How Many Moles of BaCO3 Dissolve in Water Given Kc?

[Not a Wrench]

Homework Statement

Excess BaCO3 is placed in a container containing 5L of pure water. Given the following info:
BaCO3 (s) ↔ Ba²⁺ + CO₃ ^2- and Kc = 5.7E-6
how many moles of BaCO3 dissolve?

Homework Equations

Kc=(Ba²⁺ )(CO₃ ^2- ) = 5.7E-6

The Attempt at a Solution

solved for x to get .002387 moles/5L which is incorrect. Dividing by 5L gives me .000477 moles. The correct answer is .012 and I am unsure what I have done wrong. It seemed simple enough. Could someone tell me what to do?

 

[Borek]

0.002387 is not number of moles.

 

[Not a Wrench]

0.002387 is not number of moles.

I forgot to add my last step but I know. It's the moles per liter. If I divide by 5 it gives me .000477 moles which is also not correct.

 

[Borek]

.000477 moles

No, it is not moles. Check your units.

Randomly juggling numbers is NEVER a good approach to solving problems.

 

[Not a Wrench]

No, it is not moles. Check your units.

Randomly juggling numbers is NEVER a good approach to solving problems.

Then what is x supposed to be? I was under the impression that the number by which it BaCO3 decreases is equal to the x that each of the products increases by.

 

[Borek]

So you are solving for x not knowing what it is? That's randomly juggling numbers, I told you it doesn't work.

You have calculated something in your first post. What it was? Can you post your whole solution?

 

[Not a Wrench]

So you are solving for x not knowing what it is? That's randomly juggling numbers, I told you it doesn't work.

You have calculated something in your first post. What it was? Can you post your whole solution?

So you are solving for x not knowing what it is? That's randomly juggling numbers, I told you it doesn't work.

You have calculated something in your first post. What it was? Can you post your whole solution?

Yeah, all I did was calculate 5.7E-6 = x² and solved for x which got me to .002387. Isn't its units M/5L because the container contains 5L of water?

 

[Borek]

Isn't its units M/5L

No, that's not how units work. Units don't contain numbers (or, if anything, we assume all numbers to be equal to 1). Besides, typically by M we denote molar concentration (which has its own units, mol/L ← an important hint here!), not number of moles.

5.7E-6 = x²

What is x intended to mean in this equation?

 

[Not a Wrench]

No, that's not how units work. Units don't contain numbers (or, if anything, we assume all numbers to be equal to 1). Besides, typically by M we denote molar concentration (which has its own units, mol/L ← an important hint here!), not number of moles.
What is x intended to mean in this equation?

The Kc equation contains (Ba²⁺ )(CO3^2- ) and they both gain x per the ice chart so therefore Kc = x²

 

[Borek]

And what you mean by (Ba²⁺) (or (CO₃^2-))?

 

[Not a Wrench]

And what you mean by (Ba²⁺) (or (CO₃^2-))?

Those are the products in the equilibrium. But I figured it out, anyways. I was dividing by 5L of water when I should have been multiplying by 5L because I needed to eliminate that 5L in the denominator and get moles by itself!

 

[Borek]

Those are the products in the equilibrium.

These are CONCENTRATIONS. And concentration has units of mol/L. Per ONE liter, not per 5 liters.

When you divided by 5 L you got the result in mol/L² units - these don't make sense, but you have never checked so you were not able to spot the mistake.

 

[Not a Wrench]

These are CONCENTRATIONS. And concentration has units of mol/L. Per ONE liter, not per 5 liters.

When you divided by 5 L you got the result in mol/L² units - these don't make sense, but you have never checked so you were not able to spot the mistake.

I know, thank you for the hint.