An aqueous solution is made 1.000 M in AgNO3 and 1.000 M in Fe(NO3)2 and allowed to come to equilibrium. What are the concentrations of the ions present when equilibrium is established

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This is an incomplete question, here is a complete question.

An aqueous solution is made 1.000 M in AgNO₃ and 1.000 M in Fe(NO₃)₂ and allowed to come to equilibrium. What are the concentrations of the ions present when equilibrium is established.

[tex]Ag^+(aq)+Fe^{2+}(aq)\rightleftharpoons Ag(s)+Fe^{3+}(aq)[/tex]; K = 2.89

Answer : The concentration of [tex]Fe^{3+}[/tex], [tex]Fe^{2+}[/tex] and [tex]Ag^{+}[/tex] is, 0.565 M, 0.435 M and 0.435 M respectively.

Explanation :

The balanced chemical reaction is:

                      [tex]Ag^+(aq)+Fe^{2+}(aq)\rightleftharpoons Ag(s)+Fe^{3+}(aq)[/tex]

Initial:             1.000      1.000                0        0

At eqllm:       (1.000-x)   (1.000-x)           x         x

The equilibrium expression is:

[tex]K=\frac{[Fe^{3+}]}{[Ag^{+}][Fe^{2+}]}[/tex]

Now put all the given values in this expression, we get:

[tex]2.98=\frac{(x)}{(1.000-x)\times (1.000-x)}[/tex]

x = 0.565 M and x = 1.771 M

We are neglecting value of x = 1.771 because equilibrium concentration can not be more than initial concentration.

Thus, the value of x = 0.565 M

The concentration of [tex]Fe^{3+}[/tex] = x = 0.565 M

The concentration of [tex]Fe^{2+}[/tex] = (1.000-x) = (1.000-0.565) = 0.435 M

The concentration of [tex]Ag^{+}[/tex] = (1.000-x) = (1.000-0.565) = 0.435 M

The concentration of [tex]Fe^{3+},Fe^{2+} \text{ and } Ag^+[/tex] is 0.565 M, 0.435 M and 0.435 M respectively.

Balanced chemical reaction:

[tex]Ag^++Fe^{2+}---- > Ag+Fe^{3+}[/tex]

Initial:                          1.000      1.000                0        0

At equilibrium:       (1.000-x)   (1.000-x)           x         x

The equilibrium expression is:

[tex]K=\frac{[Fe^{3+}]}{[Ag^+][Fe^{2+}]}}[/tex]

On substituting the values:

2.98 = (x) / (1.000-x) (1.000-x)

x = 0.565 M and x = 1.771 M

We are neglecting value of x = 1.771

Thus, the value of x = 0.565 M

The concentration of [tex]Fe^{3+}[/tex] = x = 0.565 M

The concentration of [tex]Fe^{2+}[/tex] = (1.000-x) = (1.000-0.565) = 0.435 M

The concentration of  [tex]Ag^+[/tex]= (1.000-x) = (1.000-0.565) = 0.435 M

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This is an incomplete question, here is a complete question.

An aqueous solution is made 1.000 M in AgNO₃ and 1.000 M in Fe(NO₃)₂ and allowed to come to equilibrium. What are the concentrations of the ions present when equilibrium is established.

[tex]Ag^++Fe^{2+}---- > Ag+Fe^{3+}[/tex]; K = 2.89