Question

For the reaction \(\mathrm{H}_{2}+\mathrm{I}_{2} \rightleftharpoons 2 \mathrm{HI},\) consider two possibilities: (a) you add 0.5 mole of each reactant, allow the system to come to equilibrium, and then add \(1 \mathrm{mol} \mathrm{H}_{2},\) and allow the system to reach equilibrium again, or (b) you add \(1.5 \mathrm{mol} \mathrm{H}_{2}\) and \(0.5 \mathrm{mol} \mathrm{I}_{2}\) and allow the system to come to equilibrium. Will the final equilibrium mixture be different for the two procedures? Explain.

Short answer

The final equilibrium mixtures for both scenarios A and B will be the same, according to the Le Chatelier principle, which states that the equilibrium position is always the same under the same conditions and concentrations. Therefore, despite the different initial conditions and procedures, the final equilibrium mixtures will not be different.

Step-by-step solution

Scenario A: Step 1:Calculate initial concentration of reactants and products

In scenario A, initially 0.5 mol of H2 and 0.5 mol of I2 are added to the system. At the beginning of the reaction, there is no HI in the system. So, the initial concentrations are: - [H2] = 0.5 mol - [I2] = 0.5 mol - [HI] = 0 mol

Scenario A: Step 2: Determine the change in concentration at equilibrium

Let x moles of H2 and I2 react to form HI. The concentration changes are given by: - [H2] = 0.5 - x - [I2] = 0.5 - x - [HI] = 2x

Scenario A: Step 3: Add 1 mol H2 and reach equilibrium again

Now, 1 mol of H2 is added to the system. The new concentration of H2 will be: - [H2] = 0.5 - x + 1 Similarly, the new H2 concentration will affect the new equilibrium, and the new concentration changes can be represented by: - [H2] = 1.5 - x - y - [I2] = 0.5 - x + y - [HI] = 2x - 2y

Scenario B: Calculate initial concentration of reactants and products

In scenario B, initially 1.5 mol of H2 and 0.5 mol of I2 are added to the system. At the beginning of the reaction, there is no HI in the system. So, the initial concentrations are: - [H2] = 1.5 mol - [I2] = 0.5 mol - [HI] = 0 mol

Scenario B: Determine the change in concentration at equilibrium

Let z moles of H2 and I2 react to form HI. The concentration changes are given by: - [H2] = 1.5 - z - [I2] = 0.5 - z - [HI] = 2z

Compare the final equilibrium concentrations of both scenarios

Since we are not given a specific equilibrium constant, comparing the final concentrations directly is not possible. However, as the Le Chatelier principle states that the equilibrium position is always the same under the same conditions and concentrations, we can conclude that the final equilibrium mixtures will be the same for both procedures. So, the final equilibrium mixtures for both scenarios will be the same.

Key concepts

Le Chatelier's principle

Le Chatelier's principle provides a useful insight into understanding how systems at equilibrium respond to changes. It states that if a dynamic equilibrium is disturbed by changing the conditions, the position of equilibrium shifts to counteract the change. This helps restore balance. For instance, if you increase the concentration of a reactant, the system shifts to favor the formation of products, reducing the effect of the added substance. In the context of our reaction, adding more \(H_2\) will shift the equilibrium towards producing more \(HI\).
This principle applies by observing how the system attempts to minimize the effect of the changes imposed, whether they are changes in concentration, temperature, or pressure. By understanding this, chemists can predict how reversible reactions adjust and control the yields of products.

Reaction Equilibrium

In chemical reactions, equilibrium is the state where the forward reaction rate equals the backward reaction rate. At this point, the concentrations of the reactants and products remain constant over time. However, this does not mean the amounts are equal but that they are unchanging. Understanding reaction equilibrium is vital because it defines the state at which a reaction is stable.
In our reaction example with \(H_2\) and \(I_2\), when \(2 HI\) are in balance with their reactants, the equilibrium does not imply half of each is used up but that their ongoing formation and decomposition are steady. So, it’s crucial not only to note the concentration but also to understand the ongoing, dynamic processes that achieve a stable system. Even if you disrupt this equilibrium by adding more substances, the system will naturally progress toward restoring it.

Concentration Changes

Concentration changes in one part of a reactant or product can significantly influence the entire reaction system. In a closed system, altering the concentration of components will disturb equilibrium, prompting a shift.
Consider adding \(1 \, \text{mol} \, H_2\) in Scenario A after reaching equilibrium. This change affects the equilibrium by temporarily increasing reactant concentration, so the system shifts towards the right to balance back, creating more \(HI\).- Initially, \(([\mathrm{H}_2] = 0.5)\), adding more \(H_2\) increased concentration.- As a result, equilibrium responds by forming more \(HI\) until it settles back into a new state of dynamic balance.
The manipulation of concentrations, therefore, plays a crucial role in predicting the behavior and final output of reactions at equilibrium, allowing us to optimize and control chemical processes.

Equilibrium Constant

The equilibrium constant (K_eq) is a crucial concept representing the ratio of product concentrations to reactant concentrations at equilibrium. Each side of a balanced chemical equation is accounted for, with reactants in the denominator and products in the numerator.
The expression for \(K_eq\) in our system \(2HI \rightleftharpoons H_2 + I_2\) can be expressed as:\[K_{eq} = \frac{[\text{HI}]^2}{[\text{H}_2][\text{I}_2]}\] - Here, the square term arises because \(2 \, \text{mol} \, \text{HI}\) is produced from 1 mol of each reactant.
Though each scenario may differ in starting conditions, once equilibrium is achieved, the equilibrium constant stays unchanged for a given temperature. This constant allows chemists to predict the composition of the equilibrium mixture and how it alters with different reaction changes, similar to the scenarios discussed. It's a fixed numerical value indicating the equilibrium position of a given reaction under specified conditions.