Question

Calculate the number of hydrogen atoms in 15 moles of ${{\text{H}}_{\text{2}}}\text{O}$ .
(A) $9.3\times {{10}^{24}}$
(B) $9.03\times {{10}^{22}}$
(C) $9.03\times {{10}^{23}}$
(D) $1.806\times {{10}^{25}}$

Answer 1

One mole is defined as the amount of a substance that contains $6.023\times {{10}^{23}}$ particles of that compound. Where the word particles may refer to atoms, molecules, ions, and other subatomic particles.

Complete step by step solution:
One mole is the unit of measurement for the amount of any chemical substance in the International System of Units (S.I.). The number $6.023\times {{10}^{23}}$ was chosen as the Avogadro’s’ number so that the mass of one mole of any chemical compound in grams is numerically equal to the average mass of one molecule of that compound in Daltons. Thus, for example, $6.023\times {{10}^{23}}$ molecules of water whose total molecular mass is $\left[ \left( \text{2 }\times\text{ 1} \right)\text{+16} \right]\text{=18 g/mol}$ . This means that the mass of one molecule of water is equal to 18 Daltons or 18 atomic mass units.
Now, one mole of water is equal to $6.023\times {{10}^{23}}$ molecules of water. Therefore, 15 moles of water is equal to $15\times 6.023\times {{10}^{23}}=9.035\times {{10}^{24}}$ molecules of water.
Now, we need to find out the number of hydrogen atoms in $9.035\times {{10}^{24}}$ molecules of water.
One molecule of water contains two atoms of hydrogen, therefore, the number of hydrogen atoms in $9.035\times {{10}^{24}}$ molecules of water is equal to $2\times 9.035\times {{10}^{24}}=1.806\times {{10}^{25}}$ atoms of hydrogen.

Note:
Let us calculate the molecular weight of water. The atomic mass of hydrogen is 1 and that of oxygen is 16. Therefore the molecular weight of water = $\left[ \left( \text{2 }\times\text{ 1} \right)\text{+16} \right]\text{=18 g/mol}$ .
The molecular weight of a compound is equal to one mole of that compound and is called the gram molecular weight of that compound. This is also called one gram mole of a compound.