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Picture it first

M = 18.02 g/mol

Mass

18.02

grams

Moles

1.00

mol

Particles

6.02×1023

molecules

mass=n×Mparticles=n×NA\text{mass} = n \times M \qquad \text{particles} = n \times N_A
Try it: the mole is the bridge — multiply by molar mass to reach grams, or by Avogadro's number to reach individual molecules. Change the substance and the same amount of moles weighs differently but always contains the same number of particles.

Advanced Placement (AP) · Practice problems

Moles & Molar Mass

16 written problems across two levels — 9 foundational · 7 advanced. Work through them on paper, then reveal every answer to check. These are not graded and are counted separately from adaptive practice.

    Foundational

  1. 1. FoundationalA solid sample of chlorine consists of two isotopes: 35Cl^{35}\text{Cl} (molar mass 34.969 g⋅mol−134.969\ \text{g·mol}^{-1}) and 37Cl^{37}\text{Cl} (molar mass 36.966 g⋅mol−136.966\ \text{g·mol}^{-1}). By mass the sample is 75.0% 35Cl75.0\%\ ^{35}\text{Cl} and 25.0% 37Cl25.0\%\ ^{37}\text{Cl}. How many grams of this sample contain exactly 6.022×10236.022\times10^{23} atoms of 35Cl^{35}\text{Cl}?

  2. 2. FoundationalA sample of a gaseous compound contains 4.00 grams of nitrogen and 8.00 grams of oxygen. What is the empirical formula of the compound?

  3. 3. FoundationalA sample of an unknown gas contains 3.40 grams and occupies a volume of 2.24 liters at standard temperature and pressure (STP). Which of the following is the molar mass of the gas?

  4. 4. FoundationalA sample of an unknown compound contains 0.480 moles of sulfur (S) and 0.960 moles of oxygen (O). What is the empirical formula of the compound?

  5. 5. FoundationalA compound is found to contain 40.0% carbon, 6.7% hydrogen, and 53.3% oxygen by mass. What is the empirical formula of this compound? Assume 100.0 g of the compound for calculation.

  6. 6. FoundationalA sample of an unknown compound contains 40.0% carbon, 6.7% hydrogen, and 53.3% oxygen by mass. What is the empirical formula of the compound?

  7. 7. FoundationalA sample of a compound contains 0.250 moles of carbon, 0.500 moles of hydrogen, and 0.125 moles of oxygen. What is the empirical formula of the compound?

  8. 8. FoundationalA sample of magnesium carbonate (MgCO₃) with a mass of 84.8 g is completely decomposed upon heating to form magnesium oxide (MgO) and carbon dioxide (CO₂). What is the mass of MgO produced? (Molar masses: Mg = 24.31 g/mol, C = 12.01 g/mol, O = 16.00 g/mol)

  9. 9. FoundationalA sample of a compound contains 3.02 grams of aluminum (Al) and 12.08 grams of chlorine (Cl). Determine the empirical formula of the compound.

    10. Advanced

  10. 10. AdvancedA 10.0 g sample of copper(II) sulfate pentahydrate, CuSO₄·5H₂O, is heated until all water of crystallization is driven off, leaving anhydrous CuSO₄. What mass of water is released?

  11. 11. AdvancedA 2.50 g sample of calcium nitrate, Ca(NO₃)₂, is completely decomposed according to the equation Ca(NO3)2  →  CaO+2 NO2+12 O2.\text{Ca(NO}_3\text{)}_2 \;\rightarrow\; \text{CaO} + 2\,\text{NO}_2 + \tfrac{1}{2}\,\text{O}_2. How many moles of CaO are produced?

  12. 12. AdvancedA sample of a hypothetical element X contains exactly 1.00×10231.00\times10^{23} atoms. Element X occurs naturally as two stable isotopes: 30X^{30}\text{X} (atomic mass 29.9738 u29.9738\ \text{u}) with an abundance of 75.0% and 31X^{31}\text{X} (atomic mass 30.9796 u30.9796\ \text{u}) with an abundance of 25.0%. Which of the following is the most accurate mass, in grams, of this sample?

  13. 13. AdvancedA 3.00 g sample of solid K2CO3\mathrm{K_{2}CO_{3}} is dissolved completely in water. How many moles of K+\mathrm{K^{+}} ions are present in the resulting solution?

  14. 14. AdvancedA sample of a compound contains 2.0 moles of carbon, 6.0 moles of hydrogen, and 1.0 mole of oxygen. What is the empirical formula of this compound?

  15. 15. AdvancedA hydrate of magnesium sulfate, MgSO4⋅xH2O\text{MgSO}_4 \cdot x \text{H}_2\text{O}, is heated until all the water is expelled, leaving an anhydrous sample. If the initial mass of the hydrate is 10.0 g and the mass of the anhydrous magnesium sulfate is 4.8 g, what is the value of xx?

  16. 16. AdvancedA sample of a diatomic gas has a mass of 28.0 grams and occupies 22.4 liters at standard temperature and pressure (STP). Which of the following gases could this be?