To solve this problem, we must assume ideal gas behaviour so that we can use Graham’s law:
vA / vB = sqrt (MW_B / MW_A)
where,
vA = speed of diffusion of A (HBR)
vB = speed of diffusion of B (unknown)
MW_B = molecular weight of B (unkown)
MW_A = molar weight of HBr = 80.91 amu
We know from the given that:
vA / vB = 1 / 1.49
So,
1/1.49 = sqrt (MW_B / 80.91)
MW_B = 36.44 g/mol
Since this unknown is also hydrogen halide, therefore this must be in the form of HX.
HX = 36.44 g/mol , therefore:
x = 35.44 g/mol
From the Periodic Table, Chlorine (Cl) has a molar mass of 35.44 g/mol. Therefore the hydrogen halide is:
HCl