significant and predictable. As seen with the methanol synthesis, the equilibrium constant changes with temperature, reflecting the heat-dependency of the reaction. An increase in temperature causes molecules to move faster and collide more energetically, which can influence whether products or reactants are favored.

For endothermic reactions, such as the forward reaction in the synthesis of methanol, elevating the temperature shifts the equilibrium position to the right; the reverse is true for exothermic reactions. However, if the reaction is heated and the equilibrium constant decreases, this signifies that the favored direction is exothermic, since more of the products are being converted back to reactants to release heat and stabilize the temperature.