Question

In white phosphorus, P atoms are joined into P4 molecules. White phosphorus is commonly supplied in chalk-like cylindrical form. Its density is 1.823 g/cm3. For a cylinder of white phosphorus 7.00 cm long and 1.26 cm in diameter, determine the number of moles of P present and the total number of P4 atoms

Answer 1

Step-by-step explanation:

It is known that volume of a cylinder is as follows.

Volume of cylinder =
`\pi * r^(2) * h`

=
`3.14 * (1.26)/(2) * 7`

= 8.72
`cm^(3)`

Therefore, mass of
`P_(4)` =
`density * volume`

=
`1.823 g/cm^(3) * 8.72 cm^(3)`

= 15.90 g

As, number of moles of a substance equals its mass divided by its molar mass.

Hence. No. of moles of
`P_(4) = \frac{mass}{\text{molar mass}}`

=
`(15.90 g)/(123.89 g/mol)`

= 0.1283 mol

According to moles concept, in one mole there are
`6.022 * 10^(23)` atoms.

Hence, in 0.1283 mol number of atoms of
`P_(4)` are calculated as follows.

Molecules of
`P_(4) = 0.1283 * 6.022 * 10^(23)`

=
`0.772 * 10^(23)` molecules

=
`7.72 * 10^(22)` molecules

Therefore, atoms of P are calculated as follows.

`4 * 7.72 * 10^(22)` molecules

=
`3.09 * 10^(23)` atoms

Thus, we can conclude that total number of
`P_(4)` atoms are
`3.09 * 10^(23)`.