Question

Solid white phosphorus melts and then vaporizes at high temperature. gaseous white phosphorus effuses at a rate that is 0.404 times that of neon in the same apparatus under the same conditions. how many atoms are in a molecule of gaseous white phosphorus?

Answer 1

rate of effusion of phosphorus / rate of effusion of neon = 0,404.
rate of effusion of neon = 1/√M(Ne).
rate of effusion of neon = 1/√20,18 = 0,222.
rate of effusion of phosphorus = rate of effusion of neon · 0,404.
rate of effusion of phosphorus = 0,222 · 0,404 = 0,0897.
rate of effusion of phosphorus = 1/√M(Pₓ).
√M(Pₓ) = 1 ÷ 0,0897 = 11,14.
M(Pₓ) = (11,15)² = 124.
N(P) = 124 g/mol ÷ 31 g/mol = 4.
There are 4 atoms in a molecule of gaseous white phosphorus.

Answer 2

The number of phosphorus atom in white phosphorus is $\boxed4$.

Further Explanation:

Effusion is the process by which molecules of gas travel through a small hole from high pressure to the low pressure. According to the graham’s law, effusion rate of a gas is inversely proportional to the square of the molar mass of gas.

${\text{Rate of effusion}}\left({\text{R}}\right)\propto\frac{1}{{\sqrt {{\mu}}}}$                                                               .....(1)

Where $\mu$is the molar mass of a gas.

${{\text{R}}_{{\text{white phosphorus}}}}\propto\frac{1}{{\sqrt{{{\text{\mu}}_{{\text{white phosphorus}}}}} }}$                                    ...... (2)

And, the rate of effusion of neon gas is expressed as

${{\text{R}}_{{\text{Neon}}}} \propto \frac{1}{{\sqrt {{{\tex{\mu }}_{{\text{Neon}}}}} }}$                                                                          ......(3)

Since rate of effusion of white phosphorus is 0.404 times of rate of effusion of neon. Therefore,

${{\text{R}}_{{\text{white phosphorus}}}}=0.404{{\text{R}}_{{\text{Neon}}}}$            ......(4)

Substitute the value of  ${{\text{R}}_{{\text{white phosphorus}}}}$ and ${{\text{R}}_{{\text{Neon}}}}$ from equation (2) and equation (3) respectively in equation (4).

$\frac{1}{{\sqrt {{\mu _{{\text{white phosphorus}}}}}}}=0.4041\sqrt{{\mu _{{\text{Neon}}}}}$                                                          ......(5)

Simplify equation (5) as follows:

$\begin{aligned}\dfrac{1}{\sqrt{\mu_{\text{White Phosphorous}}}}&=0.404\left(\dfrac{1}{\sqrt{\mu_{\text{Neon}}}}\right)\\\sqrt{\mu_{\text{White Phosphorous}}}&=\dfrac{\sqrt{\mu_{\text{Neon}}}}{0.404}\\\mu_{\text{White Phosphorous}}&=\left(\dfrac{\sqrt{\mu_{\text{Neon}}}}{0.404}\right)^{2}\\&=\dfrac{\mu_{\text{Neon}}}{(0.404)^{2}}\end{aligned}$

Therefore the molar mass of white phosphorus is,

${{{\mu}}_{{{white phosphorus}}}} = \frac{{{{{\mu}}_{{{Neon}}}}}}{{{{\left({0.404} \right)}^2}}}$                                                       ......(6)

The molar mass of neon is 20.18 g/mol.

Substitute the value of molar mass of neon in the equation number (6).

$\begin{aligned}{{t{\mu }}_{{\text{white phosphorus}}}}=\frac{{20.18{\text{g/mol}}}}{{{{\left( {0.404} \right)}^2}}}\\=123.6{\text{ g/mol}}\\\end{gathered}$

Therefore the molar mass of white phosphorus is 123.6 g/mol.

Formula to calculate the number of phosphorus atoms present in white phosphorus is,

${\text{Number of P atom}} = \frac{{{\text{molar mass of white phosphorus}}}}{{{\text{molar mass of P}}}}$                    ......(7)

The atomic mass of phosphorus atom is 30.97 g/mol.

Substitute molar mass of white phosphorus and atomic mass of phosphorus in equation (7).

$\begin{aligned}{\text{Number of P atom}}&= \frac{{{\text{123}}{\text{.6 g/mol}}}}{{{\text{30}}{\text{.97 g/mol}}}}\\&= 3.99\\&\approx4{\text{ atoms}}\\\end{aligned}$

Therefore the number of phosphorus atoms in white phosphorus is 4.

Learn more:

1. Balanced chemical equation https://brainly.com/question/1405182

2. Calculation of volume of gas: https://brainly.com/question/3636135

Answer details:

Grade: Senior School

Subject: Chemistry

Chapter: Ideal gas equation

Keywords: Effusion, rate of effusion, white phosphorus, neon, molar mass, atomic mass, number of phosphorus atoms, 4 atoms, rate of effusion of white phosphorus, rate of effusion of neon, molar mass of neon.