Question

At \(35^{\circ} \mathrm{C}, K=1.6 \times 10^{-5}\) for the reaction $$2 \mathrm{NOCl}(g) \rightleftharpoons 2 \mathrm{NO}(g)+\mathrm{Cl}_{2}(g)$$.If 2.0 moles of \(\mathrm{NO}\) and 1.0 mole of \(\mathrm{Cl}_{2}\) are placed into a \(1.0-\mathrm{L}\) flask, calculate the equilibrium concentrations of all species.

Short answer

The equilibrium concentrations of NOCl, NO, and Cl₂ are 0.074 mol/L, 1.926 mol/L, and 0.963 mol/L, respectively.

Step-by-step solution

Write the balanced reaction equation

The balanced reaction equation is given as: \[2\mathrm{NOCl}(g) \rightleftharpoons 2 \mathrm{NO}(g)+\mathrm{Cl}_{2}(g)\]

Set up an ICE table

Using the given information, we can set up an ICE table to keep track of the concentrations: | | NOCl | NO | Cl₂ | |---------|-------|------|-------| | Initial | 0 | 2.0 | 1.0 | | Change | +2x | -2x | -x | | Equil. | 2x | 2-2x | 1-x | In which x stands for the change in concentration.

Write the equilibrium expression

The equilibrium constant K expression is: \[K = \frac{[\mathrm{NO}]^2[\mathrm{Cl}_{2}]}{[\mathrm{NOCl}]^2}\]

Substitute equilibrium concentrations into the expression

Substitute equilibrium concentrations from the ICE table into the equilibrium constant expression and the given K value: \[1.6 \times 10^{-5} = \frac{(2- 2x)^2(1-x)}{(2x)^2}\]

Solve for x

Solve for x: \[x = 0.037\]

Calculate the equilibrium concentrations

Substitute the value of x back into the equilibrium row of the ICE table and calculate the equilibrium concentrations of all species: - Equilibrium concentration of NOCl = 2x = 2(0.037) = 0.074 mol/L - Equilibrium concentration of NO = 2 - 2x = 2 - 2(0.037) = 1.926 mol/L - Equilibrium concentration of Cl₂ = 1 - x = 1 - 0.037 = 0.963 mol/L So, the equilibrium concentrations of NOCl, NO, and Cl₂ are 0.074 mol/L, 1.926 mol/L, and 0.963 mol/L, respectively.

Key concepts

Equilibrium Constant

The equilibrium constant, represented by the letter 'K', is a vital tool in understanding chemical equilibria.
It quantifies the ratio of the concentrations of products to reactants at equilibrium.
Each concentration is raised to the power of its respective coefficient in the balanced reaction equation.
For the given reaction,

• the equilibrium constant expression is \[K = \frac{[\mathrm{NO}]^2[\mathrm{Cl}_{2}]}{[\mathrm{NOCl}]^2}\]

The K value indicates the extent of the reaction; a very small K, like in this problem with \(K = 1.6 \times 10^{-5}\), suggests that the reactants are predominant at equilibrium.
This helps predict the direction in which a reaction needs to go to reach equilibrium.

ICE Table

An ICE table is a systematic way to calculate changes in concentrations of species in a chemical reaction.
"ICE" stands for Initial, Change, and Equilibrium.
In this exercise, it helps track the concentration changes from initial to equilibrium states.

• **Initial**: Enter the initial concentrations of reactants and products. If not provided, assume it’s zero for products that haven't formed yet.
• **Change**: Represent the change in concentration during the reaction by adding or subtracting variables (like \(x\)). Use stoichiometry to relate these changes based on the balanced equation.
• **Equilibrium**: Calculate the resulting concentrations by combining initial concentrations and changes. The ICE table, therefore, simplifies solving for equilibrium concentrations by visualizing the concentration shifts in each species throughout the reaction.

Chemical Equilibrium

Chemical equilibrium occurs when the rate of the forward reaction equals the rate of the backward reaction.
At this point, the concentrations of all reactants and products remain constant over time.
This doesn’t mean that the concentrations are equal, but that their ratios remain constant as per the equilibrium constant. When a system reaches equilibrium:

• The macroscopic properties, such as concentration, no longer change.
• The microscopic processes continue to occur, meaning both forward and reverse reactions take place at equal rates.

Understanding this concept helps us grasp why reactions don't always proceed to completion and how conditions can affect the position of equilibrium.

Reaction Equation

The balanced reaction equation provides a complete and accurate representation of a chemical reaction.
It specifies the reactants and products involved, alongside their stoichiometry.
This is critical for writing the equilibrium expression and setting up ICE tables.
In this exercise, the balanced equation is:

• \[2\mathrm{NOCl}(g) \rightleftharpoons 2 \mathrm{NO}(g)+\mathrm{Cl}_{2}(g)\]

This equation tells us:

• The number of moles of each substance participating in the reaction, which guides us in calculating changes during the process using the ICE table.
• The direction of the reaction, which can be predicted by comparing initial concentrations to those at equilibrium.

Understanding and correctly balancing the reaction equation is crucial for successful equilibrium calculations and predictions.