Statistics Problems from Physical Chemistry

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SUMMARY

The discussion focuses on calculating the zinc content and its uncertainty at a 95% confidence limit in a high-purity gold sample (%Au > 99.99%). The provided data consists of zinc measurements in mg Zn/kg Au: 15.38, 15.17, 15.33, 14.88, 14.71, 15.42, 15.60, and 15.22. Participants emphasize the importance of finding the sample mean and sample standard deviation, followed by using the t-distribution to establish a confidence interval. The molecular weight of gold is noted as 196.966569 g mol-1, which is relevant for conversions.

PREREQUISITES
  • Understanding of sample mean and sample standard deviation
  • Familiarity with the t-distribution for confidence intervals
  • Knowledge of converting measurements (e.g., mg Zn/kg Au)
  • Basic concepts of trace elemental analysis in chemistry
NEXT STEPS
  • Learn how to calculate sample mean and standard deviation using statistical software
  • Study the application of the t-distribution for confidence intervals
  • Explore methods for converting elemental measurements in analytical chemistry
  • Review trace elemental analysis techniques and their significance in high-purity materials
USEFUL FOR

Chemistry students, analytical chemists, and professionals involved in trace elemental analysis and quality control of high-purity materials.

Ki-nana18
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Homework Statement


The following data were obtained for trace elemental zinc in a particular sample of high purity (%Au> 99.99%). The results are given in mg Zn/ kg Au.

15.38, 15.17, 15.33, 14.88, 14.71, 15.42, 15.60, 15.22

Find the zinc content and the uncertainty at 95% confidence limit.

Homework Equations



Molecular weight of gold: 196.966569 g mol-1

The Attempt at a Solution


I found the average of all the values, then converted to mg of Zinc by multiplying the kg of Au. I'm not really sure on how to find the uncertainty at 95% confidence.
 
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Ki-nana18 said:

Homework Statement


The following data were obtained for trace elemental zinc in a particular sample of high purity (%Au> 99.99%). The results are given in mg Zn/ kg Au.

15.38, 15.17, 15.33, 14.88, 14.71, 15.42, 15.60, 15.22

Find the zinc content and the uncertainty at 95% confidence limit.

Homework Equations



Molecular weight of gold: 196.966569 g mol-1

The Attempt at a Solution


I found the average of all the values, then converted to mg of Zinc by multiplying the kg of Au. I'm not really sure on how to find the uncertainty at 95% confidence.

Find the sample mean and sample standard deviation of your data above, then use the t-distribution to determine a confidence interval.

If you have never seen this type of material before, or if your textbook or notes have not done it, the assignment question could be counted as "unfair": this type of material is not always easy to grasp, and it takes practice to understand it. On the other hand, if it is in your book or notes, why don't you just follow the method therein?

RGV
 
So multiplying by kg of Au was right?
 
Ki-nana18 said:
So multiplying by kg of Au was right?

It depends on what you want to measure. You could just take the original measurements, without any multiplication, and that would give you inferences about mg of Z per kg Au. If you want something else, do the conversion.

However, this has nothing at all to do with the question you were asked, which was about confidence intervals.

RGV