Question

Question 9 (5 points) Cyclohexane, C6H12, undergoes a molecular rearrangement in the presence of a catalyst 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 CH3C5Hg if the initial concentrations are 0.200 M and 0.075 M, respectively. [C6H12] = 0.253 M, [CH3C5H9] = 0.022 M [C6H12] = 0.041 M, [CH3C5H9] = 0.041 M [C6H12] = 0.241 M, [CH3C5H9] = 0.034 M [C6H12] = 0.082 M, [CH3C5H9] = 0.062 M [C6H12] = 0.159 M, [CH3C5H9] = 0.116 M

Answer 1

We can solve given problem in following steps.

Step 1 : Calculation of Q _C

We have given reaction, C₆H₁₂ $\rightleftharpoons$ CH₃C₅H₉

Equilibrium constant for above reaction is K c= [ CH₃C₅H₉ ] / [ C₆H₁₂ ] = 0.143 at 25 ⁰ C

For above reaction, Q _C = [ CH₃C₅H₉ ] / [ C₆H₁₂ ]

Substituting given values in above equation,we get\

Q _C = 0.075 M/ 0.200 M= 0.375

Q _C > K c , hence reaction will proceed in backward direction ( to the reactant side ) to attain equilibrium.

Step 2 : Calculation of equilibrium concentrations of CH₃C₅H₉ and C₆H₁₂ .

Let's use ICE table.

Concentration ( M)	C6H12	$\rightleftharpoons$	CH3C5H9
I	0.200		0.075
C	+ X		-X
E	0.200 + X		0.075 - X

Substituting above vlaues in K c= [ CH₃C₅H₉ ] / [ C₆H₁₂ ] = 0.143, we get

0.075 - X / 0.200 + X = 0.143

0.075 - X = 0.143 ( 0.200 + X )

0.075 - X = 0.0286 + 0.143 X

0.075 - 0.0286 = 0.143 X + X

0.0464 = 1.143 X

X = 0.0464 /1.143

X = 0.04059 M

Equilibrium concentration of CH₃C₅H₉ = 0.075 - X = 0.075 - 0.04059 = 0.03441 M = 0.034 M

Equilibrium concentration of C₆H₁₂ = 0.200 + X = 0.200 + 0.04059 = 0.24059 M = 0.241 M

ANSWER : [ C₆H₁₂ ] = 0.241 M [ CH₃C₅H₉ ] = 0.034 M