How Many Moles of BaCO3 Dissolve in Water Given Kc?

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The discussion revolves around calculating the number of moles of BaCO3 that dissolve in water, given the equilibrium constant Kc of 5.7E-6. Participants highlight a misunderstanding regarding the calculation process, particularly in how to handle units and the relationship between concentration and moles. The correct approach involves recognizing that Kc represents concentrations in mol/L, not moles directly, and that the dissolution should be calculated per liter, not for the entire volume of water. The final realization is that the user mistakenly divided by the volume instead of multiplying, leading to incorrect results. Proper unit management is crucial for accurate calculations in equilibrium chemistry.
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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?
 
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0.002387 is not number of moles.
 
Borek said:
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.
 
Not a Wrench said:
.000477 moles

No, it is not moles. Check your units.

Randomly juggling numbers is NEVER a good approach to solving problems.
 
Borek said:
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.
 
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?
 
Borek said:
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?
Borek said:
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?
 
Not a Wrench said:
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.

Not a Wrench said:
5.7E-6 = x2

What is x intended to mean in this equation?
 
Borek said:
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+ )(CO32- ) and they both gain x per the ice chart so therefore Kc = x2
 
  • #10
And what you mean by (Ba2+) (or (CO32-))?
 
  • #11
Borek said:
And what you mean by (Ba2+) (or (CO32-))?
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!
 
  • #12
Not a Wrench said:
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.
 
  • #13
Borek said:
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.
 
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