Question

The density of water is 1.00 g/ml at $4^o$C. Number of water molecules (as multiples of ${N_o }$) present in 18 ml water at this temperature is _________.

Answer 1

Hint:Density is equal to the ratio of the mass per unit volume of a substance but the mass is the same as the weight on earth. The density is also known as ‘specific gravity’ when an object is made up of molecules. The density of water is directly proportional to salinity and indirectly proportional to temperature.

Complete step by step answer:
At 4 degrees C, the density of water increases. When the temperature decreases to 0 degrees C, density starts to decrease and it gets near to the freezing point of water.
We use the density of water at $4^\circ $C and the volume of the sample to find its mass by using the molar mass of water. Density is represented as the ratio of mass per unit of volume. Given: a density of 1.00 g/ml shows that every milliliter of water has a mass of 1.00 g.
18 ml has a mass of $18ml \times 1g/1ml = 18g$
Water has a molar mass of 18.015 g/mol. Every mole of water has a mass of \[18.015{\text{ }}g\]. According to the question, $18g \times 1mole/18.015g = 1mole$ of water.
The number of moles and the number of molecules can be found by Avogadro’s number.
Every mole of a substance contains exactly$6.022 \times {10^{23}}$.
 Number of molecules =$1mole \times 6.022 \times {10^{23}}/1mole = 6.022 \times {10^{23}}$molecules.
So, 18 ml of water at a temperature of $4^o $C contains a total of $6.022 \times {10^{23}}$molecules of water.

Note:
Another method to solve this problem.
Density of water =1g/ml
Mass of 18ml of water = 18x1 =18gm.
Moles of water = 18/18 = 1 mole.
So, the number of water molecules = ${N_o }$=$6.022 \times {10^{23}}$ molecules.