Question

The number of molecules in 1 mL of water is:
A.\[3.3\times {{10}^{22}}\]
B.1
C.\[6.02\times {{10}^{23}}\]
D.18

Answer 1

Hint: This problem is based on the mole concept and stoichiometry. 1 mole of a substance is defined as \[6.02 \times {10^{23}}\] particles of that substance, where the particles can be defined as molecules, atoms, electrons, protons, neutrons and others. We shall calculate the mass of water from the density and then calculate the molecules using mole concept.
Formula Used:
${\text{number of molecules}} = \dfrac{{6.02 \times {{10}^{23}}}}{{{\text{molar mass}}}} \times {\text{mass }}$

Complete step by step solution:
The molecular weight of water = $\left( 2\times 1 \right)+16=18$.
Therefore 18 g of water contains \[6.02\times {{10}^{23}}\]molecules of water.
Considering the density of water to be equal to 1, 18 g of water = 18 ml of water, according to the formula, $\text{d = }\dfrac{\text{M}}{\text{V}}$.
Hence, 18 ml of water = \[6.02\times {{10}^{23}}\]molecules of water
Therefore, 1 ml of water = \[\dfrac{6.02\times {{10}^{23}}}{18}\]=\[3.3\times {{10}^{22}}\]molecules of water.

Hence, the correct answer is option C.

Note:
The molecular weight of a compound is equal to 1 mole of that compound and this is called the gram molecular weight of the compound. Similarly, the atomic weight of an element is equal to 1 mole of that element and this is called the gram atomic weight of the compound.
For gases, 1 mole of the gas is also equal to $22.4$ litres at standard conditions of temperature and pressure.
The number\[6.02\times {{10}^{23}}\], i.e., 1 mole of a substance is called the Avogadro’s number or Avogadro’s constant.
The concept of 1 mole of a substance was introduced to measure the number to subatomic particles as they are too small to be measured directly using a measuring balance or any other measuring equipment.