Question

The empirical formula of styrene is $\mathbf{CH}$; the molar mass of styrene is$\mathbf{104}\mathbf{.}\mathbf{14}\raisebox{1ex}{$\mathbf{}\mathbf{g}$}\!\left/ \!\raisebox{-1ex}{$\mathbf{mol}$}\right.$.How many H atoms are present in a $\mathbf{2}\mathbf{.}\mathbf{00}\mathbf{}\mathbf{g}$sample of styrene?

Short answer

$9.25\times {10}^{22}$Moles of H present in a $2.00\mathrm{g}$sample of styrene.

Step-by-step solution

Definition

The molar mass of a material is defined asthe mass of the substance contained in one moleof the substance, and it is equal to the total massof the component atoms. It may be stated mathematically as follows:

$\mathrm{Molar}\mathrm{mass}=\frac{\mathrm{Weight}\mathrm{in}\mathrm{g}}{\mathrm{Number}\mathrm{of}\mathrm{moles}}$

Determine the value of n

Styrene's molecular formula is ${\mathrm{C}}_{\mathrm{n}}{\mathrm{H}}_{\mathrm{n}}$, where n is an integer, because its empirical formula is $\mathrm{CH}$. Divide the molecular weight by the empirical weight to get n.

The molar weights of the elements are as follows:

$$\begin{gathered} \mathrm{H}:1.01\raisebox{1ex}{$\mathrm{g}$}\!\left/ \!\raisebox{-1ex}{$\mathrm{mol}$}\right. \\ \mathrm{C}:12.01\raisebox{1ex}{$\mathrm{g}$}\!\left/ \!\raisebox{-1ex}{$\mathrm{mol}$}\right. \end{gathered}$$

Add the values together to getthe empirical weight:

$1.01\raisebox{1ex}{$\mathrm{g}$}\!\left/ \!\raisebox{-1ex}{$\mathrm{mol}$}\right.+12.01\raisebox{1ex}{$\mathrm{g}$}\!\left/ \!\raisebox{-1ex}{$\mathrm{mol}=13.02{\displaystyle \raisebox{1ex}{$\mathrm{g}$}\!\left/ \!\raisebox{-1ex}{$\mathrm{mol}$}\right.}$}\right.$

To obtain the value of n, divide the empirical weight by the

specified molecular weight:

$n=\frac{104.14}{13.02}\approx 8$

Determine the total number of H atoms

The molecular formula is now known to be ${\mathrm{C}}_8{\mathrm{H}}_8$. Divide the value by the molecular weight to find the moles of ${\mathrm{C}}_8{\mathrm{H}}_8$in a 2 gram sample:

$\frac{2}{104.14}\approx 0.01920\mathrm{Moles}\mathrm{of}{\mathrm{C}}_8{\mathrm{H}}_8$

For every mole of ${\mathrm{C}}_8{\mathrm{H}}_8$, there are 8 moles of H. To calculate the total number of atoms, multiply the value obtained in the previous step by 8:

$0.01920\times 8\approx 0.1536\mathrm{Moles}\mathrm{of}\mathrm{H}$

To find the total number of H atoms by multiplying the Avogadro’s number

$$\begin{gathered} =0.1536\times 6.022\times {10}^{23} \\ =9.25\times {10}^{22}\mathrm{Moles}\mathrm{of}\mathrm{H} \end{gathered}$$

Therefore $9.25\times {10}^{22}$Moles of H is present in styrene.