Question

A given volume of methane diffuses in 20 seconds. How long will it take the same volume of hydrogen to diffuse under the same conditions? [CH4 = 16; H2 = 2]​

Answer 1

The time taken for the same volume of methane gas to diffuse is 7.1 s.

Rate of gas diffusion

The rate at which a given mass of diffuses is inversely proportional to the molar mass of the gas.

$\frac{t_2}{t_1} = \sqrt{\frac{M_2}{M_1} }$

where;

• M1 is the molar mass of methane (CH4) = 16 g
• M2 is the molar mass of hydrogen as = 2
• t1 is time taken for methane = 20 s
• t2 is the time taken for hydrogen = ?

$\frac{t_2}{t_1} = \sqrt{\frac{M_2}{M_1} }\\\\\frac{t_2}{20} = \sqrt{\frac{2}{16} }\\\\\frac{t_2}{20} = \frac{\sqrt{2} }{4} \\\\t_2 = \frac{20\sqrt{2} }{4} \\\\t_2 = 5\sqrt{2} \\\\t_2 = 7.1 \ s$

Thus, the time taken for the same volume of methane gas to diffuse is 7.1 s.

Learn more about rate of gas diffusion here: brainly.com/question/26696466

Answer 2

The time it takes for hydrogen to diffuse is 7.07 seconds

Graham's law of diffusion

To calculate the time it will take hydrogen gas to diffuse, we use the formula from Graham's law of diffusion.

Formula:

• T'/T = √(M'/M)........... Equation 1

Where:

• T' = Time taken for menthane to diffuse
• T = Time take for hydrogen to diffuse
• M' = Relative molecular mass of menthane
• M = Relative molecular mass of hydrogen.

Make T the subject of the equation

• T = T'/[√(M'/M)]................ Equation 2

From the question,

Given:

• T' = 20 seconds
• M' = 16
• M = 2

Substitute these values into equation 2

• T = 20/[√(16/2)]
• T = 20/[√(8)]
• T = 20/(2.828)
• T = 7.07 seconds

Hence, The time it takes for hydrogen to diffuse is 7.07 seconds.

Learn more about Graham's law of diffusion here: brainly.com/question/22359712