Questions: Molar Mass Calculations and Mole Conversions

Question 1

A student calculates the number of grams in 2.00 mol of H₂O by computing: 2.00 × (18.02 mol/g). What error has the student made?

• A. Used the wrong molar mass for water — it should be 16.00 g/mol
• B. Inverted the conversion factor — it should be 18.02 g/mol, multiplied as 2.00 mol × (18.02 g/mol)
• C. Failed to multiply by Avogadro's number before converting to grams
• D. Should have divided by 2 to account for the two hydrogen atoms

Answer: (B)

The molar mass conversion factor is 18.02 g/mol — grams per mole. To go from moles to grams, you multiply: 2.00 mol × (18.02 g/mol) = 36.04 g. The student flipped it to mol/g, which gives units of mol²/g — dimensionally nonsensical. Dimensional analysis catches this immediately: the 'mol' units don't cancel when the factor is inverted. This is exactly why tracking units through every calculation is so valuable. The answer should be 36.04 g, not a tiny fraction.

Question 2

How many molecules of glucose (C₆H₁₂O₆, molar mass 180.16 g/mol) are contained in 18.016 g of glucose?

• A. 6.022 × 10²³ molecules — one full mole
• B. 1.801 × 10²⁴ molecules
• C. 6.022 × 10²² molecules — one-tenth of a mole
• D. 3.011 × 10²³ molecules — half a mole

Answer: (C)

First convert grams to moles: 18.016 g ÷ 180.16 g/mol = 0.1000 mol. Then convert moles to molecules: 0.1000 mol × 6.022 × 10²³ molecules/mol = 6.022 × 10²² molecules. The most common error is treating 18.016 g as approximately 18.02 g/mol (the molar mass of water) and concluding there is 1 mole, giving 6.022 × 10²³. This confuses two different substances. Molar mass must match the specific compound being converted.

Question 3

The molar mass of a compound can be calculated by adding the atomic masses of the elements present, without regard to how many atoms of each element are in the formula.

• T. True
• F. False

Answer: False

The number of atoms of each element in the formula is critical. For water (H₂O), the molar mass is 2(1.008) + 1(16.00) = 18.02 g/mol — not simply 1.008 + 16.00 = 17.008 g/mol. For glucose (C₆H₁₂O₆), you must multiply each atomic mass by the subscript: 6(12.01) + 12(1.008) + 6(16.00) = 180.16 g/mol. Ignoring subscripts is one of the most common errors in molar mass calculations and leads to systematically wrong answers in every stoichiometry problem that follows.

Question 4

The numerical value of an element's atomic mass in atomic mass units (amu per atom) equals the numerical value of its molar mass in grams per mole (g per mole of atoms).

• T. True
• F. False

Answer: True

This equivalence is built into the definition of the mole. Carbon has an atomic mass of 12.01 amu per atom, and one mole of carbon atoms has a mass of 12.01 grams. The numbers are the same; only the scale changes — from individual atoms to 6.022 × 10²³ atoms. This is not a coincidence but a design feature: the mole was defined precisely so that atomic mass numbers could be read directly as molar masses in g/mol, creating a seamless bridge between the atomic and macroscopic worlds.

Question 5

Explain why dimensional analysis is particularly useful in molar mass conversions, and what specific error it helps you catch.

Model answer: Dimensional analysis ensures units cancel correctly at each step. In molar mass conversions, the key error is inverting the conversion factor. If you want grams from moles, you need mol × (g/mol) = g; the 'mol' cancels. If you accidentally write mol × (mol/g), you get mol²/g — a nonsensical unit that immediately signals the error. Tracking units forces you to orient every conversion factor correctly, which prevents both the inversion error and forgetting to apply Avogadro's number when converting between moles and particles.

The power of dimensional analysis is that it makes errors visible before you calculate a wrong number. If the units of your answer are wrong, the calculation is wrong — no need to check arithmetic. This is especially valuable in multi-step problems (e.g., grams → moles → particles) where a flip at step one propagates through every subsequent step.