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Mass-Mole Calculations (moles = mass ÷ molar mass)

Key Concepts

  • 1 mole of a pure substance has a mass equal to its molecular mass expressed in grams.
      This is known as the molar mass, M, and has the units g mol-1
          So 2 moles of a substance would have a mass = 2 x molar mass
          3 moles of a substance would have a mass = 3 x molar mass etc

  • This leads to the formula: mass = moles x molar mass
      If we let:
          m = mass of substance in grams,
          n = moles of pure substance,
          M = molar mass of the pure substance in g mol-1
     we can write the equation: m = n x M

  • This equation can be rearranged to give the following:
          n = m ÷ M   (moles = mass ÷ molar mass)
          M = m ÷ n   (molar mass = mass ÷ moles)

Examples

1. mass = moles x molar mass

Calculate the mass of 0.25 moles of water

  1. Write the equation:
    m (in grams) = n x M

  2. Extract the data from the question:
    n = 0.25 mol

  3. Calculate the molar mass of the substance using the periodic table:
    M(H2O) = (2 x 1.008) + 16.00 = 18.016 g mol-1

  4. Substitute the values into the equation and solve:
    mass = 0.25 x 18.016 = 4.504 g

2. moles = mass ÷ molar mass

Calculate the moles in 124.5 g of oxygen gas.

  1. Write the equation:
    n = m ÷ M

  2. Extract the data from the question:
    m = 124.5 g

  3. Calculate the molar mass of the substance using the periodic table:
    M(O2) = 2 x 16.00 =32.00 g mol-1

  4. Substitute the values into the equation and solve:
    n = 124.5 ÷ 32.00 = 3.89 mol

3. molar mass = mass ÷ moles

Calculate the molar mass of a pure substance if 1.75 moles of the substance has a mass of 29.792 g

  1. Write the equation:
    M = m ÷ n

  2. Extract the data from the question:
    m = 29.792 g
    n = 1.75 mol

  3. Substitute the values into the equation and solve:
    M = 29.792 ÷ 1.75 = 17.024 g mol-1


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