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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

\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

11 problems, including 11 🔥 challenging (exam-level, multi-step). Work through them on paper, then reveal every answer to check.

  1. 1. 🔥 ChallengingConsider a sample of a hydrated salt, \text{CuSO}_4 \times x \text{H}_2\text{O} , weighing 2.50\text{ g}. After heating, the sample loses water and the anhydrous salt, \text{CuSO}_4 , has a mass of 1.60\text{ g}. Calculate the number of moles of water per formula unit (x). Molar masses: \text{CuSO}_4 = 159.61\text{ g/mol}, \text{H}_2\text{O} = 18.02\text{ g/mol}.

  2. 2. 🔥 ChallengingA compound contains 40.0\text{ wt\text{\%}} carbon, 6.7\text{ wt\text{\%}} hydrogen, and the rest is oxygen. Calculate the empirical formula of this compound. The atomic masses are: \text{C} = 12.01\text{ g/mol}, \text{H} = 1.008\text{ g/mol}, \text{O} = 16.00\text{ g/mol}.

  3. 3. 🔥 ChallengingGiven that 1.00\text{ g} of a compound \text{M} \text{Cl}_2 contains 0.74\text{ g} of chlorine, calculate the molar mass of the metal \text{M} . The atomic mass of chlorine is 35.45\text{ g/mol}.

  4. 4. 🔥 ChallengingA 0.250\text{ mol} sample of a gas occupies a volume of 5.60\text{ L} at 300\text{ K}. Using the ideal gas law, calculate the pressure of the gas in atm. (Ideal gas constant R = 0.0821\text{ L atm/mol K})

  5. 5. 🔥 ChallengingA sample of a gaseous hydrocarbon contains 0.500 moles of carbon atoms and 1.000 moles of hydrogen atoms. When the sample is combusted in excess oxygen, it produces 44.0 grams of carbon dioxide and 18.0 grams of water. Identify the molecular formula of the hydrocarbon. (Assume the atomic masses: C = 12.01 g/mol, H = 1.008 g/mol, and O = 16.00 g/mol.)

  6. 6. 🔥 ChallengingA 10.0 g sample of a hydrated copper(II) sulfate compound, \text{CuSO}_4 \bullet x\text{H}_2\text{O}, is fully dehydrated by heating to produce 6.40 g of anhydrous copper(II) sulfate, \text{CuSO}_4. Determine the number of water molecules x in one formula unit of the hydrate. Assume complete dehydration and no loss of \text{CuSO}_4. The molar mass of \text{CuSO}_4 is 159.61 g/mol and that of \text{H}_2\text{O} is 18.02 g/mol.

  7. 7. 🔥 ChallengingA mixture contains three different gases: oxygen (\text{O}_2), nitrogen (\text{N}_2), and carbon dioxide (\text{CO}_2). The mixture has a total mass of 100 g and consists of 20 g of oxygen. The molar mass of \text{O}_2 is 32 g/mol, \text{N}_2 is 28 g/mol, and \text{CO}_2 is 44 g/mol. The number of moles of nitrogen is equal to the number of moles of carbon dioxide. Calculate the mass of carbon dioxide in the mixture.

  8. 8. 🔥 ChallengingConsider a compound consisting of chromium, sulfur, and oxygen with the empirical formula CrSO_4. A sample of the compound weighing 1.500 grams is analyzed, and it is found that the sample contains 0.250 grams of sulfur. Determine the molar mass of the compound and identify its molecular formula. Given: Atomic masses are Cr = 51.9961 g/mol, S = 32.06 g/mol, and O = 16.00 g/mol.

  9. 9. 🔥 ChallengingA sealed, rigid container holds a 3.00 g sample of an unknown pure gas at a pressure of 2.50 atm and a temperature of 298 K. The volume of the container is 2.00 L. Determine the molar mass of the gas. Use the ideal gas law PV = nRT where R = 0.0821 \, \text{L atm K}^{-1} \text{mol}^{-1}.

  10. 10. 🔥 ChallengingA 10.00 g sample of an unknown hydrated salt, \text{M}_x\text{A}_y \cdot n\text{H}_2\text{O}, is heated until all the water is driven off, leaving 5.68 g of the anhydrous salt \text{M}_x\text{A}_y. A separate experiment determines that the molar mass of the anhydrous salt \text{M}_x\text{A}_y is 120.00 g/mol. Finally, it is known that the ratio x:y is 2:3. Determine the formula of the hydrated salt and the value of n in the hydrate.

  11. 11. 🔥 ChallengingA sample of a hydrous compound A_xB_y \times nH_2O has a molar mass of 256 g/mol. On heating, the compound loses all its water molecules and the anhydrous compound A_xB_y has a molar mass of 160 g/mol. Given that the atomic masses of A and B are 24 g/mol and 56 g/mol respectively, determine the values of x, y, and n.