Please help me understand how to solve this: given: .02 M Cl2 initial; .10 M PCl
ID: 984945 • Letter: P
Question
Please help me understand how to solve this:
given: .02 M Cl2 initial; .10 M PCl5
PCl5 <---> PCl3 + Cl2
PCl5
PCl3
Cl2
I
.10
0
.02
C
-x
+x
+x
E
.1 – x
x
.02 + x
k= 5.0 x 10^(-2)
5.0 x 10^(-2) = (x) (.02 + x)/ (.1-x)
I dont know how to solve this equation but my professor got x^2+.070x - .005=0 and then were suppost to plug this into the quadratic formula getting x1 =.044m and x2= 0.114m.
I need help getting to the x^2+.070x - .005=0 part i don't know how to do the math... please show all steps!! thank you
PCl5
PCl3
Cl2
I
.10
0
.02
C
-x
+x
+x
E
.1 – x
x
.02 + x
Explanation / Answer
PCl5 <---> PCl3 + Cl2
K = Equilibrium concentration of products / Equilibrium concentration of reactants
From the given data,
K = [PCl3] [Cl2] / [PCl5]
5.0 x 10^(-2) = (x) (0.02 + x)/ (0.1-x)
0.05 = 0.02 x + x2 / (0.1-x)
(0.05 ) (0.1-x ) = 0.02 x + x2
0.005 - 0.05x = 0.02 x + x2
x2 + 0.02 x + 0.05 x - 0.005 = 0
x2 + 0.07 x - 0.005 = 0
On solving, we will get
x1 = 0.043 x2 = -0.114