Question

How many atoms of hydrogen are in a $ 10 $ gram sample of water?

Answer 1

Hint :To determine the number of atoms of hydrogen present in a $ 10 $ gram sample of water, we have to convert the grams into moles, then the number of moles should be used to find the number of molecules and from the number of molecules we have to find the number of atoms.

Complete Step By Step Answer:
The number of moles of any substance is given by the ratio of mass of substance by the molecular weight of the substance. The molecular weight of water is obtained by adding the atomic weights of all the atoms present in the molecule. The atomic weight of hydrogen is $ 1.00794 $ and the atomic weight of oxygen is $ 15.9994 $ . There are two hydrogen atoms in one water molecule. So, molecular weight of water $ = 1.00794 + 1.00794 + 15.9994 = 18.015g $
Mass of water $ = 10g $
Molecular weight of water $ = 18.015g $
We know that, the number of moles of any substance is:
 $ \Rightarrow $ $ n = \dfrac{{{\text{mass of substance}}}}{{{\text{molecular weight of substance}}}} $
 $ \Rightarrow $ $ n = \dfrac{{10}}{{18.015}} = 0.5551{\text{ moles of }}{{\text{H}}_2}O $
We know that one mole of any substance contains $ 6.023 \times {10^{23}} $ units of ions, atoms or molecules.
So, one mole of water contains $ 6.023 \times {10^{23}} $ number of water molecules.
As we know that one molecule of water contains two moles of hydrogen and one mole of oxygen,
One mole of water contains $ 2 \times 6.023 \times {10^{23}} = 12.046 \times {10^{23}} $ atoms of hydrogen
 $ 0.5551{\text{ moles of }}{{\text{H}}_2}O $ contains $ = \dfrac{{0.5551 \times 12.046 \times {{10}^{23}}}}{1} $ atoms of hydrogen
 $ \Rightarrow $ $ 0.5551{\text{ moles of }}{{\text{H}}_2}O $ contains $ = 6.7\; \times {10^{23}} $ atoms of hydrogen
Therefore, $ 6.7\; \times {10^{23}} $ atoms of hydrogen are present in a $ 10 $ gram sample of water.

Note :
Note that a molecule and a mole are not the same. They are two different terms in chemistry. A mole refers to the mass of a substance which contains $ 6.023 \times {10^{23}} $ units of ions, atoms or molecules. This number is also known as Avogadro’s number.