Chemical Equilibrium

W+X⇌Y+Z
Initial concentrations:
W starts at 2x,X starts at x, and both Y and Z start at 0 .
At equilibrium:
Let the amount of Y and Z formed be y. So, at equilibrium:
‌W=2x−y
‌X=x−y
‌Y=y
‌Z=y
Relationship between Y and X at equilibrium:
At equilibrium, the amount of Y is four times the amount of X . This gives us:
[Y]eq=4[X]eq
So, y=4(x−y)
Solve for y :
y=4x−4y
y+4y=4x
5y=4x
y=‌

4

5

x
Write Kc expression and substitute values:
The equilibrium constant is:
Kc=‌

[Y][Z]

[W][X]

Plug in the equilibrium values:
Kc=‌

( 4 5 x)( 4 5 x)

(2x−‌ 4 5 x)(x−‌ 4 5 x)

Simplify:
Numerator: (‌

4

5

x)2=‌

16

25

x2
Denominator:
‌2x−‌

4

5

x=‌

10x−4x

5

=‌

6x

5

‌x−‌

4

5

x=‌

5x−4x

5

=‌

x

5

So denominator: ‌

6x

5

⋅‌

x

5

=‌

6x2

25

Therefore, Kc=‌

16x2∕25

6x2∕25

=‌

16

6

=2.666