Relative Atomic Mass, Relative Formula Mass, and Percentage Mass Calculations

Fundamentals of Mass Number and Relative Atomic Mass ($A_r$)

• Mass Number: Located in the top left corner of an element's nuclear symbol; equals the total number of protons plus neutrons in the nucleus.

• Relative Atomic Mass ($A_r$): The weighted average mass of all naturally occurring isotopes of an element relative to their abundances (e.g., Chlorine has isotopes of mass $35$ and $37$, giving an $A_r$ of $35.5$).

Determining Relative Formula Mass ($M_r$)

• Relative Formula Mass ($M_r$): The sum of the relative atomic masses ($A_r$) of all atoms in a compound's formula.

• Examples:

  • Magnesium Chloride ($MgCl_2$):     $24 + (35.5 \times 2) = 95$

  • Sulfuric Acid ($H_2SO_4$):     $(2 \times 1) + 32 + (4 \times 16) = 98$

Calculating Percentage Mass by Element

• Formula:   $\text{Percentage Mass} = \frac{A_r \text{ of element} \times \text{number of atoms}}{M_r \text{ of compound}} \times 100$

• Worked Examples:

  • Sulfur in $H_2SO_4$:     $\frac{32 \times 1}{98} \times 100 = 32.7\%$

  • Oxygen in $Ca(OH)_2$ :

  • Compound $M_r$: $40 + (2 \times 16) + (2 \times 1) = 74$

  • Oxygen mass: $16 \times 2 = 32$

  • Percentage: $\frac{32}{74} \times 100 = 43.2\%$