molar mass

Molar Mass Overview

  • Definition: A mole is a counting unit for chemists and is used to convert between mass and number of molecules.
  • Use of Balances: Lab balances can measure the mass of a substance, which can then be used to calculate the number of moles present.

Molar Mass of Molecules and Ionic Compounds

  • Composition of Molecules and Ionic Compounds:

    • Molecules can consist of the same atom (e.g., O<em>2O<em>2) or different atoms (e.g., H</em>2OH</em>2O).
    • Ionic compounds have a fixed formula (e.g., NaNO3NaNO_3).

  • Calculation of Molar Mass:

    • To find the molar mass of a compound, sum the relative atomic masses of all atoms present in the formula.
    SubstanceElemental CompositionMolar Mass CalculationMolar Mass (g mol^-1)
    H2OH_2O2(H)+1(O)2(H) + 1(O)(2imes1.0)+16.0(2 imes 1.0) + 16.018.0
    CO2CO_21(C)+2(O)1(C) + 2(O)(1imes12.0)+(2imes16.0)(1 imes 12.0) + (2 imes 16.0)44.0
    NaNO3NaNO_31(Na)+1(N)+3(O)1(Na) + 1(N) + 3(O)23.0+14.0+(3imes16.0)23.0 + 14.0 + (3 imes 16.0)85.0

Molar Mass of Elements

  • Definition: The mass (in grams) of one mole of an element is its molar mass (symbol: M, units: g mol^-1).

  • Relationship with Relative Atomic Mass:

    • M=AM = A (where A is the relative atomic mass)

  • Example Table:

    ElementRelative Atomic Mass (A)Molar Mass (M in g mol^-1)
    O16.016.0
    Fe55.855.8
    Ag107.9107.9

Practical Calculation Examples

Example: Calculate Molar Mass of CO₂
  • Formula: M=(1imesA(C))+(2imesA(O))M = (1 imes A(C)) + (2 imes A(O))
  • Calculation:
    • M<em>CO</em>2=(1imes12.0)+(2imes16.0)=44.0extgmol−1M<em>{CO</em>2} = (1 imes 12.0) + (2 imes 16.0) = 44.0 ext{ g mol}^{-1}
Example: Calculate Amount from Mass
  • Formula for Moles:n=mMn = \frac{m}{M} where
    • mm = mass in grams
    • MM = molar mass in g mol^-1
  • Example Calculation:
    • For 250 g of NaClNaCl
    • Molar mass of NaClNaCl = 23.0+35.5=58.5extgmol−123.0 + 35.5 = 58.5 ext{ g mol}^{-1}
    • Amount in moles:
      n=25058.5=4.27extmoln = \frac{250}{58.5} = 4.27 ext{ mol}
Example: Determine the Mass from Moles
  • Use Formula:
    m=nimesMm = n imes M
  • Example Calculation:
    • To find the mass of 0.35 mol of Mg(NO<em>3)</em>2Mg(NO<em>3)</em>2:
    • M=24.3+(2imes14.0)+(6imes16.0)=148.3extgmol−1M = 24.3 + (2 imes 14.0) + (6 imes 16.0) = 148.3 ext{ g mol}^{-1}
    • m=0.35imes148.3=52extgm = 0.35 imes 148.3 = 52 ext{ g}

Avogadro’s Constant and Molecular Counts

  • Avogadro’s Constant (Nₐ): 6.02imes10236.02 imes 10^{23} represents the number of molecules in one mole of a substance.
  • Calculating Number of Molecules:
    • N=nimesNAN = n imes N_{A}
      where nn = number of moles.
  • Example Calculation:
    • For 22 g of CO2CO₂:
    • n=2244.0=0.50extmoln = \frac{22}{44.0} = 0.50 ext{ mol}
    • N=0.50imes6.02imes1023=3.0imes1023extmoleculesN = 0.50 imes 6.02 imes 10^{23} = 3.0 imes 10^{23} ext{ molecules}

Case Study: Bee Sting Pheromone

  • Pentyl Ethanoate (C₅H₁₀O₂):
    • Released by bees when they sting.
    • One bee sting releases 1.0imes10−6extg1.0 imes 10^{-6} ext{ g}.
  • Calculations Related to Pentyl Ethanoate:
    1. Calculate its molar mass.
    2. Determine moles released from one sting: n=massmolarmassn = \frac{mass}{molar mass}.
    3. Calculate the total number of molecules: N=nimesNAN = n imes N_{A}.