Question

What is the mass of one molecule of yellow phosphorus? (Atomic mass, ${\text{P = 30}}$)
A. ${\text{1}}{\text{.993 \times 1}}{{\text{0}}^{{\text{22}}}}{\text{ mg}}$
B. ${\text{1}}{\text{.993 \times 1}}{{\text{0}}^{{\text{ - 19}}}}{\text{ mg}}$
C.${\text{4}}{\text{.983 \times 1}}{{\text{0}}^{{\text{ - 20}}}}{\text{ mg}}$
D. ${\text{4}}{\text{.983 \times 1}}{{\text{0}}^{{\text{ - 23}}}}{\text{ mg}}$

Answer 1

Hint: As we know that, one mole has ${\text{6}}{\text{.023 $\times$ 1}}{{\text{0}}^{23}}$ molecules. So, here as to calculate the mass of one molecule of the compound, we divide the mass of the compound by the number of molecules. Here, the atomic mass of phosphorus is ${\text{30}}$. Mass of four molecules of phosphorus ${\text{(}}{{\text{P}}_{\text{4}}}{\text{)}}$ will be ${\text{4 $\times$ 30 = 120 g}}$.

COMPLETE STEP BY STEP ANSWER:
Yellow phosphorus is an impure form of white phosphorus ${\text{(}}{{\text{P}}_{\text{4}}}{\text{)}}$. Yellow phosphorus is formed by a small amount of red phosphorus. Moreover, it is used in the manufacture of fireworks and fertilizers. ${{\text{P}}_{\text{4}}}$ exists as a molecule made up of four atoms. Therefore, molecular mass of yellow phosphorus $ = $ ${\text{30$\times$ 4 = 120 g }}$
As we discussed above,
${\text{1 mole = 6}}{\text{.023$\times$ 1}}{{\text{0}}^{{\text{23}}}}{\text{molecules}}$
So, according to Avogadro’s hypothesis,
Mass of ${\text{6}}{\text{.022$\times$ 1}}{{\text{0}}^{{\text{23}}}}{\text{ = 120 g}}$and mass of one molecule
Therefore, $\dfrac{{{\text{120$\times$ 1}}}}{{{\text{6}}{\text{.022 $\times$ 1}}{{\text{0}}^{{\text{23}}}}}}$
${\text{ = 19}}{\text{.926$\times$ 1}}{{\text{0}}^{ - 23}}{\text{ g}}$
${\text{ = 1}}{\text{.993$\times$ 1}}{{\text{0}}^{ - 22}}{\text{ g}}$
${\text{ = 1}}{\text{.993$\times$ 1}}{{\text{0}}^{{\text{ - 19}}}}{\text{ mg}}$
ADDITIONAL INFORMATION: The sum of atomic masses of all atoms in a molecule, which is based on a scale in which the atomic mass of hydrogen, carbon, oxygen is ${\text{1, 12, 14}}$ respectively. Mainly, talking about the functions of phosphorus is in the formation of bones and teeth. It is required for our body growth, maintenance and repair of cells and tissues to make proteins.
So, the option B) is correct i.e. ${\text{1}}{\text{.993$\times$ 1}}{{\text{0}}^{{\text{ - 19}}}}{\text{ mg}}$.

Note: Talking about the term milligram, it is a unit of measurement of mass in the metric system which is equal to the thousandth of a gram.
Mathematically,
${\text{1000 mg = 1 g}}$