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### Topic: Determining the product of a reaction based on mean wt% and Standard Deviation  (Read 5296 times)

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#### x12179x

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##### Determining the product of a reaction based on mean wt% and Standard Deviation
« on: February 11, 2006, 05:33:56 PM »
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= [ |xmean1-xmean2 | / 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
« Last Edit: February 11, 2006, 05:35:44 PM by x12179x »

#### Borek

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##### Re:Determining the product of a reaction based on mean wt% and Standard Deviatio
« Reply #1 on: February 11, 2006, 06:36:45 PM »
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)

Instead of looking for correct statistical approach to the problem, I would go the shortest route first. Note that in all three cases average was almost identical. Instructor results (±0.5%) are precise enough to check what value of x can be expected. If x=0 salt was not hydrate, if x>0 - it was a hydrate.

There is more to this question (at least two layers more) but I am not going to spoil your fan explaining everything before you will do your calculations

I must admit I have no idea why the final result is such as it is.
ChemBuddy chemical calculators - stoichiometry, pH, concentration, buffer preparation, titrations.info, pH-meter.info

#### x12179x

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##### Re:Determining the product of a reaction based on mean wt% and Standard Deviatio
« Reply #2 on: February 12, 2006, 01:14:47 AM »
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.

But thanks, that was a lot of help....or guidance.
« Last Edit: February 12, 2006, 01:44:31 AM by x12179x »

#### Borek

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##### Re:Determining the product of a reaction based on mean wt% and Standard Deviatio
« Reply #3 on: February 12, 2006, 05:28:23 AM »
So I think my answer would be that the product is most likely CuCO3 and not CuCO3 * xH2O.

OK

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