Respuesta :
Explanation:
It is known that rate of effusion of gases are inversely proportional to the square root of their molar masses.
And, half of the helium (1.5 L) effused in 24 hour. So, the rate of effusion of He gas is calculated as follows.
[tex]\frac{1.5 L}{24 hr}[/tex]
= 0.0625 L/hr
As, molar mass of He is 4 g/mol and molar mass of [tex]O_{2}[/tex] is 32 g/ mol.
Now,
[tex]\frac{\text{Rate of He}}{\text{Rate of Oxygen}} = \sqrt{\frac{32}{4}[/tex]
= 2.83
or, rate of [tex]O_{2} = \frac{\text{Rate of He}}{2.83}[/tex]
= [tex]\frac{0.0625 L/hr}{2.83}[/tex]
Rate of [tex]O_{2}[/tex] = 0.022 L/hr.
This means that 0.022 L of [tex]O_{2}[/tex] gas effuses in 1 hr
So, time taken for the effusion of 1.5 L of [tex]O_{2}[/tex] gas is calculated as follows.
[tex]\frac{1.5 L}{0.022 L/hr}[/tex]
= 68.18 hour
Thus, we can conclude that 68.18 hours will it take for half of the oxygen to effuse through the membrane.
It will take 68.18 hours for half of the oxygen to effuse through the membrane.
Rate of effusion:
It is known that rate of effusion of gases are inversely proportional to the square root of their molar masses. And, half of the helium (1.5 L) effused in 24 hour. So, the rate of effusion of He gas is calculated as follows:
[tex]\frac{1.5L}{24 hr} = 0.0625 L/hr[/tex]
Molar mass of He is 4 g/mol and molar mass of O is 32 g/ mol.
Thus,
[tex]\frac{\text{Rate of He}}{\text{Rate of O}}=\sqrt{\frac{32}{4} } =2.83[/tex]
or, Rate of O = [tex]\frac{\text{Rate of He}}{2.83} =\frac{0.0625L/hr}{2.83} =0.022L/hr[/tex]
This means that 0.022 L of gas effuses in 1 hr.
So, time taken for the effusion of 1.5 L of gas is calculated as follows:
[tex]\frac{1.5L}{0.022L/ hr} = 68.18hr[/tex]
Thus, we can conclude that it will take 68.18 hours for half of the oxygen to effuse through the membrane.
Find more information about Rate of effusion here:
brainly.com/question/10973414
