What is the final concentration of D at equilibrium if the initial concentrations are [A] = 1.00 M and [B] = 2.00 M ?
The reversible chemical reaction
A+B⇌C+D
has the following equilibrium constant:
Kc=[C][D][A][B]=1.8
The reversible chemical reaction
A+B⇌C+D
has the following equilibrium constant:
Kc=[C][D][A][B]=1.8
1 Answer
Explanation:
You know that this reaction
#"A " + " B " rightleftharpoons " C " + " D"#
consumes
Moreover, you know that the equilibrium constant that describes this equilibrium is equal to
#K_c = (["C"] * ["D"])/(["A"] * ["B"]) = 1.8#
Now, if you take
So you can say that the equilibrium concentrations of the four chemical species will be
#["A"] = (1.00 - x) quad "M"#
#["B"] = (2.00 - x) quad "M"#
#["C"] = x quad "M"#
#["D"] = x quad "M"#
This means that the expression of the equilibrium constant will take the form
#K_c = (x * x)/((1.00-x)(2.00-x))#
#1.8 = x^2/((1.00-x)(2.00-x))#
Rearrange to quadratic equation form to get
#0.2x^2 + 5.40 * x - 3.60 = 0#
This quadratic equation will produce two solutions, one positive and one negative. Since we've taken
#x = 0.651#
This means that the equilibrium concentration of
#["D"] = color(darkgreen)(ul(color(black)("0.651 M")))#
The answer is rounded to three sig figs.