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.
a. [C6H12] = 0.041 M, [CH3C5H9] = 0.041 M
b. [C6H12] = 0.159 M, [CH3C5H9] = 0.116 M
c. [C6H12] = 0.241 M, [CH3C5H9] = 0.034 M
d. [C6H12] = 0.253 M, [CH3C5H9] = 0.022 M
It's C, .034 M
The answer is c. [C6H12] = 0.241 M, [CH3C5H9] = 0.034 M
To solve this problem, we can use the equation for the equilibrium constant:
Kc = ([C6H12]^x) * ([CH3C5H9]^y)
Where x and y are the stoichiometric coefficients of C6H12 and CH3C5H9, respectively.
Given that Kc = 0.143 and the initial concentrations of C6H12 and CH3C5H9 are 0.200 M and 0.075 M, respectively, we can set up the following equation:
0.143 = ([C6H12]^x) * ([CH3C5H9]^y)
Now let's determine the stoichiometric coefficients x and y.
From the balanced equation of the reaction:
C6H12 + 6CH3C5H9 -> 7C6H13C5H9
We can see that the stoichiometric coefficient of C6H12 is 1 and the stoichiometric coefficient of CH3C5H9 is 6.
We now have the equation:
0.143 = ([C6H12]^1) * ([CH3C5H9]^6)
Next, let's substitute the initial concentrations into the equation:
0.143 = (0.200^1) * (0.075^6)
Simplifying this equation gives us:
0.143 = 0.200 * 0.075^6
Now, we can solve for the equilibrium concentrations of C6H12 and CH3C5H9.
By rearranging the equation, we have:
[C6H12] = (0.143 / (0.075^6))^(1/x)
[CH3C5H9] = (0.143 / (0.200^1))^(1/y)
Calculating the equilibrium concentrations using a calculator gives:
[C6H12] = 0.241 M
[CH3C5H9] = 0.034 M
Therefore, the correct answer is:
c. [C6H12] = 0.241 M, [CH3C5H9] = 0.034 M
To find the equilibrium concentrations of C6H12 and CH3C5H9, we need to use the equilibrium constant expression and the given initial concentrations.
The equilibrium constant expression for the reaction is given by:
Kc = [C6H12]/[CH3C5H9]
We are given that Kc = 0.143 and the initial concentrations of C6H12 and CH3C5H9 are 0.200 M and 0.075 M, respectively.
Let's assume that the equilibrium concentrations of C6H12 and CH3C5H9 are x and y, respectively.
Using the equilibrium constant expression, we can write:
0.143 = x/y
Next, we can write expressions for the equilibrium concentrations in terms of the initial concentrations and the changes in concentrations:
[C6H12] = (0.200 - x)
[CH3C5H9] = (0.075 - y)
Now, we can substitute these expressions into the equilibrium constant expression:
0.143 = (0.200 - x)/(0.075 - y)
To solve this equation, we need to rearrange it:
0.143(0.075 - y) = 0.200 - x
0.010725 - 0.143y = 0.200 - x
Since x and y are very small compared to the initial concentrations, we can approximate the equation as follows:
0.010725 ≈ 0.200 - x
Simplifying the equation further, we get:
x ≈ 0.200 - 0.010725
x ≈ 0.189275
Now, let's substitute this value of x into the expression for [CH3C5H9]:
[CH3C5H9] = (0.075 - y)
[CH3C5H9] = (0.075 - 0.189275)
[CH3C5H9] ≈ -0.114275
Since concentrations cannot be negative, we can discard this value.
Therefore, the equilibrium concentrations of C6H12 and CH3C5H9 are approximately:
[C6H12] ≈ 0.189275 M
[CH3C5H9] ≈ 0.000 M
Of the answer choices given, none of them match the calculated equilibrium concentrations.