Question

Ascorbic acid or vitamin C $\left(C_6{H}_8{O}_6\right)$ is an essential vitamin. It cannot be stored by the body and must be present in the diet. What is the molar mass of ascorbic acid? Vitamin C tablets are taken as a dietary supplement. If a typical tablet contains 500.0 mg vitamin C, what amount (moles) of vitamin C is contained in 10 tablets? What numbers of vitamin C molecules are in 8 tablets?

Short answer

The numbers of vitamin C molecules are $1.37\times {10}^{22}\mathrm{molecules}$

Step-by-step solution

Definition of molar mass

The molar mass of ascorbic acid (vitamin C) equals the sum of the average masses of its constituents (elements present in a compound).

Calculation of molecular formula

The ascorbic acid is $\left({\mathrm{C}}_6{\mathrm{H}}_8{\mathrm{O}}_6\right)$, and the molar mass is equal as:

$$\begin{gathered} =6\times 12.011\frac{\mathrm{g}}{\mathrm{mol}}+8\times 1.008\frac{\mathrm{g}}{\mathrm{mol}}+6\times 15.999\frac{\mathrm{g}}{\mathrm{mol}} \\ =\left(72.066+8.064+95.994\right)\frac{\mathrm{g}}{\mathrm{mol}} \\ =176.124\frac{\mathrm{g}}{\mathrm{mol}} \\ \mathrm{The}\mathrm{Vitamin}\mathrm{C}\mathrm{molar}\mathrm{mass}\mathrm{is}176.124\frac{\mathrm{g}}{\mathrm{mol}} \end{gathered}$$

Calculation of moles for 10 tablets

For 10 tablets,

$$\begin{gathered} =0.5\mathrm{g}\times 10 \\ =5\mathrm{g} \end{gathered}$$

Now, the moles' amount is given as:

$$\begin{gathered} \mathrm{n}=5\mathrm{g}\times \frac{1\mathrm{mol}}{176.124\mathrm{g}} \\ \mathrm{n}=0.028\mathrm{mol} \end{gathered}$$

Calculation of moles for 8 tablets

For 8 tablets,

$$\begin{gathered} =0.5\mathrm{g}\times 8 \\ =4\mathrm{g} \end{gathered}$$

Now, the moles' amount is given as:

$$\begin{gathered} \mathrm{n}=4\mathrm{g}\times \frac{1\mathrm{mol}}{176.124\mathrm{g}} \\ \mathrm{n}=0.023\mathrm{mol} \end{gathered}$$

Calculation of vitamin C molecules

The number of vitamin C molecules:

$$\begin{gathered} =0.023\mathrm{mol}\times \frac{6.022\times {10}^{23}\mathrm{molecules}}{1\mathrm{mol}} \\ =0.137\times {10}^{23} \\ =1.37\times {10}^{22}\mathrm{molecules} \end{gathered}$$