Question

Due to the lack of other methods in the middle of the 19th century a chemist determining the molar mass of a new element X chose the following procedure: He succeeded in preparing four compounds A, B, C, and D containing the element X and determined its content (in mass%) in each of the compounds. At 250°C all four compounds were in gaseous state. They were individually transferred into previously evacuated flasks until the pressure reached the value of 1.013.105 Pa and then the flasks were weighed. After subtracting the weight of the empty flask, the mass of the gas inside was determined. This procedure was repeated with nitrogen. Thus the following Table of data was obtained:  

Gas	Total mass of gas	Content of element X in gas (mass %)
N2	0.652 g	0
A	0.849 g	97.3
B	2.398 g	68.9
C	4.851 g	85.1
D	3.583 g	92.2

 Determine the probable molar mass of element X. 

Answer 1

At a temperature of 250°C all the substances A, B,C, and D are considered to behave as ideal gases and according to Avogadro's law: 

n(N2) = n(A) = n(B) = n(C) = n(D) 

The mass of element X in one mole of A, B, C or D: 

A: M(A) × 0.973 = 35.45 g mol^-1  

B: M(B) × 0.689 = 70.91 g mol^-1  

C: M(C) × 0.851 = 177.17 g mol^-1  

D: M(D) × 0.922 = 141.78 g mol^-1  

Because in one molecule of a compound there must be at least one atom X or its integer multiple, we must calculate the highest common measure of the molar masses obtained. It is in our case equal to 35.45 g mol⁻¹ in average which can be considered as the probable molar mass of element X. It is only the most probable value because its integer fraction cannot be excluded.