FUNDAMENTALS OF ANALYTICAL CHEMISTRY
CHE 311
PROBLEM SET II (due: end of 3rd week)
Hint: Microsoft Excel may be used for certain calculations. Table with t values is attached at the end.
1. The following results were obtained for the analysis of aspirin in aspirin tablets.
Determination % Aspirin
1 91.30
2 91.25
3 91.20
4 91.31
5 91.26
Calculate
a) The mean of the data set
b) The median of the data set
c) The absolute deviation from the mean of the 3rd determination
d) The absolute average deviation from the mean of the data set
e) The relative deviation from the mean of the 4th determination in parts per thousand (“‰”).
f) The relative average deviation from the mean of the data set in ‰.
2. A California chardonnay wine was analyzed for the alcohol content with the following results:
Determination % Alcohol (v/v)
1 9.21
2 9.15
3 9.16
4 9.18
Calculate
a) The mean of the data set
b) The median of the data set
c) The standard deviation
d) The confidence limits at the 90% confidence level
3. The following results were obtained for Dioxin in a sample of drinking water.
Determination Dioxin, ppb
1 54.1
2 55.5
3 63.8
4 54.4
5 55.8
6 57.9
1
Calculate
a) The mean of the data set
b) The median of the data set
c) The standard deviation
d) The confidence interval at the 90% confidence level
4. A sample of steel was analyzed for carbon with the following results:
Determination % Carbon
1 2.10
2 2.05
3 2.13
4 2.08
5 2.11
Calculate the following:
a) the mean of the set of results
b) the median of the set of results
c) the absolute deviation from the mean of the 3 rd determination
d) the relative deviation from the mean of the 4 th determination in ‰.
5. A National Institute of Science and Technology (NITS) standard known to contain 22.52%
chloride was analyzed by a gravimetric method to give the following results:
Determination % Cl-
1 22.46
2 22.53
3 22.51
4 22.48
Calculate the following:
a) the median of the set of results
b) the absolute error of the 3rd determination
c) the relative error of the set of results in ppm
d) the relative precision of the set of results in ‰.
6. The following results were obtained for the analysis of cholesterol in blood serum taken from a
patient as a part of their annual check-up.
Determination Cholesterol, mg/dL
1 120
2 125
3 119
4 137
5 118
6 126
7 124
2
Calculate the following:
a) the standard deviation of the set of results
b) the 90% confidence interval
7. A certain analytical balance has an error of ±0.2 mg. Calculate the minimum sample mass you would
have to weigh out such that the relative error of your weighing measurement would be a) not larger
than (“>≠”) 1%) , b) >≠ 3 ‰, c) >≠ 6 ppm, d) >≠ 4 ppb.
8. A 25 mL buret has a tolerance of ±0.03 mL. What volume of titrant must be delivered from the buret
for the relative error to be < 5‰?
9. The relative error in measuring a volume of 10.00 mL is 4‰. What is the absolute error in the
measurement?
N-1
3
Answers:
1. a) 91.26% aspirin
b) 91.26% aspirin
c) 0.06% aspirin
d) 0.03% aspirin [(sum |xi-xmean|)/n]
e) 0.55 (or 0.50) ‰ [(xi-xmean)/xmean×1000]
f) 0.35 ppt [sum(|(xi-xmean)/xmean|)×1000/n]
2. a) 9.18% alcohol
b) 9.17% alcohol
c) 0.0271% alcohol
d) 9.18 ± 0.032% alcohol
3. a) 56.9 ppb dioxin
b) 55.7 ppb dioxin
c) 3.6 ppb dioxin
d) 56.9 ±3.0 ppb dioxin
4. a) 2.09%
b) 2.10%
c) 0.04%
d) -4.78‰
5. a) 22.50%
b) -0.01%
c) [(mean-true)/true ×1e6] = -888.1 ppm
d) [(s/true)×1000 ] = 1.38 ‰
6. a) s = 6.47 mg/dL, b) = 124 ±4.74 mg/dL
7. a) 0.0200 g, b) 0.0666 g, c) 33.33 g, d) 5.000 ×104 g or 50.00 kg
8. ~6.00 mL
9. 0.04 mL
