Question

Cyclohexane, C6H12, undergoes a molecular rearrangement in the presence of AlCl3 to form methylcyclopentane, CH3C5H9, according to the equation:
C6H12 ⇌ CH3C5H9
If Kc = 0.143 at 25°C for this reaction, find the equilibrium concentrations of C6H12 and CH3C5H9 if the initial concentrations are 0.200 M and 0. 075 M, respectively.

Answer 1

Answer:

$[CH_3C_5H_9]=0.03441\ M$

$[C_6H_{12}]=0.24059\ M$

Explanation:

The given equilibrium reaction and the equilibrium concentrations are shown below as:-

$\begin{matrix}&C_6H_{12}&\rightleftharpoons &CH_3C_5H_9\\ At\ time, t = 0 &0.200&&0.075\\At\ time, t=t_{eq}&-x&&+x\\ ----------------&-----&-&-----\\Concentration\ at\ equilibrium:-&0.200-x&&0.075+x\end{matrix}$

The Kc of an equilibrium reaction measures relative amounts of the products and the reactants present during the equilibrium.

It is the ratio of the concentration of the products and the reactants each raised to their stoichiometric coefficients. The concentration of the liquid and the gaseous species does not change and thus is not written in the expression.

The expression for the Kc is:-

$K_c=\frac{[CH_3C_5H_9]}{[C_6H_{12}]}$

Given that:- Kc = 0.143

Thus, applying the values as:-

$0.143=\frac{0.075+x}{0.200-x}$

$0.143\left(0.2-x\right)=0.075+x$

$-0.143x=x+0.0464$

$x=-0.04059$

Thus,

$[CH_3C_5H_9]=0.075+x=0.075-0.04059=0.03441\ M$

$[C_6H_{12}]=0.200-x=0.200-(-0.04059)=0.24059\ M$