Question

The atomic weight of phosphorus is $$30.974u$$. What is the mass of a phosphorus sample which contains $${0.834}_{}moles$$ of phosphorus atoms?

Answer 1

Hint: The molar mass of a compound is equal to the sum of the atomic mass of its constituent atom. To convert between mass and number of moles, we can use the molar mass of the substance. Then, you can use Avogadro’s number to convert the number of moles to the number of atoms.

Complete answer:
Chemists generally use the mole as the unit for the number of atoms or molecules of a material. One mole is equal to $6.022\times {10}^{23}$ molecular entities and each element has a different molar mass depending on the weight of $6.022\times {10}^{23}$ of its atoms.
The unified atomic mass unit is defined as ${\displaystyle \frac{1}{12}}th$ of the mass of a single unbounded carbon-$12$ atom in its ground state and is equivalent to: $1u=1.66\times {10}^{-24}g$
This means that mass of one phosphorus atom will be: $30.974u\times {\displaystyle \frac{1.66\times {10}^{-24}g}{1u}}=5.1433\times {10}^{-23}g$
Now, we know the mass of one phosphorus atom, we can use Avogadro’s number to determine what the mass of one mole of phosphorus atom will be:
$5.1433\times {10}^{-23}\times {\displaystyle \frac{6.022\times {10}^{23}}{1mole}}=30.974g_{}mo{l}^{-1}$
Finally, if one mole of phosphorus atom has a mass of $30.974g_{}mo{l}^{-1}$ then $0.585$ moles will have a mass of: ${0.585}_{}\times {\displaystyle \frac{30.974}{1_{}mole}}=25.8g$

Note:
In chemistry, the mole unit is extremely significant and useful. It is the foundation of stoichiometry, and it is the most accurate way of representing the amounts of reactants and products consumed and created during a chemical reaction. All chemical reactions can be written as a mole reaction. To determine the molar mass , we simply add the atomic masses of the atoms in the formula where the masses can be taken from the periodic table.