1.71 x 10²¹ molecules of ascorbic acid.
Further explanation
The Problem:
How many molecules of ascorbic acid (vitamin C or C₆H₈O₆) are in a 500 mg tablet?
The Process:
Step-1
We prepare the molar mass of ascorbic acid or C₆H₈O₆.
Relative atomic mass (in rounding to integers):
- C = 12 g/mol
- H = 1 g/mol
- O = 16 g/mol
In ascorbic acid, there are six carbon atoms, eight hydrogen atoms, and six oxygen atoms. Therefore the molar mass is given by
[tex]\boxed{(12 \times 6) + (1 \times 8) + (16 \times 6) = 176 \ g/moles}[/tex]
Step-2
We calculate the moles of 500 mg ascorbic acid. Let us convert it to 0.5 g.
[tex]\boxed{ \ moles = \frac{mass}{molar \ mass} \ } \rightarrow \boxed{ \ moles = \frac{0.5 \ g}{176 \ g/mol} \ }[/tex]
Therefore we get 2.84 x 10⁻³ moles.
Step-3
Remember this, one mole contains 6.02 x 10²³ molecules, which is called The Avogadro's number.
Let us convert 2.84 x 10⁻³ moles to the number of molecules (N).
[tex]\boxed{ \ moles = \frac{N}{6.02 \times 10^{23}} \ } \rightarrow \boxed{ \ N = moles \times 6.02 \times 10^{23} \ } [/tex]
[tex]\boxed{ \ N = 2.84 \times 10^{-3} \ moles \times 6.02 \times 10^{23} \ \frac{molecules}{mol} \ }[/tex]
Thus the amount of molecules in 500 mg C₆H₈O₆ are [tex]\boxed{ \ 1.71 \times 10^{21} \ molecules \ }[/tex].
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Quick Steps
[tex]\boxed{ \ \frac{6.02 \times 10^{23} \ molecules}{1 \ mol} \times \frac{1 \ mole}{176 \ gram} \times 0.5 \ grams \ } = \boxed{ \ 1.71 \times 10^{21} \ molecules \ }[/tex]
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