Q: A student measures the pH of a solution as $$4.00 \pm 0.02. $$What is the relative uncertainty in the hydrogen ion concentration $$[H^+]$$?

Relative uncertainty in $$[H^+] is$$ $$2.303 \times \Delta pH$$

Question 1

A laboratory technician measures the mass of a sample as $$0.2222 \pm 0.0002 g $$and its molecular mass as $$214.0010 \pm 0.0009 g/$$mol. The sample is dissolved in $$50.00 \pm 0.05 mL of $$solution. What is the correct formula to calculate the relative uncertainty in the molarity ($$M) of $$the solution?

Accepted Answer

Combine the relative uncertainties using the square root of the sum of squares: $$	ext{Relative uncertainty in } M = \sqrt{\left(\frac{\Delta m}{m}\$$right)^2$$ + \left(\frac{\Delta MM}{MM}\$$right)^2$$ + \left(\frac{\Delta V}{V}\$$right)^2$$}$$

Question 2

Which statistical test should you use to determine if the means of two sets of measurements are significantly different, assuming their variances are equal?

Accepted Answer

t-test

Question 3

A student measures the pH of a solution as $$4.00 \pm 0.02. $$What is the relative uncertainty in the hydrogen ion concentration $$[H^+]$$?

Accepted Answer

Relative uncertainty in $$[H^+] is$$ $$2.303 	imes \Delta pH$$

Question 4

You are given two sets of measurements with standard deviations $$s_1 = 0.12$ and s_2$ = 0.08. $$Which formula should you use to compare their precision using the F-test?

Accepted Answer

$$F = \frac{s_1$^2}{s_2$^2}$$

Question 5

A pipet consistently delivers 0.5 mL more than intended. What type of error does this represent?

Accepted Answer

Systematic error

Question 6

If you reverse a chemical reaction, how does the equilibrium constant ($$K_{eq}) $$change?

Accepted Answer

It becomes the reciprocal of the original $$K_{eq}$$

Question 7

A set of measurements yields the following values: 8.1, 8.2, 8.3, 8.4, and 9.5. Which statistical test should you use to determine if 9.5 is an outlier?

Accepted Answer

Grubbs test

Question 8

Which formula correctly describes the calculation of the sample standard deviation ($$s) $$for a set of $$n$$ measurements $$x_i$$?

Accepted Answer

$$s = \sqrt{\frac{\sum (x_i - \bar{x})^2$}{n-1}}$$

Question 9

You are asked to combine uncertainties for the sum $$z = x + y. $$Which formula should you use for the absolute uncertainty in $$z$$?

Accepted Answer

$$\Delta z = \sqrt{(\Delta x)^2$ + (\Delta y)^2$}$$

Question 10

A solution contains $$1$$ ppb of a solute. What is the approximate mass of solute per liter in micrograms ($$\mug$$)?

Accepted Answer

$$1$$ $$\mug/L$$

Question 11

Which of the following best describes precision in analytical chemistry?

Accepted Answer

The repeatability or closeness of multiple measurements to each other

Question 12

A chemist calculates the mean and standard deviation of a dataset and suspects one value is an outlier. What is the correct formula for the Grubbs statistic ($$G$$)?

Accepted Answer

$$G = \frac{|x_{suspect} - \bar{x}|}{s}$$

Question 13

Which of the following is NOT a correct rule for propagating uncertainty?

Accepted Answer

For multiplication/division, combine absolute uncertainties directly

Question 14

A reagent is labeled as 99.9% pure, but the experimental uncertainty is 0.1345%. What should you do regarding the purity correction?

Accepted Answer

Ignore the purity correction if its effect is smaller than the experimental uncertainty

Question 15

Which of the following scenarios best illustrates random error?

Accepted Answer

Fluctuating chromatographic peak areas from run to run

Question 16

If you add two chemical reactions together, how do you determine the new equilibrium constant ($$K_{eq}$$)?

Accepted Answer

Multiply the equilibrium constants

Question 17

A student calculates the F-test value as $$F_{calc} = 2.5$$ and the critical value as $$F_{crit} = 3.0. $$What is the correct interpretation?

Accepted Answer

The standard deviations are not significantly different

Question 18

Which formula is used to convert pH to hydrogen ion concentration $$[H^+]$$?

Accepted Answer

$$[H^+] = 10$$^{-pH}$$

Question 19

Which of the following best describes accuracy in analytical chemistry?

Accepted Answer

How close a measurement is to the true value

Analytical Chemistry: Statistical Measures, Uncertainty, and Error Analysis

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