Chemical Forums
Chemistry Forums for Students => High School Chemistry Forum => Topic started by: ch3mical on August 03, 2021, 12:04:35 PM

Hi,
I have attempted an answer to the question below. Please let me know if my reasoning is correct. Thanks.
Q) You have a 1L solution of barium chromate, where the concentration of chromate ions is 110nM. How many mols of barium chloride should be added in order to reduce the concentration of the chromate ions to 12nM?
My attempt
Equation for barium chromate in solution:
BaCrO_{4} ::equil:: Ba^{2+} + CrO_{4}^{2}
When we add barium chloride, the balanced equation will be:
Ba^{2+} + CrO_{4}^{2} + BaCl_{2} ::equil:: BaCrO_{4} + BaCl_{2}^{}
We are told that [CrO_{4}^{2}] = 110nM, and we want to reduce it to 12nM. We have 1L, so that means we want to go from 110 mols down to 12 mols (mols = M×volume). This is a difference of 98 mols. From the equations above, 1 mol of barium chloride eliminates 1 mol of chromate ions. Therefore the mols of barium chloride required to consume 98 mols of chromate ions are 98 mols of barium chloride. So, my answer is 98 mols of BaCl_{2}.
Are my steps of reasoning correct? I don't know what the correct answer is.

I doubt that 98 moles (20 kg) of BaCl_{2} can be dissolved in less than 1 liter of water.
But  does this problem does not need use of the solubility product ?

We are told that [CrO_{4}^{2}] = 110nM, and we want to reduce it to 12nM. We have 1L, so that means we want to go from 110 mols down to 12 mols (mols = M×volume).
Nope.
n in nM stands for nano, metric prefix used with units.
(and  as Orcio already suggested  this question is about solubility product)

Thank you both. Ah yes, I meant 98 nano mols.
Could you please show me how to apply the solubility product equation in this case?

Here's my thinking about how I would apply the solubility product.
K_{sp} of barium chromate = [Ba^{2+}] [CrO_{4}^{2}]
We are given that [CrO_{4}^{2}] = 11μM, therefore [Ba^{2+}] is also 11μM, and K_{sp}=121×10^{12}.
The question states that we add barium chloride in order to get a new [CrO_{4}^{2}] of 12nM. Given that we've calculated K_{sp}=121×10^{12}, we can substitute in the new [CrO_{4}^{2}], and solve for [Ba^{2+}] to get 1×10^{20}M. I have assumed that one mole of barium chloride eliminates one mole of the barium ions.
Thoughts?

The question states that we add barium chloride in order to get a new [CrO42] of 12nM. Given that we've calculated Ksp=121×1012, we can substitute in the new [CrO42], and solve for [Ba2+] to get 1×1020M. I have assumed that one mole of barium chloride eliminates one mole of the barium ions.
It does not "eliminate" anything. K_{sp} has the value 1,21 x 10^{10} and concentration of the CrO_{4}^{2} should be smaller than 12 x 10^{9} M, so concentration of the Ba^{2+} should be bigger than.... ?

It does not "eliminate" anything. K_{sp} has the value 1,21 x 10^{10} and concentration of the CrO_{4}^{2} should be smaller than 12 x 10^{9} M, so concentration of the Ba^{2+} should be bigger than.... ?
I think I see what you are saying. K_{sp} is a constant, so if the chromate ion concentration goes down, then the barium ion concentration must go up to K_{sp}/[CrO_{4}^{2}] = 10 mM. So, the required concentration of barium ions is this value. In my post below, I try to work back from this to the required moles of barium chloride...

Is the following approach correct?
We started off with 11uM of barium ions, which equated to 11μmol in our 1L solution.
Based on the working out above, we end up with 10mM of barium ions after adding the barium chloride. This means we now have 10mmols. The difference in mols after adding barium chloride is 10mmols  11μmols ≈ 9.99mmols. This represents the amount of barium chloride we needed to add, because 1 mol of barium chloride reacts with 1 mol of chromate ions. I am not sure if my answer is correct.

110 nM is 0,11 not 11 uM, but the rest is aprox. true (concentration of Ba^{2+} should be bigger than 10 mM)  of course if dissolving 2,08 g BaCl_{2} will not change volume of 1 liter solution.

110 nM is 0,11 not 11 uM, but the rest is aprox. true (concentration of Ba^{2+} should be bigger than 10 mM)  of course if dissolving 2,08 g BaCl_{2} will not change volume of 1 liter solution.
Thank you