Intro to Chemistry Exam 2: Step-by-Step Study Guidance (Chapters 5–7)

Q1. How many O atoms are present in 1.04 mol of MgSO4?

Background

Topic: Mole Concept & Avogadro's Number

This question tests your ability to relate moles of a compound to the number of atoms of a specific element using Avogadro's number and the chemical formula.

Key Terms and Formulas

• Mole (mol): A unit representing $6.022 \times 10^{23}$ particles (Avogadro's number).

• Avogadro's Number: $6.022 \times 10^{23}$ particles/mol.

• MgSO4 contains 4 O atoms per formula unit.

Step-by-Step Guidance

1. Start by identifying how many O atoms are in one formula unit of MgSO4 (look at the subscript for O in the formula).

2. Multiply the number of moles of MgSO4 by the number of O atoms per formula unit to get moles of O atoms.

3. Convert moles of O atoms to number of O atoms using Avogadro's number: $\text{number of O atoms} = \text{moles of O atoms} \times 6.022 \times 10^{23}$.

Try solving on your own before revealing the answer!

Final Answer: 2.51 × 1024 O atoms

We multiply 1.04 mol MgSO4 × 4 O/mol × $6.022 \times 10^{23}$ to get the total number of O atoms.

Q2. How many molecules are present in 0.140 g of HCl?

Background

Topic: Mole Calculations, Avogadro's Number

This question tests your ability to convert mass to moles using molar mass, then to number of molecules using Avogadro's number.

Key Terms and Formulas

• Molar Mass of HCl: $1.008 + 35.45 = 36.46$ g/mol

• Avogadro's Number: $6.022 \times 10^{23}$ molecules/mol

Step-by-Step Guidance

1. Calculate the number of moles of HCl: $\text{moles} = \frac{0.140\ \text{g}}{36.46\ \text{g/mol}}$

2. Convert moles to molecules: $\text{molecules} = \text{moles} \times 6.022 \times 10^{23}$

Try solving on your own before revealing the answer!

Final Answer: 2.31 × 1021 molecules

First, find moles, then multiply by Avogadro's number to get the number of molecules.

Q3. What is the mass of 1.36 × 1022 molecules of HCl?

Background

Topic: Mole Calculations, Mass-Molecule Conversions

This question tests your ability to convert number of molecules to moles, then to mass using molar mass.

Key Terms and Formulas

• Avogadro's Number: $6.022 \times 10^{23}$ molecules/mol

• Molar Mass of HCl: $36.46$ g/mol

Step-by-Step Guidance

1. Convert molecules to moles: $\text{moles} = \frac{1.36 \times 10^{22}}{6.022 \times 10^{23}}$

2. Convert moles to mass: $\text{mass} = \text{moles} \times 36.46$ g/mol

Try solving on your own before revealing the answer!

Final Answer: 0.824 g

First, find moles from molecules, then multiply by the molar mass to get the mass in grams.

Q4. What is the molar mass of calcium sulfate?

Background

Topic: Molar Mass Calculation

This question tests your ability to calculate the molar mass of a compound by summing the atomic masses of all atoms in the formula.

Key Terms and Formulas

• CaSO4: 1 Ca, 1 S, 4 O

• Atomic masses: Ca = 40.08, S = 32.07, O = 16.00 (approximate values)

• Molar mass = sum of atomic masses in the formula

Step-by-Step Guidance

1. Multiply the number of each atom by its atomic mass: $1 \times 40.08$ (Ca), $1 \times 32.07$ (S), $4 \times 16.00$ (O)

2. Add the results to get the total molar mass: $40.08 + 32.07 + 64.00$

Try solving on your own before revealing the answer!

Final Answer: 136.14 g/mol

Adding the atomic masses gives the molar mass of calcium sulfate.

Q5. What is the percent by mass of carbon in carbon dioxide?

Background

Topic: Percent Composition by Mass

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

Key Terms and Formulas

• CO2: 1 C, 2 O

• Atomic masses: C = 12.01, O = 16.00

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

Step-by-Step Guidance

1. Calculate the molar mass of CO2: $12.01 + 2 \times 16.00$

2. Calculate the percent by mass of C: $\frac{12.01}{\text{molar mass of CO}_2} \times 100$

Try solving on your own before revealing the answer!

Final Answer: 27.28%

Carbon's mass divided by the total molar mass, times 100, gives the percent by mass.

Q6. What is the molecular formula of a compound with the empirical formula CH and molar mass of 26.04 g?

Background

Topic: Empirical and Molecular Formulas

This question tests your ability to determine the molecular formula from the empirical formula and the molar mass.

Key Terms and Formulas

• Empirical formula: simplest whole-number ratio of atoms

• Molecular formula: actual number of atoms in a molecule

• Find n: $n = \frac{\text{molar mass}}{\text{empirical formula mass}}$

Step-by-Step Guidance

1. Calculate the mass of the empirical formula CH: $12.01 + 1.008$

2. Divide the given molar mass by the empirical formula mass to find n.

3. Multiply the subscripts in CH by n to get the molecular formula.

Try solving on your own before revealing the answer!

Final Answer: C2H2

The empirical formula mass fits into the molar mass twice, so the molecular formula is C2H2.

Q35. What is the empirical formula of a substance that contains 3.09% hydrogen, 31.60% phosphorous, and 65.31% oxygen?

Background

Topic: Empirical Formula Determination

This question tests your ability to convert percent composition to an empirical formula.

Key Terms and Formulas

• Empirical formula: simplest whole-number ratio of atoms

• Convert % to grams (assume 100 g sample), then to moles

• Divide all mole values by the smallest to get ratios

Step-by-Step Guidance

1. Assume 100 g sample: 3.09 g H, 31.60 g P, 65.31 g O

2. Convert each to moles:

   • H: $\frac{3.09}{1.0079}$

   • P: $\frac{31.60}{30.974}$

   • O: $\frac{65.31}{15.999}$

3. Divide each mole value by the smallest to get the simplest ratio.

4. Round to nearest whole numbers to write the empirical formula.

Try solving on your own before revealing the answer!

Final Answer: H3PO4

The ratios simplify to 3:1:4 for H:P:O, so the empirical formula is H3PO4.

Q36. A substance is found to consist of 1.900 g of silver, 0.250 g of nitrogen, and 0.850 g of oxygen. What is the percent by mass of oxygen in the compound?

Background

Topic: Percent Composition by Mass

This question tests your ability to calculate the percent by mass of an element in a compound given the masses of all elements present.

Key Terms and Formulas

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

Step-by-Step Guidance

1. Calculate the total mass of the compound: $1.900 + 0.250 + 0.850$ g

2. Divide the mass of oxygen by the total mass, then multiply by 100 to get the percent by mass.

Try solving on your own before revealing the answer!

Final Answer: 28.3%

Oxygen's mass divided by the total mass, times 100, gives the percent by mass of oxygen.