Find No of Moles

Question

Atomic Weight of two elements 'A' and 'B' respectively are 32  and 16 .They combine to form two gases AB₂ and AB₄ and the Mixture is found to have a vapor  density of 38.4. the no of moles of AB₂ in 50 moles of the mixture is?

Answer 1

Molecular Weight of AB2 = 32 + (2*16) = 64

 

Molecular Weight of AB4 = 32 + (4*16) = 96

 

Vapor density is defined at  http://en.wikipedia.org/wiki/Vapour_density

 

Gas Mixture vapor density = 38.4*2.016 = 77.4 = Molar mass of gas mixture

 

 

Molar mass of Gas mixture = x * AB2 + (1-x)*AB4

 

==>  77.4 = x*64 + (1-x)*96

 

Solve for x:  

 

x*64 + (1-x)*96 = 77.4

64x +96 - 96x = 77.4

-32x = -76.95

x = 0.5808

1-x = 0.4192

 

Thus, the mole fraction of AB2 in the gas mixture is 0.5808 (AB2 = 58.1% of the mixture. btw, the AB4 gas comprises 41.92% of the gas mixture.)

 

So, the number of moles of AB2 in 50 moles of the gas mixture is 50*0.5808 = 29.04 = 29.0 (sig fig = 3).

 

How many moles of AB4 are in the Gas Mixture?