Introductory Chemistry: Mass, Moles, Percent Composition, and Atomic Ratios Practice

Q1. What is the mass of 90 apples if one dozen apples have a mass of 2.0 kg?

Background

Topic: Unit Conversions and Dimensional Analysis

This question tests your ability to use conversion factors to relate a count of objects (apples) to a mass, using the concept of a dozen as an intermediate unit.

Key Terms and Formulas

• Conversion factor: a ratio used to convert from one unit to another.

• 1 dozen = 12 apples

• 1 dozen apples = 2.0 kg

Step-by-Step Guidance

1. Start by identifying the known values: 90 apples, 1 dozen = 12 apples, 1 dozen apples = 2.0 kg.

2. Set up the conversion from apples to dozens:

   $\text{Number of dozens} = 90\ \text{apples} \times \frac{1\ \text{dozen}}{12\ \text{apples}}$

3. Convert dozens to kilograms using the mass per dozen:

   $\text{Mass (kg)} = (\text{Number of dozens}) \times \frac{2.0\ \text{kg}}{1\ \text{dozen}}$

4. Multiply the conversion factors together to set up the calculation:

   $90\ \text{apples} \times \frac{1\ \text{dozen}}{12\ \text{apples}} \times \frac{2.0\ \text{kg}}{1\ \text{dozen}}$

Try solving on your own before revealing the answer!

Final Answer: 15 kg

$90 \times \frac{1}{12} \times 2.0 = 15$ kg

This makes sense because 90 apples is 7.5 dozen, and each dozen is 2.0 kg, so $7.5 \times 2.0 = 15$ kg.

Q2. If 0.20 bushel is one dozen apples, and the mass of one dozen apples is 2.0 kg, what is the mass of 0.50 bushel?

Background

Topic: Multi-step Unit Conversions

This question tests your ability to convert between bushels, dozens, and mass using given relationships.

Key Terms and Formulas

• 0.20 bushel = 1 dozen apples

• 1 dozen apples = 2.0 kg

Step-by-Step Guidance

1. Identify the known values: 0.50 bushel, 0.20 bushel = 1 dozen apples, 1 dozen apples = 2.0 kg.

2. Set up the conversion from bushels to dozens:

   $0.50\ \text{bushel} \times \frac{1\ \text{dozen}}{0.20\ \text{bushel}}$

3. Convert dozens to kilograms:

   $\text{Mass (kg)} = (\text{Number of dozens}) \times \frac{2.0\ \text{kg}}{1\ \text{dozen}}$

4. Combine the conversion factors:

   $0.50\ \text{bushel} \times \frac{1\ \text{dozen}}{0.20\ \text{bushel}} \times \frac{2.0\ \text{kg}}{1\ \text{dozen}}$

Try solving on your own before revealing the answer!

Final Answer: 5.0 kg

$0.50 \div 0.20 = 2.5$ dozen; $2.5 \times 2.0 = 5.0$ kg.

This makes sense because 0.50 bushel is 2.5 times as much as 0.20 bushel, so the mass is 2.5 times 2.0 kg.

Q3. If an apple has eight seeds, and one apple has a mass of 0.2 kg, how many apple seeds are in 14 kg of apples?

Background

Topic: Multi-step Unit Conversions (Mass to Count)

This question tests your ability to convert from mass to number of objects, and then to a total count of a subcomponent (seeds).

Key Terms and Formulas

• 1 apple = 0.2 kg

• 1 apple = 8 seeds

Step-by-Step Guidance

1. Start with the total mass: 14 kg apples.

2. Convert mass to number of apples:

   $\text{Number of apples} = 14\ \text{kg} \times \frac{1\ \text{apple}}{0.2\ \text{kg}}$

3. Convert apples to seeds:

   $\text{Number of seeds} = (\text{Number of apples}) \times 8$

Try solving on your own before revealing the answer!

Final Answer: 560 seeds

$14 \div 0.2 = 70$ apples; $70 \times 8 = 560$ seeds.

This makes sense because each apple has 8 seeds, and 70 apples come from 14 kg.

