Question

The density of water is 1.00 g/mL at $4^\circ C$. How many water molecules are present in 2.46 mL of water at this temperature?

Answer 1

Hint: In this question, the value of density and volume is known so the mass can be calculated by multiplying the density by the volume. After obtaining mass, the number of moles can be calculated by dividing the mass by the molecular weight obtained with the help of a periodic table.

Complete step by step answer:
Given,
The density of the water is 1.00 g/mL.
The temperature is $4^\circ C$.
The volume of water is 2.46 mL.
As the value of density and volume are given, the mass can be calculated by the formula of density.
The formula of density is shown below.
$D = \dfrac{m}{V}$
D is the density
m is the mass
V is the volume.
To calculate the mass, substitute the values in the above equation.
$ \Rightarrow 1.00g/mL = \dfrac{m}{{2.46mL}}$
$ \Rightarrow m = 1.00g/mL \times 2.46mL$
$ \Rightarrow m = 2.46g$
The molecular weight of water is 18g/mol.
The formula to calculate the number of moles is shown below.
$n = \dfrac{m}{M}$
Where,
n is the number of moles
m is the mass
M is the molecular weight
To calculate the moles of water, substitute the values in the above equation.
$ \Rightarrow n = \dfrac{{2.46g}}{{18g/mol}}$
$ \Rightarrow n = 0.136$mol
Therefore, the number of moles present in water is 0.136 mol.
We know that 1 mole of any substance is equal to $6.022 \times {10^{23}}$ molecules where the value is known as the Avagadro’s number and the constant is said as Avagadro’s constant.
So, the number of molecules is calculated as shown below.
$ \Rightarrow 0.136 \times 6.022 \times {10^{23}}$
$ \Rightarrow 8.189 \times {10^{22}}$
Therefore, $8.189 \times {10^{22}}$ water molecules are present in 2.46 mL of water $4^\circ C$.

Note:
In this question we have asked for the number of molecules but for calculating the number atoms also the same method is applied as 1 mole of any substance is equal to $6.022 \times {10^{23}}$ number of atoms or molecules.