# Solid white phosphorous melts then vaporizes at high temperatures. Gaseous white phosphorous...

## Question:

Solid white phosphorous melts then vaporize at high temperatures. Gaseous white phosphorous 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?

## Phase Transitions:

Pure substances go through well-defined phase transitions. At low temperatures, they tend to be solids - highly rigid with low entropy, dominated entirely by the forces between particles. At higher temperatures, the solid's lattice degrades, though the intermolecular forces remain dominant, which is why liquids can flow but are still condensed. At very high temperatures, the liquid boils and becomes a gas. The kinetic energy of the particles is large enough to entirely overcome the intermolecular forces, and the particles are usually better described as independently flying billiard balls than an interdependent network.

## Answer and Explanation:

How many phosphorous atoms are in one particle of gaseous white phosphorous? It's hard to say off the top of your head. We can use the data we are given on the effusion to figure this out. To use the effusion data, we need Graham's Law, which relates effusion rates to molar masses. With the molar mass of the phosphorous compound, we can figure out the number of phosphorous atoms involved.

{eq}\rm\dfrac{rate_{Ne}}{rate_{WP}} = \sqrt{\dfrac{M_{WP}}{M_{Ne}}} {/eq}

Now we can plug in the information we know to determine the molar mass of the white phosphorous (WP).

{eq}\rm\dfrac{rate_{WP}}{rate_{Ne}} = \sqrt{\dfrac{M_{Ne}}{M_{WP}}}\\ 0.404 = \sqrt{\dfrac{20.18g/mol}{M_{WP}}}\\ M_{WP} = 124g/mol {/eq}

To find the number of atoms of phosphorous in one particle of WP gas, we divide the WP molar mass by the molar mass of a single P atom.

{eq}\rm M_{WP} = 124g/mol\\ \#\ atoms = \dfrac{M_{WP}}{M_P} = \dfrac{124g/mol}{30.97g/mol}\\ \#\ atoms = 4.00 {/eq}

There are exactly 4 atoms of phosphorous in one molecule of white phosphorous.

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