Answer
$M=4.00\frac{g}{mol}$
Work Step by Step
We know that
$PV=nRT$
But $n=\frac{m}{M}$ Where $m$ and$M$ are mass in grams and molar mass respectively
$\implies PV=\frac{mRT}{M}$
This can be rearranged as
$M=\frac{mRT}{PV}$...........eq(1)
$T=55+273.15=328.15K$
$P=886mmHg\times\frac{1atm}{760mmHg}=1.1658atm$
We plug in the known values in eq(1)to obtain:
$M=\frac{38.8\times 10^{-3}\times 0.08206\times 328.15}{1.1658\times 224\times 10^{-3}}=4.00\frac{g}{mol}$