Question

The industrial process for producing hydrogen gas involve reacting methane and steam at a high temperature. $$ \mathrm{CH}_{4}(g)+\mathrm{H}_{2} \mathrm{O}(g)+\text { heat } \rightleftarrows \mathrm{CO}(g)+3 \mathrm{H}_{2}(g) $$ Predict the direction of equilibrium shift for each of the following stresses: (a) increase \(\left[\mathrm{CH}_{4}\right]\) (b) decrease \(\left[\mathrm{H}_{2} \mathrm{O}\right]\) (c) increase [CO] (d) decrease \(\left[\mathrm{H}_{2}\right]\) (e) increase temperature (f) decrease temperature (g) increase volume (h) decrease volume (i) add \(\mathrm{Zn}\) dust (j) add Xe inert gas

Short answer

(a) Right, (b) Left, (c) Left, (d) Right, (e) Right, (f) Left, (g) Right, (h) Left, (i) No change, (j) No change.

Step-by-step solution

Analyzing Le Chatelier's Principle

Le Chatelier's principle states that if a stress is applied to a system at equilibrium, the system adjusts to counteract that stress and re-establish equilibrium. We will apply this principle to each scenario.

Increase in \( \left[\mathrm{CH}_{4}\right] \)

Increasing the concentration of \(\mathrm{CH}_{4}\) will shift the equilibrium to the right to consume the added \(\mathrm{CH}_{4}\) and produce more products.

Decrease in \( \left[\mathrm{H}_{2} \mathrm{O}\right] \)

Decreasing the concentration of \(\mathrm{H}_{2}\mathrm{O}\) will shift the equilibrium to the left to produce more reactants and increase \(\mathrm{H}_{2}\mathrm{O}\) levels.

Increase in [CO]

Increasing the concentration of \(\mathrm{CO}\) will shift the equilibrium to the left to reduce the excess \(\mathrm{CO}\) by forming more reactants.

Decrease in \( \left[\mathrm{H}_{2}\right] \)

Decreasing the concentration of \(\mathrm{H}_{2}\) will shift the equilibrium to the right, producing more \(\mathrm{H}_{2}\) to replace the lost hydrogen gas.

Increase in Temperature

The reaction is endothermic (heat is a reactant), so increasing the temperature will shift the equilibrium to the right to absorb the additional heat by producing more products.

Decrease in Temperature

Decreasing the temperature will shift the equilibrium to the left, as the reaction releases heat and will form more reactants to compensate for the removed heat.

Increase in Volume

Increasing the volume results in a decrease in pressure. The equilibrium will shift towards the side with more moles of gas, which is the right side (4 moles of gas), to increase pressure.

Decrease in Volume

Decreasing the volume increases the pressure. The equilibrium will shift towards the side with fewer moles of gas, which is the left side (2 moles of gas), to decrease pressure.

Addition of \(\mathrm{Zn}\) Dust

Adding \(\mathrm{Zn}\), a solid, does not affect the gaseous equilibrium because it does not change the concentration of the reacting gases.

Addition of Inert Gas (Xe)

Adding an inert gas like xenon at constant volume does not affect the equilibrium position because it does not change the partial pressures of the reacting gases.

Key concepts

Equilibrium Shift

In chemical reactions, equilibrium shift is an essential concept to understand how systems at equilibrium respond to changes. Le Chatelier's Principle provides insight into these adjustments. When a change is applied to a system at equilibrium, such as altering concentrations, temperature, or pressure, the system shifts in a direction that counteracts the change. This shift is aimed at maintaining a balance in the system.
For example:

• Increasing the concentration of a reactant like ext{CH}_{4} will shift equilibrium to the right, producing more products such as CO and ext{H}_{2}.
• Conversely, if the concentration of a product like CO is increased, the system will shift to the left to reduce CO levels by producing more reactants.

This ability to predict shifts helps in controlling and optimizing reactions, which is vital in industrial processes like hydrogen production.

Endothermic Reaction

An endothermic reaction is a process where heat is absorbed from the surroundings, which means heat acts as a reactant. A perfect example is the given industrial reaction ext{CH}_{4}(g)+ ext{H}_{2} ext{O}(g)+ ext{heat} ightleftarrows ext{CO}(g)+3 ext{H}_{2}(g).
In such reactions, adding heat will shift the equilibrium to the right, resulting in the formation of more products as the system absorbs additional heat.

• Conversely, decreasing the temperature causes the equilibrium to shift left, forming more reactants to release heat.
• This behavior reflects the need of endothermic reactions to "consume" heat to progress, which is crucial when manipulating chemical systems that require specific temperature control.

This knowledge allows chemists to adjust conditions like temperature to enhance product yield, critical in large-scale chemical manufacturing.

Gas Laws

Gas laws are fundamental when dealing with reactions involving gases, as they help predict changes in equilibrium when volume and pressure conditions vary. For the reaction involving gases: ext{CH}_{4}(g)+ ext{H}_{2} ext{O}(g) ightleftarrows ext{CO}(g)+3 ext{H}_{2}(g), understanding gas behavior is essential.

• When the system's volume increases, the pressure decreases. The equilibrium, therefore, shifts to the side with more moles of gas, which is the right side here (4 moles), to increase pressure.
• If the volume decreases, the pressure increases, causing the system to shift to the left, where there are fewer moles (2 moles), to reduce the pressure.

This interaction illustrates Boyle's Law and how pressure and volume changes influence equilibrium in reactions involving gases, crucial for predicting outcomes in processes like gas production. Understanding these principles is essential for reaction optimization and safety control in chemical processes.