Question

Calculate the molar mass of butane. Butane's rate of diffusion is 3.8 times slower than that of hleium.

Answer 1

Answer:

58 g/mol

Explanation:

According to Graham's law, the rate of diffusion of a gas (r) is inversely proportional to the square root of its molar mass (M). Butane's rate of diffusion is 3.8 times slower than that of helium, that is, rButane = rHe/3.8, or rHe/rButane = 3.8. Then,

$\frac{rHe}{rButane} =3.8=\sqrt{\frac{M(Butane)}{M(He)} } =\sqrt{\frac{M(Butane)}{4.00g/mol} } \\M(Butane)=3.8^{2} \times 4.00g/mol\\M(Butane)=58g/mol$

Answer 2

Answer:

The molar mass of butane ≈ 58 g/mol

Explanation:

Step 1: Data given

diffusion rate of butane is 3.8 slower than helium

Let's say the diffusion rate of butane is 1 and helium its diffusion rate = 3.8

Step 2: Calculate the molar mass of butane

Rate 1 / rate 2 = √(MM2 / MM1)

⇒ with rate 1 = the rate of diffusion of helium = 3.8

⇒ with rate 2= the rate of diffusion of butane = 1

⇒ with MM1 = the molar mass of helium = 4.00 g/mol

⇒ with MM2 = the molar mass of butane = TO BE DETERMINED

rate helium / Rate butane  = √(MM of butane / MM helium)

3.8 /1 = √(MMbutane/4)

3.8² *4.00 = MMbutane

MM of butane = 57.8 g/mol ≈58 g/mol

The molar mass of butane ≈ 58 g/mol