Question

How can I calculate the percentage by mass of sodium in sodium azide, $Na{N_3}$, used in automobile airbags?

Answer 1

Mass percentage is one way of representing the concentration of an element in a compound or a component in a mixture. The mass percentage is calculated as the mass of a component divided by the total mass of the mixture, multiplied by $100\%$. To calculate the mass percent of an element in a compound, we divide the mass of the element in $1$ mole of the compound by the compound's molar mass and multiply the result by $100$.

Complete answer:
Mass percent is the mass of the element or solute divided by the mass of the compound or solute. The result is multiplied by $100$ to give a percent.
The formula for the amount of an element in a compound is:
mass percent = $\dfrac{{\text{mass of element in 1 mole of compound}}}{{\text{mass of 1 mole of compound}}}$ $\times 100$
The percentage of sodium in this compound is the molar mass of sodium divided by the molar mass of sodium azide.
The molar mass (atomic weight ) of sodium is $23.0\dfrac{{grams}}{{mole}}$ and the molar mass of sodium azide, $Na{N_3}$, is the mass of sodium, $23.0\dfrac{{grams}}{{mole}}$ added to the molar mass of three atoms of nitrogen ($14.0 \times 3 = 42\dfrac{{grams}}{{mole}}$) which equals $65.0\dfrac{{grams}}{{mole}}$.
The percentage of sodium is $\dfrac{{23.0}}{{65.0}} \times 100\% = 35\%$.

Note:
A percentage is a general term for a proportion out of a hundred, so we can only calculate percentages into grams when it's a percentage of a certain mass. To calculate it, you convert the percentage you want into a decimal proportion and then multiply that proportion by the mass of the whole $100$ percent