Problem 11 - Chemistry and Chemical Reactivity

Question

A mixture of \(\mathrm{CO}\) and \(\mathrm{Cl}_{2}\) is placed in a reaction flask: \([\mathrm{CO}]=0.0102 \mathrm{mol} / \mathrm{L}\) and \(\left[\mathrm{Cl}_{2}\right]=0.00609 \mathrm{mol} / \mathrm{L} .\) When the reaction $$ \mathrm{CO}(\mathrm{g})+\mathrm{Cl}_{2}(\mathrm{g}) \rightleftarrows \mathrm{COCl}_{2}(\mathrm{g}) $$ has come to equilibrium at \(600 \mathrm{K},\left[\mathrm{Cl}_{2}\right]=0.00301 \mathrm{mol} / \mathrm{L}\) (a) Calculate the concentrations of \(\mathrm{CO}\) and \(\mathrm{COCl}_{2}\) at equilibrium. (b) Calculate \(K\)

Step-by-Step Solution

Answer

(a) \([\mathrm{CO}] = 0.00712 \ \text{mol/L}\), \([\mathrm{COCl}_{2}] = 0.00308 \ \text{mol/L}\) (b) \(K \approx 1.41 \times 10^{2}\)

Step 1: Determine the Change in Concentration of Cl2

Initially, the concentration of \( \mathrm{Cl}_{2} \) was \( 0.00609 \ \text{mol/L} \), but at equilibrium, it's \( 0.00301 \ \text{mol/L} \). The change in concentration \( \Delta [\mathrm{Cl}_{2}] = 0.00609 - 0.00301 = 0.00308 \ \text{mol/L} \).

Step 2: Relate Changes to the Balanced Reaction

According to the balanced equation: \( \mathrm{CO} + \mathrm{Cl}_{2} \rightarrow \mathrm{COCl}_{2} \), the change in concentration of \( \mathrm{CO} \) will be equal to that of \( \mathrm{Cl}_{2} \), both will decrease by \( 0.00308 \ \text{mol/L} \). Thus, \([\mathrm{CO}] = 0.0102 - 0.00308 = 0.00712 \ \text{mol/L} \).Also, the \( \mathrm{COCl}_{2} \) concentration formed will equal this change, \([\mathrm{COCl}_{2}] = 0.00308 \ \text{mol/L} \).

Step 3: Calculate Equilibrium Constant K

At equilibrium, we have:- \([\mathrm{CO}] = 0.00712 \ \text{mol/L} \)- \([\mathrm{Cl}_{2}] = 0.00301 \ \text{mol/L} \)- \([\mathrm{COCl}_{2}] = 0.00308 \ \text{mol/L} \)The equilibrium expression is:\[ K = \frac{[\mathrm{COCl}_{2}]}{[\mathrm{CO}][\mathrm{Cl}_{2}]} \]Substitute the equilibrium concentrations:\[ K = \frac{0.00308}{0.00712 \times 0.00301} \approx 1.41 \times 10^{2} \]

Key Concepts

Chemical Equilibrium

Chemical equilibrium is a state in chemical reactions where the concentrations of reactants and products remain constant over time. It occurs because the rate of the forward reaction equals the rate of the reverse reaction. Even though reactions continue, they do so at an equal and unchanging rate, leading to no net change in the concentration of reactants and products.

In the given reaction:

• \[ \mathrm{CO}(\mathrm{g}) + \mathrm{Cl}_{2}(\mathrm{g}) \rightleftharpoons \mathrm{COCl}_{2}(\mathrm{g}) \]

The mixture reaches equilibrium when the rate at which \( \mathrm{CO} \) and \( \mathrm{Cl}_{2} \) combine to form \( \mathrm{COCl}_{2} \) is the same as the rate at which \( \mathrm{COCl}_{2} \) decomposes back into \( \mathrm{CO} \) and \( \mathrm{Cl}_{2} \).

Achieving equilibrium doesn't necessarily mean the concentrations of the reactants and products are equal, but they remain constant. This means that the reaction has reached a state where, for a given temperature and pressure, the ratio of concentrations for products over reactants stays steady.

Reaction Quotient

The reaction quotient \( Q \) is a measure of the relative amounts of products and reactants present during a reaction at any given point in time. It is calculated in the same way as the equilibrium constant \( K \), but using the concentrations at that particular moment.

The formula to determine the reaction quotient \( Q \) is:

• For the reaction \[ \mathrm{CO}(\mathrm{g}) + \mathrm{Cl}_{2}(\mathrm{g}) \rightleftharpoons \mathrm{COCl}_{2}(\mathrm{g}) \]
• \[ Q = \frac{[\mathrm{COCl}_{2}]}{[\mathrm{CO}][\mathrm{Cl}_{2}]} \]

If \( Q < K \), the forward reaction is favored, meaning the reaction will continue to produce more product until \( Q = K \). If \( Q > K \), the reverse reaction is favored, decreasing the concentration of products over time until equilibrium is achieved.

Calculating \( Q \) at different points in time can help predict the direction in which a reaction will proceed to reach equilibrium.

Concentration Changes

In any chemical equilibrium, concentration changes occur as the system shifts to achieve equilibrium. The given exercise helps illustrate how concentrations shift from initial values to their equilibrium values.

Understanding how concentrations change is essential for predicting reaction outcomes. For the reaction:

• \[ \mathrm{CO}(\mathrm{g}) + \mathrm{Cl}_{2}(\mathrm{g}) \rightleftharpoons \mathrm{COCl}_{2}(\mathrm{g}) \]
• The initial concentration of \( \mathrm{Cl}_{2} \) is \( 0.00609 \ \text{mol/L} \) and the equilibrium concentration is \( 0.00301 \ \text{mol/L} \).
• This shift indicates a decrease, which is also mirrored in the concentration of \( \mathrm{CO} \).

This change, equivalent for both \( \mathrm{CO} \) and \( \mathrm{Cl}_{2} \), defines how much \( \mathrm{COCl}_{2} \) is formed. Such calculations provide insights into how reaction components vary and help in determining equilibrium concentrations accurately by using stoichiometric relations and initial concentrations.

These changes, once understood, allow for the correct calculation of the equilibrium constant \( K \), which will quantitatively describe the position of equilibrium.