Question

The recommended daily allowance of niacin (vitamin B3) is 12 mg per day for children. The molecular formula for niacin is C6H5NO2. Calculate the number of molecules of niacin in 12 mg .

Answer 1

5.87 ×10¹⁹ molecules.

Step-by-step explanation:

From the question given above, the following data were obtained:

Mass of C₆H₅NO₂ = 12 mg

Number of molecules of C₆H₅NO₂ =?

Next, we shall convert 12 mg to g. This can be obtained as follow:

1 mg = 10¯³ g

Therefore,

12 mg = 12 mg × 10¯³ g / 1 mg

12 mg = 0.012 g

Next, we shall determine the mass of 1 mole of C₆H₅NO₂. This can be obtained as follow:

1 mole of C₆H₅NO₂ = (12×6) + (5×1) + 14 + (16×2)

= 72 + 5 + 14 + 32

= 123 g

Finally, we shall determine the number of molecules present in 12 mg (i.e 0.012 g) of C₆H₅NO₂. This can be obtained as follow:

From Avogadro's hypothesis,

1 mole of C₆H₅NO₂ = 6.02×10²³ molecules

123 g of C₆H₅NO₂ = 6.02×10²³ molecules

Therefore,

0.012 g of C₆H₅NO₂ = 0.012 × 6.02×10²³ / 123

0.012 g of C₆H₅NO₂ = 5.87 ×10¹⁹ molecules.

Thus, 12 mg (i.e 0.012 g) of C₆H₅NO₂ contains 5.87 ×10¹⁹ molecules.