Q4. A case of paper has a mass of 2000 g. A case of paper contains 10 reams of paper. One ream of paper is 500 sheets. What is the mass, in grams, of 50 sheets of paper?

Background

Topic: Multi-step Unit Conversions (Mass to Count)

This question tests your ability to use ratios and conversion factors to relate mass to a smaller count of items.

Key Terms and Formulas

• 1 case = 2000 g

• 1 case = 10 reams

• 1 ream = 500 sheets

Step-by-Step Guidance

1. Find the total number of sheets in a case:

   $\text{Total sheets} = 10\ \text{reams} \times 500\ \text{sheets/ream}$

2. Find the mass per sheet:

   $\text{Mass per sheet} = \frac{2000\ \text{g}}{\text{Total sheets}}$

3. Find the mass of 50 sheets:

   $\text{Mass of 50 sheets} = 50 \times (\text{mass per sheet})$

Try solving on your own before revealing the answer!

Final Answer: 20 g

There are 5000 sheets in a case, so each sheet is 0.4 g. $50 \times 0.4 = 20$ g.

This makes sense because 50 sheets is 1% of a case, and 1% of 2000 g is 20 g.

Q5. What is the molar mass of hydrazine (N2H4)?

Background

Topic: Molar Mass Calculation

This question tests your ability to calculate the molar mass of a compound by summing the atomic masses of its constituent elements.

Key Terms and Formulas

• Molar mass: the mass of one mole of a substance (g/mol)

• Atomic mass of N = 14.0 g/mol

• Atomic mass of H = 1.0 g/mol

Step-by-Step Guidance

1. Identify the number of each atom in the formula: N2H4 has 2 N and 4 H.

2. Multiply the number of each atom by its atomic mass:

   $2 \times 14.0\ \text{g} = 28.0\ \text{g N}$

   $4 \times 1.0\ \text{g} = 4.0\ \text{g H}$

3. Add the masses together to get the molar mass:

   $28.0\ \text{g} + 4.0\ \text{g}$

Try solving on your own before revealing the answer!

Final Answer: 32.0 g/mol

The sum of the atomic masses gives the molar mass of hydrazine.

Q6. Calculate the molar mass of calcium chloride (CaCl2).

Background

Topic: Molar Mass Calculation

This question tests your ability to sum atomic masses for a compound with more than two elements.

Key Terms and Formulas

• Atomic mass of Ca = 40.1 g/mol

• Atomic mass of Cl = 35.5 g/mol

Step-by-Step Guidance

1. Identify the number of each atom in CaCl2: 1 Ca, 2 Cl.

2. Multiply the number of each atom by its atomic mass:

   $1 \times 40.1\ \text{g} = 40.1\ \text{g Ca}$

   $2 \times 35.5\ \text{g} = 71.0\ \text{g Cl}$

3. Add the masses together to get the molar mass:

   $40.1\ \text{g} + 71.0\ \text{g}$

Try solving on your own before revealing the answer!

Final Answer: 111.1 g/mol

The sum of the atomic masses gives the molar mass of calcium chloride.

Q7. What is the mass, in grams, of 0.250 mol K2CO3?

Background

Topic: Moles to Mass Conversion

This question tests your ability to use the molar mass of a compound to convert from moles to grams.

Key Terms and Formulas

• Moles ($n$): amount of substance

• Molar mass ($M$): mass per mole (g/mol)

• Mass ($m$): $m = n \times M$

Step-by-Step Guidance

1. Find the molar mass of K2CO3:

   $2 \times 39.1\ \text{g (K)} + 12.0\ \text{g (C)} + 3 \times 16.0\ \text{g (O)}$

2. Add the masses to get the total molar mass.

3. Multiply the number of moles by the molar mass:

   $\text{Mass} = 0.250\ \text{mol} \times (\text{molar mass})$

Try solving on your own before revealing the answer!

Final Answer: 34.6 g

$0.250 \times 138.2 = 34.6$ g

This makes sense because 0.25 mol is a quarter of a mole, so the mass is a quarter of the molar mass.

Q8. How many moles are in 20.0 g of sulfur tetroxide (SO4)?

