Question 1

Which of the following best describes the purpose of the equation $$\mathrm{AM} = f_1M_1 + f_2M_2 + \ldots + f_nM_n$$?

Accepted Answer

To determine the average atomic mass of an element based on the masses and abundances of its isotopes.

Question 2

A sample of chlorine contains two isotopes: $$^{35}\mathrm{Cl} ($$mass = $$34.97\ \mathrm{amu}$$, abundance = $$75.77\%) $$and $$^{37}\mathrm{Cl} ($$mass = $$36.97\ \mathrm{amu}$$, abundance = $$24.23\%). $$What is the average atomic mass of chlorine? Use the formula $$\mathrm{AM} = f_1M_1 + f_2M_2.$$

Accepted Answer

$$35.45\ \mathrm{amu}$$

Question 3

If an element has three naturally occurring isotopes with the following data: $$f_1 = 0.50$, M_1$ = 10\ \mathrm{amu}$$; $$f_2 = 0.30$, M_2$ = 11\ \mathrm{amu}$$; $$f_3 = 0.20$, M_3$ = 12\ \mathrm{amu}$$, what is the average atomic mass?

Accepted Answer

$$10.7\ \mathrm{amu}$$

Question 4

In the formula $$\mathrm{AM} = f_1M_1 + f_2M_2 + \ldots + f_nM_n$$, what does $$f_n$$ represent?

Accepted Answer

The fractional abundance of the $$nth $$isotope.

Question 5

A sample of magnesium contains $$79.0\%$$ $$^{24}\mathrm{Mg} ($$mass = $$23.99\ \mathrm{amu}$$), $$10.0\%$$ $$^{25}\mathrm{Mg} ($$mass = $$24.99\ \mathrm{amu}$$), and $$11.0\%$$ $$^{26}\mathrm{Mg} ($$mass = $$25.98\ \mathrm{amu}). $$What is the average atomic mass of magnesium?

Accepted Answer

$$24.31\ \mathrm{amu}$$

Question 6

Why must the fractional abundances ($$f_1$$, $$f_2$$, \ldots, f_n$$) in the average atomic mass formula always add up to 1?

Accepted Answer

Because they represent the fraction of each isotope in a sample, and all fractions together must account for the whole sample.

Question 7

If an element has two isotopes, $$A$$ and $$B$$, with $$f_A = 0.60$$, $$M_A = 20\ \mathrm{amu}$$, and $$f_B = 0.40$$, $$M_B = 22\ \mathrm{amu}$$, what is the average atomic mass?

Accepted Answer

$$20.8\ \mathrm{amu}$$

Question 8

Which of the following statements is true regarding the calculation of average atomic mass?

Accepted Answer

The average atomic mass is a weighted average based on the relative abundances and masses of all isotopes.

Question 9

A student calculates the average atomic mass of an element with two isotopes as $$0.25 	imes 10\ \mathrm{amu} + 0.75 	imes 12\ \mathrm{amu} = 11.5\ \mathrm{amu}. $$What mistake, if any, did the student make?

Accepted Answer

No mistake; the calculation is correct.

Question 10

If the average atomic mass of boron is $$10.81\ \mathrm{amu}$$, and it has two isotopes, $$^{10}\mathrm{B} ($$mass = $$10.01\ \mathrm{amu}) $$and $$^{11}\mathrm{B} ($$mass = $$11.01\ \mathrm{amu}$$), which isotope is more abundant?

Accepted Answer

$$^{11}\mathrm{B}$$

CHEM 170 Exam 1 Study Guide: Foundations of Chemistry

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