Question

When 3.51 g of phosphorus was burned in chlorine, the product was a phosphorus chloride. Its vapor took 1.77 times as long to effuse as the same amount of CO2 under the same conditions of temperature and pressure. What is the molar mass of the phosphorus chloride

Answer 1

molar mass of the phosphorus chloride = 138.06 g/mol

Step-by-step explanation:

mass of phosphorus will be the same as mass of CO2, since it is stated that they are of equal amount.

mass = 3.51 g

lets assume that it took the CO2 1 sec to effuse, then the time taken by the phosphorus chloride will be 1.77 sec

From this we can say that

rate of effusion of CO2 = 3.51/1 = 3.51 g/s

rate of effusion of the phosphorus chloride = 3.51/1.77 = 1.98 g/s

From graham's equation of effusion,

`(Rc)/(Rp)` =
`\sqrt{(Mp\\)/(Mc) }`

Rc = rate of effusion of CO2 = 3.51 g/s

Rp = rate of effusion of phosphorus chloride = 1.98 g/s

Mc = molar mass of CO2 = 44.01 g/mol

Mp = molar mass of the phosphorus chloride = ?

Imputing values into the equation, we have

`(3.51)/(1.98)` =
`\sqrt{(Mp\\)/(44.01) }`

1.77 =
`(√(Mp) )/(6.64)`

11.75 =
`√(Mp)`

Mp =
`11.75^(2)`

Mp = molar mass of the phosphorus chloride = 138.06 g/mol