Question

(a) How many moles of Catoms are in 1 mol of sucrose$\mathbf{\left(}{\mathbf{C}}_{\mathbf{12}}{\mathbf{H}}_{\mathbf{22}}{\mathbf{O}}_{\mathbf{11}}\mathbf{\right)}\mathbf{?}$(b) How many Catoms are in 2 mol of sucrose?

Short answer

(a) There are12 mol $\mathbf{C}$atoms in 1 mol of sucrose.

(b) There are $\mathbf{1}\mathbf{.}\mathbf{45}\mathbf{\times }{\mathbf{10}}^{\mathbf{23}}\mathbf{}\mathit{C}\mathit{a}\mathit{t}\mathit{o}\mathit{m}\mathit{s}$in 2 mol of sucrose.

Step-by-step solution

Calculating the moles of C atoms in 1 mole of sucrose

Since 12 moles of C atoms are present in 1 mole of sucrose.

Thus, the number of moles of Cis:

$$\begin{gathered} \mathrm{moles}\mathrm{of}\mathrm{C}=\left(1\mathrm{mol}\mathrm{of}{\mathrm{C}}_{12}{\mathrm{H}}_{22}{\mathrm{O}}_{11}\right)\times \frac{12\mathrm{mol}\mathrm{of}\mathrm{C}\mathrm{atoms}}{1\mathrm{mol}\mathrm{of}{\mathrm{C}}_{12}{\mathrm{H}}_{22}{\mathrm{O}}_{11}} \\ =12\mathrm{mol}\mathrm{of}\mathrm{C}\mathrm{atoms} \end{gathered}$$

Calculating the number of C atoms in 2 mole of sucrose

The number of moles can be converted into atoms by using Avogadro’s number. So, the number of atoms is calculated as:

$$\begin{gathered} \mathrm{number}\mathrm{of}\mathrm{C}\mathrm{atoms}=(2\mathrm{mol}\mathrm{of}{\mathrm{C}}_{12}{\mathrm{H}}_{22}{\mathrm{O}}_{11})\times \left(\frac{12\mathrm{mol}\mathrm{of}\mathrm{C}\mathrm{atoms}}{1\mathrm{mol}\mathrm{of}{\mathrm{C}}_{12}{\mathrm{H}}_{22}{\mathrm{O}}_{11}}\right)\times \frac{6.022\times {10}^{23}\mathrm{Catoms}}{1\mathrm{mol}\mathrm{of}\mathrm{Catoms}} \\ =1.45\times {10}^{23}\mathrm{Catoms} \end{gathered}$$