Question

In the \(1980 \mathrm{~s}, \mathrm{CFC}-11\) was one of the most heavily produced chlorofluorocarbons. The last step in its formation is $$ \mathrm{CCl}_{4}(g)+\mathrm{HF}(g) \rightleftharpoons \mathrm{CFCl}_{3}(g)+\mathrm{HCl}(g) $$ If you start the reaction with equal concentrations of \(\mathrm{CCl}_{4}\) and \(\mathrm{HF}\), you obtain equal concentrations of \(\mathrm{CFCl}_{3}\) and \(\mathrm{HCl}\) at equilibrium. Are the final concentrations of \(\mathrm{CFCl}_{3}\) and \(\mathrm{HCl}\) equal if you start with unequal concentrations of \(\mathrm{CCl}_{4}\) and HF? Explain.

Short answer

No, when initial concentrations are unequal, final concentrations of \( \text{CFCl}_3 \) and \( \text{HCl} \) will generally not be equal.

Step-by-step solution

Write the equilibrium expression

For the reaction: \ \( \text{CCl}_4(g) + \text{HF}(g) \rightleftharpoons \text{CFCl}_3(g) + \text{HCl}(g) \), \ the equilibrium expression is: \ \[ K_c = \frac{[\text{CFCl}_3][\text{HCl}]}{[\text{CCl}_4][\text{HF}]} \]

Analyze given conditions

Initially, it is given that the concentrations of starting materials and products are equal at equilibrium when equal amounts of \( \text{CCl}_4 \) and \( \text{HF} \) are used. This tells us \( K_c = 1 \).

Change in initial conditions

Suppose the initial concentrations of \( \text{CCl}_4 \) and \( \text{HF} \) are different, let them be \( [\text{CCl}_4]_0 = a \) and \( [\text{HF}]_0 = b \).

Apply reaction stoichiometry

Let x be the amount of \( \text{CCl}_4 \) and \( \text{HF} \) that react: \ At equilibrium: \ \( [\text{CCl}_4]_e = a - x \) \ \( [\text{HF}]_e = b - x \) \ \( [\text{CFCl}_3]_e = x \) \ \( [\text{HCl}]_e = x \)

Set up the equilibrium expression

Substitute the equilibrium concentrations into the equilibrium expression: \ \[ K_c = \frac{x \times x}{(a - x)(b - x)} \]

Solve for x

Given \( K_c = 1 \), \ \[ 1 = \frac{x^2}{(a - x)(b - x)} \] \ Rearrange and solve for x to determine equilibrium concentrations.

Verify if final concentrations are equal

In general, x needs to satisfy both initial conditions and the equilibrium constant. Thus, if \( a eq b \), \( x \) may adjust such that at equilibrium, \( [\text{CFCl}_3]_e eq [\text{HCl}]_e \). The exact values depend on the specific amounts of \( a \) and \( b \) but the final concentrations are not necessarily equal.

Key concepts

equilibrium constant

The equilibrium constant (K_c) is a crucial concept in understanding chemical equilibria.
It represents the ratio of the concentrations of products to reactants at equilibrium, raised to the power of their respective coefficients in the balanced chemical equation.
For the given reaction: \[ \text{CCl}_4(\text{g}) + \text{HF}(\text{g}) \rightleftharpoons \text{CFCl}_3(\text{g}) + \text{HCl}(\text{g}) \] the equilibrium expression would be: \[ K_c = \frac{[\text{CFCl}_3][\text{HCl}]}{[\text{CCl}_4][\text{HF}]} \]
When the initial concentrations of \text{CCl}_4 and \text{HF} are equal, we find that K_c equals 1.
This means, the products and reactants are equally distributed at equilibrium under those conditions.
However, when we start with unequal amounts of reactants, K_c remains constant, but the equilibrium concentrations will depend on the initial amounts of the reactants and will not necessarily be equal.

reaction stoichiometry

Reaction stoichiometry involves the quantitative relationships between reactants and products in a chemical reaction.
It is based on the coefficients of each species in the balanced chemical equation.
For the formation of CFCl_3 from CCl_4 and HF, the balanced chemical reaction is: \[ \text{CCl}_4(\text{g}) + \text{HF}(\text{g}) \rightleftharpoons \text{CFCl}_3(\text{g}) + \text{HCl}(\text{g}) \] Each mole of CCl_4 reacts with one mole of HF to produce one mole of CFCl_3 and one mole of HCl.
At equilibrium, let x be the moles of each product formed and the moles of each reactant consumed.
The relationships are:

• [\text{CCl}_4]_{e} = initial concentration of CCl_4 - x
• [\text{HF}]_{e} = initial concentration of HF - x
• [\text{CFCl}_3]_{e} = x
• [\text{HCl}]_{e} = x

Therefore, changes in the initial concentrations will affect the final equilibrium concentrations.
Understanding stoichiometry helps predict how much of each substance remains or forms at equilibrium.

chlorofluorocarbons

Chlorofluorocarbons (CFCs) are compounds composed of chlorine, fluorine, and carbon, once commonly used as refrigerants and in aerosol propellants.
CFC-11, or trichlorofluoromethane (CFCl_3), was a widely produced CFC.
They are chemically stable and can remain in the atmosphere for a long time.
However, their stability also means they can drift into the stratosphere, where UV radiation breaks them down.
This releases chlorine atoms, which then deplete the ozone layer.
Understanding the equilibrium process in making CFC-11 is crucial since it involves the reaction: \[ \text{CCl}_4(\text{g}) + \text{HF}(\text{g}) \rightleftharpoons \text{CFCl}_3(\text{g}) + \text{HCl}(\text{g}) \] . The equilibrium concentrations of reactants and products are important for determining the manufacturing efficiency and environmental impact.
Reducing the production of CFCs has been essential in efforts to protect the ozone layer.

equilibrium concentrations

Equilibrium concentrations are the amounts of reactants and products present once the reaction has reached a state of balance.
This occurs when the rate of the forward reaction equals the rate of the reverse reaction.
In our example reaction: \[ \text{CCl}_4(\text{g}) + \text{HF}(\text{g}) \rightleftharpoons \text{CFCl}_3(\text{g}) + \text{HCl}(\text{g}) \] , starting with equal concentrations of CCl_4 and HF results in equal equilibrium concentrations of CFCl_3 and HCl.
But what if the starting concentrations are different?

• Let initial concentrations be a for CCl_4 and b for HF.
• At equilibrium: [\text{CCl}_4]_{e} = a - x
• [\text{HF}]_{e} = b - x
• [\text{CFCl}_3]_{e} = x
• [\text{HCl}]_{e} = x

With K_c = 1, we have \[ 1 = \frac{x^2}{(a - x)(b - x)} \] .
This equation shows that x adjusts based on a and b, leading to equilibrium concentrations that are not necessarily equal unless a = b.
By understanding how initial amounts affect equilibrium, we can predict the product yields better.