Q3.2P - Chemistry: Molecular Nature Of Matter And Change

Question

(a) How many moles of C atoms 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 C atoms are in 2 mol of sucrose?

Step-by-Step Solution

Answer

(a)  There are 12 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 1: 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 C is:

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

Step 2: 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:

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