Question

Arsenic(III) sulfide sublimes readily, even below its melting point of 320 °C. The molecules of the vapor phase are found to effuse through a tiny hole at 0.28 times the rate of effusion of Ar atoms under the same conditions of temperature and pressure. What is the molecular formula of arsenic(III) sulfide in the gas phase?

Answer 1

The molecular formula : As₄S₆

Further explanation

Given

Rate of effusion of arsenic(III) sulfide = 0.28 times the rate of effusion of Ar atoms

Required

The molecular formula

Solution

Graham's law: the rate of effusion of a gas is inversely proportional to the square root of its molar masses or  

the effusion rates of two gases = the square root of the inverse of their molar masses:  

$\rm \dfrac{r_1}{r_2}=\sqrt{\dfrac{M_2}{M_1} }$

or  

$\rm M_1\times r_1^2=M_2\times r_2^2$

Input the value :

1 = Arsenic(III) sulfide

2 = Ar

MM Ar = 40 g/mol

0.28 = √(40/M₁)

M₁=40 : 0.28²

M₁=510 g/mol

The empirical formula of arsenic(III) sulfide =  As₂S₃

(Empirical formula)n = molecular formula

( As₂S₃)n = 510 g/mol

(246.02 g/mol)n = 510 g/mol

n = 2

So the molecular formula : As₄S₆