The rate of diffusion depends on the following factors.

r $$\propto$$ P and r $$\propto$$ $$\sqrt {1/M} $$

Taking these together, we get

$${{{r_2}} \over {{r_1}}} = {{{P_2}} \over {{P_1}}}{\left( {{{{M_1}} \over {{M_2}}}} \right)^{1/2}}$$

or $${{{n_1}} \over {{t_1}}} \times {{{t_2}} \over {{n_2}}} = {{{P_1}} \over {{P_2}}} \times \sqrt {{{{M_2}} \over {{M_1}}}} $$

or $${1 \over {38}} \times {{57} \over 1} = {{0.8} \over {1.6}} \times \sqrt {{{{M_2}} \over {28}}} $$

or $${M_2} = {{57 \times 57} \over {38 \times 38}} \times {{1.6 \times 1.6} \over {0.8 \times 0.8}} \times 28 = 252$$

Let the molecular formula of the unknown compound be XeF_n. We will have

$${M_{xe}} + n{M_f} = 252$$ g mol^$$-$$1 i.e. $$[131 + n(19)]$$ g mol^$$-$$1 = 252 g mol^$$-$$1

$$n = {{252 - 131} \over {19}} = 6.36 \simeq 6$$

Hence, the molecular formula of the gas is $$Xe{F_6}$$.