Chapter 13, Problem 42P

To determine

To Find: The number of moles of water present in the given volume.

Answer to Problem 42P

The moles of the water is $55.55\text{moles}$ and the number of molecules present in the solution is $3.346\times {10}^{25}$ molecules.

Explanation of Solution

Given info:

The volume of the water $\mathrm{V}=1\mathrm{L}=1000\text{mL}$ ,

The molecular weight of the water is $\mathrm{M}=2\times 1+1\times 16=18$ ,

The mass of the water $\mathrm{m}=1000\times 1=1000\text{g}$ .

Formula used:

Write the expression for calculation of the number of moles.

  $\mathrm{n}=\frac{{\mathrm{m}}_{\text{water}}}{\mathrm{M}}$

Here, ${\mathrm{m}}_{\text{water}}$ is the mass of the water,

  $\mathrm{M}$ is the molecular mass.

Calculation:

By substituting the given values in the formula and then the number of moles is,

  $\mathrm{n}=\frac{1000}{18}=55.55\text{moles}$

The number of molecules present in the one-liter volume is,

  $=\mathrm{n}\times {\mathrm{N}}_{\mathrm{A}}$

Where ${\mathrm{N}}_{\mathrm{A}}$ is the Avogadro number

So, the number of molecules is,

  $\begin{array}{l}=55.55\text{moles}\times 6.023\times {10}^{23}\\ =3.346\times {10}^{25}\text{molecules}\end{array}$

Conclusion:

The moles of the water is $55.55\text{moles}$ and the number of molecules present in the solution is $3.346\times {10}^{25}$ molecules.