The degree of dissociation of PCl5 is 60%,then find out the observed molar mass of the mixture.Option: 1 130.3Option: 2 135Option: 3 229.5Option: 4 206.5

we know this formula

Theoretical moles X Theoretical molar mass = Observed moles X Observed molar mass

for solving we have to find other values.

Below I have given the process.

We have been given that the degree of dissociation is 60% means 60/100 =0.6

$\mathrm{PCl}_{5(\mathrm{g})} \rightleftharpoons \mathrm{PCl}_{3(\mathrm{g})}+\mathrm{Cl}_{2(\mathrm{g})}$?
Initial moles      1                     0                  0
At equilibrium   1-$\alpha$?                  $\alpha$?                  $\alpha$?
Where, $\alpha$? = degree of dissociation = 0.6
Total number of moles at equilibrium(observed moles) = 1 - $\alpha$? +  $\alpha$? +  $\alpha$

= 1+ $\alpha$ = 1.6

Total number of moles at equilibrium(theoretical moles) = initial moles

= 1 + 0 + 0 = 1

Theoretical molar mass = molar mass of PCl5 = 208.5

Now. from mass conservation we have

Theoretical moles X Theoretical molar mass = Observed moles X Observed molar mass

$\Rightarrow\mathrm{1 \times 208.5 = 1.6 \times M_{obs}}$?

$\therefore \mathrm{M_{obs} = \frac{208.5}{1.6}=130.3}$?

Therefore, option(1) is correct