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50 mL of hydrogen diffuses out through a small hole from a vessel in 20 minutes. The time needed for 40 mL of oxygen to diffuse out is:

A) 8 min
B) 32 min
C) 12 min
D) 64 min

Answer :

Using Graham's Law of Effusion, the time needed for 40 mL of oxygen to diffuse out was calculated to be 64 minutes, making option D the correct answer.

The problem presented involves the concept of gas diffusion, and Graham's Law of Effusion can be used to solve for the time required for different volumes of gases to diffuse. According to Graham's Law, the rate of effusion for a gas is inversely proportional to the square root of its molar mass. Therefore, we can compare the rates of hydrogen (H2, molar mass of 2 g/mol) and oxygen (O2, molar mass of 32 g/mol).


Let's calculate the rate of diffusion for hydrogen, which we will call RH, and oxygen, RO. Since 50 mL of hydrogen diffuses out in 20 minutes, the rate of hydrogen is RH = 50 mL / 20 min. We now want to calculate how long it would take for 40 mL of oxygen to diffuse out, which we can find as time (TO) = 40 mL / RO. Using Graham's Law, we establish the relative rate of diffusion:

RH/RO = sqrt(MO/MH)
Substituting the molar masses, we find:

RH/RO = sqrt(32/2)

RH/RO = sqrt(16)

RH/RO = 4

Since RH = 50 mL / 20 min, then RO is RH / 4 = (50 mL / 20 min) / 4 = 50 mL / 80 min. The time needed for 40 mL of oxygen to diffuse out is TO = 40 mL / (50 mL / 80 min) which simplifies to TO = (40 mL * 80 min) / 50 mL = 64 min. Therefore, the correct option is D) 64 min.

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