Background

Topic: Mass to Moles Conversion

This question tests your ability to use the molar mass of a compound to convert from grams to moles.

Key Terms and Formulas

• Moles ($n$): $n = \frac{\text{mass}}{\text{molar mass}}$

• Molar mass of SO4: $32.1\ \text{g (S)} + 4 \times 16.0\ \text{g (O)}$

Step-by-Step Guidance

1. Calculate the molar mass of SO4:

   $32.1 + 4 \times 16.0$

2. Divide the given mass by the molar mass:

   $n = \frac{20.0\ \text{g}}{\text{molar mass}}$

Try solving on your own before revealing the answer!

Final Answer: 0.200 mol

$n = 20.0 \div 100 = 0.200$ mol (using approximate molar mass of 100 g/mol).

This makes sense because 20 g is 1/5 of 100 g, so you have 0.2 mol.

Q9. A 10.0 g sample of a compound made of aluminum and selenium contains 8.0 g of selenium. What is the percent composition of this compound?

Background

Topic: Percent Composition by Mass

This question tests your ability to calculate the percent by mass of each element in a compound.

Key Terms and Formulas

• Percent by mass: $\% = \frac{\text{mass of element}}{\text{mass of compound}} \times 100\%$

Step-by-Step Guidance

1. Find the mass of aluminum: $10.0\ \text{g} - 8.0\ \text{g} = 2.0\ \text{g}$

2. Calculate percent selenium:

   $\%\ \text{Se} = \frac{8.0}{10.0} \times 100\%$

3. Calculate percent aluminum:

   $\%\ \text{Al} = \frac{2.0}{10.0} \times 100\%$

Try solving on your own before revealing the answer!

Final Answer: 80.0% Se, 20.0% Al

Most of the mass is selenium, so the percent is high for Se.

Q10. Zinc carbonate (ZnCO3) is used as a zinc supplement in animal feed. What is the percent composition of zinc carbonate?

Background

Topic: Percent Composition by Mass

This question tests your ability to calculate the percent by mass of each element in a compound using molar mass.

Key Terms and Formulas

• Molar mass of ZnCO3: $65.4\ \text{g (Zn)} + 12.0\ \text{g (C)} + 3 \times 16.0\ \text{g (O)}$

• Percent by mass: $\% = \frac{\text{mass of element in 1 mol}}{\text{molar mass}} \times 100\%$

Step-by-Step Guidance

1. Calculate the molar mass of ZnCO3:

   $65.4 + 12.0 + 48.0 = 125.4$ g/mol

2. Calculate percent Zn:

   $\%\ \text{Zn} = \frac{65.4}{125.4} \times 100\%$

3. Calculate percent C:

   $\%\ \text{C} = \frac{12.0}{125.4} \times 100\%$

4. Calculate percent O:

   $\%\ \text{O} = \frac{48.0}{125.4} \times 100\%$

Try solving on your own before revealing the answer!

Final Answer: 52.2% Zn, 9.6% C, 38.3% O

Check that the percentages add up to about 100%.

Q11. Which of these compounds has the largest percent by mass of nitrogen? (A) N2O (B) NO (C) NO4 (D) N2O3 (E) N2O4

Background

Topic: Percent Composition and Atomic Ratios

This question tests your ability to compare the percent by mass of nitrogen in different nitrogen oxides by considering the ratio of nitrogen to oxygen atoms.

Key Terms and Formulas

• Percent by mass: $\% = \frac{\text{mass of N in formula}}{\text{molar mass of compound}} \times 100\%$

• Atomic mass of N = 14.0 g/mol, O = 16.0 g/mol

Step-by-Step Guidance

1. For each compound, write the formula and count the number of N and O atoms.

2. Calculate the total mass of N and O in each compound.

3. Calculate the percent by mass of N for each compound:

   $\%\ \text{N} = \frac{\text{mass of N}}{\text{total mass}} \times 100\%$

4. Compare the values to determine which is largest.

Try solving on your own before revealing the answer!

Final Answer: N2O

N2O has the highest ratio of N to O, so it has the largest percent by mass of nitrogen.