Question

The number of molecules in 1.5 litres of water are:
(Density of water is 1g/$c{m^3}$.
A. $83.33 \times 6.023 \times {10^{21}}$
B. $83.33 \times 6.023 \times {10^{23}}$
C. $53.33 \times 6.023 \times {10^{23}}$
D. $73.33 \times 6.023 \times {10^{21}}$

Answer 1

Hint: To find out the number of molecules first we need to determine the mass of the water by using the formula of density which says that density is equal to mass by volume. The 1 mol of any substance contains $6.022 \times {10^{23}}$molecules (Avagadro’s number).

Complete step by step answer:
Given,
Volume of water is 1.5 litres
Density of water is 1g/$c{m^3}$.
The relation between the volume and density is that density is equal to mass divided by volume.
The formula for calculating the density is shown below.
\[D = \dfrac{M}{V}\]
Where,
D is the density
M is the mass
V is the volume
To calculate the mass of water, the formula of density is rearranged and new formula iis generated as shown below.
$Mass = Density \times Volume$
To calculate the mass of water, substitute the values volume of water and density of water in the above equation.
$\Rightarrow Mass = 1000 \times 1.5$
$\Rightarrow Mass = 1500g$
The formula for calculating the number of moles is shown below.
$n = \dfrac{m}{M}$
Where,
n is the number of moles.
m is the given mass
M is the molar mass
The molar mass of water is 18g/mol.
To calculate the moles of the water, substitute the values of mass and molar mass in the above expression.
$\Rightarrow n = \dfrac{{1500g}}{{18g/mol}}$
The one mol of substance contain $6.022 \times {10^{23}}$molecules (Avagadro’s number)
So, 83.33 mol of water contains,
$\Rightarrow 83.33 \times 6.023 \times {10^3}$ molecule.

So, the correct answer is Option B.

Note: You can see that in place of density the value instead of 1g/$c{m^3}$, 1000 is used which is used in terms of kg/${m^3}$as volume is present in litres. 1mL = 1 $c{m^3}$, so 1 g/mL = 1g/$c{m^3}$