Waste Water treatment plant problem

[ghostanime2001]

Homework Statement

Barium chloride is a toxic compound used in waste water treatment and many manufacturing processes. A 20 mL solution of 0.200 M Na₂SO₄ is added to a 10.0 mL water sample containing an unknown concentration of BaCl₂ that was concentrated by 100 fold after being taken from a waste water treatment plant. After filtration of the solution, 0.7800g of the insoluble BaSO_4(s) is obtained. Provide a balanced chemical equation and determine the concentration of the Ba²⁺ from the sample taken at the waste water treatment plant.

The Attempt at a Solution

BaCl_2(aq) + Na₂SO₄ $$\rightarrow$$ BaSO_4(s) + 2NaCl

Using dilution equation:
C₁V₁=C₂V₂
C₁(0.01)=(0.2)(0.02)
C₁=0.4M = [BaCl₂]

After Barium chloride is concentrated to a 100 fold which means the solution decreased volume. So 0.4M x 100 = 40M

BUT, this solution isn't re-reacted with sodium sulfate therefore the 100x concentrated part doesn't matter in the problem.

n_BaSO4 = 0.78g / 233.3896 g/mol = 0.00334 mol BaSO₄

[BaSO₄] = [Ba²⁺]

What I don't understand is why do I need to consider the 100x problem when i am given the mass of the precipitate and therefore just calculate how much barium ions I have ? The 0.78g is fixed because that's what the experimentalists got. If the concentration of barium chloride is changed to 40M and then used to calculate the amount of Barium sulfate what does 0.78 grams measured from filtration matter then?

 

[Borek]

1. Not 40M, recheck your thinking. Which solution has a higher concentration - initial, or concentrated one?

2. You are asked to calculate concentration in water sample BEFORE it was concentrated, that is, in a sample taken just from the waste water.

Trick is, in such water concentration of barium was rather low, and determination of low concentrations is often difficult, thus we start concentrating samples, to make determination easier.

 

[ghostanime2001]

1. I don't understand what you are saying here. Is it Na2SO4 ?

2. IF that's the case then I don't need to consider the 100x concentrated part. What do I do ?

 

[ghostanime2001]

[Ba²⁺] = 0.4M before it was concentrated

 

[ghostanime2001]

But wait the question asks to determine the concentration of Barium ions which means the only contributer of barium is barium chloride and the only way barium ion can be calculated is from Barium chloride. I know that the two solutions are mixed together to precipitate out Barium sulfate so its a dilution problem? Actually what I mean is 20 mL solution and 10 mL solution are coming together. So the total volume is 30 mL solution containing both compounds. therefore to calculate concentration of barium ions I need volume. I am given the mass and i determined the molar mass I just need volume and I think the only way I can get volume to calculate concentration is from 30 mL because the two solutions are mixed together and filtrated out to get Barium sulfate.

Does this kinda make sense. I know it sounds a little mixed up but please correct my way of thinking.

 

[ghostanime2001]

or is it 0.00334 mol BaSO₄ x 1 mol BaCl₂/1 mol BaSO₄ x 1 mol Ba²⁺ \ 0.01 L = 0.334M Ba²⁺

 

[Borek]

Seems like you are completely confused. 10 mL sample is the one AFTER concentration. The original volume was 100 times larger.

You know that 10 mL contained 0.00334 mole Ba²⁺ - so the same 0.00334 mole of Ba²⁺ was present in the original volume (100 times 10 mL).

 

[ghostanime2001]

Is that the answer then ?

 

[ghostanime2001]

So the concentration of barium ions before the 100x concentration was 3.34 x 10^-6 ?

 

[ghostanime2001]

IF you say:

in the original volume (100 times 10 mL).

That means 100 x 10 mL = 1000 mL = 1 L

Before 100x concentration:
C₁ = [Ba²⁺] = $$\frac{\mbox{3.34 x 10^{-3} mol}}{1 L}= 3.34 \mbox{ x } 10^{-3}M$$

After 100x concentration:
C₂ = [Ba²⁺] = $$\frac{\mbox{3.34 x 10^{-3} mol}}{0.01 L}= 0.334 M$$

Is this correct ?

 

[Borek]

Looks OK.

 

[ghostanime2001]

OK? How would you have done it differently ??

 

[ghostanime2001]

Is the question asking before 100x or after 100x ?