* a1-4 The method described in Problem al-3 is to be used to analyze an ore that

Question

* a1-4 The method described in Problem al-3 is to be used to analyze an ore that contains about 43% copper. What minimum sample weight should be taken if the relative er- ror due to a 0.5-mg loss is to be smaller than (a) 0.1%2 (b) 0.5%2 (c) 0.8%? (d) 1.2%? a1-5 A certain instrumental technique has a standard deviation of 1.0%. How many repli- be 0.01%? cate measurements are necessary if the standard error of the mean is to *a1-6 A certain technique is known to have a mean of 0.500 and standard deviation of 1.84 × 10-3. It is also known that Gaussian statistics apply. How many replicate de- terminations are necessary if the standard error of the mean is not to exceed 0.100%? al-7 A constant solubility loss of approximately 1.8 mg is associated with a particular method for the determination of chromium in geological samples. A sample contain- ing approximately 18% Cr was analyzed by this method. Predict the relative error (in parts per thousand) in the results due to this systematic error if the sample taken for analysis weighed 0.400 g.

Explanation / Answer

a1-4)percent relative error =(absolute error/true value)*100

a) percent relative error =0.1%

absolute error=0.5 mg (loss)

So,true value=minimum sample weight =(100*absolute error/percent relative error)=100*0.5mg/0.1=500 mg=0.5g

b)percent relative error =0.5%

true value=(100*absolute error/percent relative error)=100*0.5mg/0.5=100 mg=0.1g

c) percent relative error =0.8%
true value=(100*absolute error/percent relative error)=100*0.5mg/0.8=62.5 mg=0.0625 g

d) c) percent relative error =1.2 %
true value=(100*absolute error/percent relative error)=100*0.5mg/1.2=41.7mg=0.0417 g

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