Determining the product of a reaction based on mean wt% and Standard Deviation

[x12179x]

I have no idea how to start this problem or what equations I would need, if any. Below is the problem, and after that, I include my failed attempts at this problem.

The problem:
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Students at Eastern Illinois University intended to prepare copper(II) carbonate by adding a solution of CuSO₄ * 5 H₂O to a solution of Na₂CO₃.

CuSO₄ * 5 H₂O(aq) + NaCO₃(aq) ----> CuCO₃(s) + Na₂SO₄(aq) + 5 H₂O(l)

After warming the mixture to 60 degree C, the gelantinous blue precipitate coagulated into an easily filterable pale green solid. The product was filtered, washed, and dried at 70 degree C. Copper in the product was measured by heating .4g of solid in a stream of methane at high temerpature to reduce the solid to pure Cu, which is weighed.

4 CuCO₃(s) + CH₄(g) --heat--> 4 Cu(s) + 5 CO₂(g) + 2 H₂O(l)

In 1995, 43 students found a mean value of 55.6 wt% Cu with a standard deviation of 2.7 wt%. In 1996, 39 students found 55.9 wt% with a standard deviation of 3.8 wt%. The instructor tried the experiment 9 times and measured 55.8% with a standard deviation of 0.5 wt%. Was the product of the reaction probably CuCO₃? Could it have been a hydrate, CuCO₃ * xH₂O?

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First since there are many different data sets, so I thought it was probably a comparison of t values for the 3 data sets. The equation is t= [ |x_mean1-x_mean2 | / s ]* sqrt(n₁n₂/n₁+n₂). and it seems like there was values to plug into each to them, but then I realized the question was not asking for a comparison of values, but to determine what the product was.

I looked through the sections in the textbook that we went over in class, but none of them expained how to do this or showed any similar examples. So can anyone help?

Even if you don't know the answer or aren't certain of how to solve this problem, can you at least explain how you might possibly sovle/start this problem yourselves? (it might give me ideas)

Thanks

 

[Gokul43201]

First answer this question, or give it a shot : If I had 100g of CuCO3, how much of this weight comes from Cu ?

 

[x12179x]

hmmm, I think I might know what I'm suppose to do now.


So I calculated 51.432g Cu in 100g CuCO3, which makes the wt%, 51.4%.

The I calulated it for CuCO3* x H2O and got 44.888g if x was 1, and less if it were more than 1. which makes the wt% no higher than 44.8% in that compound.

So I think my answer would be that the product is most likely CuCO3 and not CuCO3 * xH2O.

But when I calulated the confidence interval, none of those values fit in.

So is the answer neither?


But thanks, that was a lot of help...or guidance.

 

[Gokul43201]

Very good.

The significance of the very high t-value is that the probability of it being anhydrous CuCO3 is pretty low (in fact you can determine the probability assuming the distribution is a Gaussian). However, as you correctly said, the probability of it Being CuCO3.xH2O becomes even lower still. This is all that the question is really asking, and you have done everything it wanted, but if you want to get to the bottom of it all...

...you might want to know that the common form of copper carbonate (known also as cupric carbonate-hydroxide) is CuCO3.Cu(OH)2, which has a molecular weight of about 221 g/mol and the %Cu in it comes out to be roughly 57%, which is a lot closer to the determined values. In fact, if you consider the possibility of there being about 1% impurity (typically from Fe) in the reactants you will get very close to the measured values.