Cyclohexane, C6H12, a hydrocarbon, can isomerize or change into methylcyclopentane, a compound of the same formula (C5H9CH3) but with a different molecular structure.
The equilibrium constant is 0.12 at 25°C. If you had originally placed 0.036 mol of cyclohexane in a 1.0 L flask, what would be the concentrations of cyclohexane and methylcyclopentane when equilibrium is established?
For [C6H12]?
For [C5H9CH3]?
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To determine the concentrations of cyclohexane ([C6H12]) and methylcyclopentane ([C5H9CH3]) at equilibrium, we can use the equilibrium constant (K) and the given initial moles of cyclohexane (C6H12).
The balanced equation for the isomerization reaction is:
C6H12 (cyclohexane) ⇌ C5H9CH3 (methylcyclopentane)
The equation for the equilibrium constant expression is:
K = [C5H9CH3] / [C6H12]
Given:
Initial moles of cyclohexane (C6H12) = 0.036 mol
Volume of the flask = 1.0 L
Equilibrium constant (K) = 0.12
To find the concentrations of [C6H12] and [C5H9CH3], we need to convert the moles to concentrations using the volume of the flask.
Concentration is calculated using the formula:
Concentration (C) = Moles (n) / Volume (V)
Concentration of cyclohexane ([C6H12]):
[C6H12] = (moles of cyclohexane at equilibrium) / (volume of the flask)
[C6H12] = (moles of cyclohexane at equilibrium) / 1.0 L
From the given information, we know that [C6H12] = 0.036 mol / 1.0 L = 0.036 M
Now, let's calculate the concentration of methylcyclopentane ([C5H9CH3]) using the equilibrium constant.
[C5H9CH3] = (K * [C6H12]) / (1.0 L)
[C5H9CH3] = (0.12 * 0.036 M) / 1.0 L
[C5H9CH3] = 0.00432 M
Therefore, at equilibrium, the concentration of cyclohexane ([C6H12]) would be 0.036 M, and the concentration of methylcyclopentane ([C5H9CH3]) would be 0.00432 M.
To determine the concentrations of cyclohexane ([C6H12]) and methylcyclopentane ([C5H9CH3]) when the equilibrium is established, we need to use the information given about the equilibrium constant (K) and the initial amount of cyclohexane present.
The equilibrium constant expression for the reaction is:
K = [C5H9CH3] / [C6H12]
where [C5H9CH3] represents the concentration of methylcyclopentane and [C6H12] represents the concentration of cyclohexane.
Given that the equilibrium constant (K) is 0.12, and the initial amount of cyclohexane is 0.036 mol in a 1.0 L flask, we can determine the concentration of cyclohexane ([C6H12]) when equilibrium is reached.
The equation of the reaction is:
C6H12 ⇌ C5H9CH3
At equilibrium, let's assume the concentration of cyclohexane is x (mol/L) and the concentration of methylcyclopentane is y (mol/L).
Therefore, at equilibrium, the equilibrium constant expression becomes:
0.12 = y / x
To solve for y (the concentration of methylcyclopentane), we can rearrange the equation as:
y = 0.12x
Since the initial amount of cyclohexane is 0.036 mol in a 1.0 L flask, the initial concentration of cyclohexane is:
[C6H12]initial = 0.036 mol / 1.0 L = 0.036 mol/L
Now, we can substitute the initial concentration of cyclohexane ([C6H12]initial) into the equation to find the concentration of methylcyclopentane ([C5H9CH3]):
y = 0.12 * 0.036
y = 0.00432 mol/L
So, the concentration of methylcyclopentane ([C5H9CH3]) when equilibrium is established is 0.00432 mol/L.
To summarize:
- The concentration of cyclohexane ([C6H12]) when equilibrium is established is 0.036 mol/L.
- The concentration of methylcyclopentane ([C5H9CH3]) when equilibrium is established is 0.00432 mol/L.
Is this Kc or Kp = 0.12? I will assume it is Kc.
What is the reaction for K. I will assume it is
cyclohexane ==> methyl cyclopentane
K = 0.12 = (mcyp)/(cyh)
Set up an ICE chart.
...........mcyh ==> mcyp
initial....0.036....0
change.....-x.......x
equil.....0.036-x...x
Substitute the equilibrium values into the Kc expression and solve for x.