In: Chemistry
1) The reversible chemical reaction
A(aq)+B(aq)⇌C(aq)+D(aq)
has the following equilibrium constant:
K=[C][D][A][B]=5.2
a) Initially, only A and B are present, each at 2.00 mol L−1. What is the final concentration of A once equilibrium is reached?
b) What is the final concentration of D at equilibrium if the initial concentrations are [A] = 1.00 mol L−1 and [B] = 2.00 mol L−1 ?
a)
A + B ßà C + D
2 2 0 0
2-x 2-x x x
Kc = x^2 / (2-x)^2
5.2 = (x/(2-x))^2
x/(2-x) = sqrt (5.2)
x/(2-x) = 2.28
x = 4.56 – 2.28*x
3.28*x = 4.56
x = 1.39 M
[A] = 2-x = 2 – 1.39 = 0.61 M
Answer: 0.61 M
b)
A + B ßà C + D
1 2 0 0
1-x 2-x x x
Kc = x^2 / (2-x)(1-x)
5.2 = x^2 / (2-3x+x^2)
5.2*x^2 -15.6*x +10.4 = x^2
4.2*x^2 – 15.6*x + 10.4 = 0
solving above quadratic equation we get,
x = 2.84 and x=0.87
x can’t be 2.84 as it will make concentration of A and B negative
so,
x = 0.87 M
[D] = 0.87 M
Answer: 0.87 M