Question

The Vitamin A molecule has the formula C₂₀H₃₀O and a molecule of vitamin A₂ formula C₂₀H₂₈O. Determine what many moles of Vitamin A₂ contain the same number of an atom as 1.000 moles of Vitamin A?

Short answer

1.04 mol

Step-by-step solution

Calculating the number of atoms in Vitamin A  

Vitamin A is afat-soluble vitamin and an important nutrient for humans.

Structure of vitamin A

As per the chemical formula, vitamin A has 20 carbons, 30 hydrogens, and 1 oxygen.

Total number of atoms in vitamin A = 20 carbon atoms + 30 hydrogen atoms + 1 oxygen atom

= 51 atoms

Calculating the total number of atoms in 1 mole of vitamin

One mole means $6.023\times {10}^{23}$atoms of the vitamin.

One molecule of vitamin A has 51 atoms.

$$\begin{gathered} So,6.023\times {10}^{23}\mathrm{atoms}\mathrm{have}=6.023\times {10}^{23}\times 51 \\ =3.071\times {10}^{25}\mathrm{atoms} \end{gathered}$$

Calculating the number of atoms in vitamin A2

Vitamin A₂ has 20 carbons, 28 hydrogens, and 1 oxygen.

$$\begin{gathered} So,\mathrm{the}\mathrm{total}\mathrm{number}\mathrm{of}\mathrm{atoms}\mathrm{in}\mathrm{vitamin}{\mathrm{A}}_2=20\mathrm{C}+28\mathrm{H}+1\mathrm{O} \\ =49\mathrm{atoms} \end{gathered}$$

One mole means $6.023\times {10}^{23}$atoms of the vitamin. One molecule of vitamin A₂ has 49 atoms.

$$\begin{gathered} \mathrm{So},6.023\times {10}^{23}\mathrm{molecules}\mathrm{have}=6.023\times {10}^{23}\times 49 \\ =2.951\times {10}^{25}\mathrm{atoms} \end{gathered}$$

Calculating the total number of moles of Vitamin A that contain the same number of vitamin A2

$$\begin{gathered} \mathrm{Moles}\mathrm{of}\mathrm{vitamin}{\mathrm{A}}_2=\frac{3.071\times {10}^{25}\mathrm{atoms}\mathrm{of}\mathrm{vitamin}\mathrm{A}}{2.951\times {10}^{25}\mathrm{atoms}\mathrm{of}\mathrm{vitamin}{\mathrm{A}}_2} \\ =1.04 \end{gathered}$$

Thus, the number of moles of vitamin A that contain the same number of atoms as Vitamin A₂ is 1.04.