Chemical equilibrium concentrations

[cj2222]

I have a problem in which It asks to find the equilibrium concentrations but it only give the value of the equilibrium constant and the chemical equation. Is this even possible to solve or does it not have enough information?

Here is the problem

Determine the equilibrium concentrations for the reaction below. K = 2.6 x 10^-6.

Mg²⁺ + 2OH^- <====> Mg(OH^-) (solid)

 

[Borek]

Mg(OH^-) or Mg(OH)₂?

Write expression for the equilibrium constant. Is there any dependence between concentrations of the ions produced when solid dissolves?

 

[cj2222]

Can you use 1 as the equilibrium concentration of Mg(OH)₂ and use this on the ICE table to find the other equilibrium concentrations or would this give you the wrong answer?

because k = 1/[Mg²⁺][OH^-]

or would the answer be

1/(x)(2x)^2 = 2.6 x 10^-6

where x = the equilibrium concentration of Mg2+

 

[Borek]

1 is OK, but not as a concentration - magnesium hydroxide is a solid, so its activity is assumed to be 1. There is no need for ICE table - as long as there is solid present, its activity is 1. Just 1.

Your k is wrong - please write balanced reaction of magnesium dissolution first, then use it to construct reaction quotient.

 

[cj2222]

Mg²⁺ + 2OH^- <===> Mg(OH)₂k = 1/[Mg²⁺][OH^-]²

The concentrations of OH^- is going to be 2 times the concentration of Mg²⁺

so 2.6 x 10^-6 = 1/(x)(2x)²so x = 45.81

the concentration of Mg²⁺ is 45.81

the concentration of OH^- is 91.62

Is this correct or not because I can't think of any other way to do it?

 

[Borek]

You are on the right track, but numbers you get are absurd (BTW, you should list units in your answer).

IMHO that's because your initial reaction equation and value given for k are not consistent with chemical reality, which is probably not your fault.

 

[cj2222]

yeah, the reaction is supposed to be reversed, k is correct.

The reaction is supposed to be


Mg(OH)₂ <===> Mg²⁺ + 2OH^-


which would give much smaller and more reasonable concentrations.

 

[Borek]

My sources give pK_sp for Mg(OH)₂ as something between 10 and 11, which means k should be around 10^-10 or 10^-11. 10^-6 looks way too large.