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A vessel of volume 20 L contains a mixtu...

A vessel of volume `20 L` contains a mixture o hydrogen and helium at temperature of `27^(@)C` and pressure `2.0 atm` The mass of the mixture is `5 g`. Assuming the gases to be ideal, the ratio of the mass of hydrogen to heat of helium in the given mixture will be

A

`1 :2`

B

`2 : 3`

C

`2 : 1`

D

`2 : 5`

Text Solution

Verified by Experts

The correct Answer is:
D
Suppose there are `n_(1)` moles of hydrogen and `n_(2)` moles of helium in the given mixture. Then the pressure of the mixture will be
`P = (n_(1) RT)/(V) + (n_(2) RT)/(V) = (n_(1) + n_(2)) (RT)/(V)` (i)
`2 xx 101.3 xx 10^(3) = (n_(1) + n_(2)) ((8.3)(300))/(20 xx 10^(-3))`
`(n_(1) + n_(2)) = (2 xx 101.3 xx 3 xx 10^(3) xx 20 xx 10^(-3))/((8.3) (300)) = 1.62` (ii)
The mass of the mixture is (in grams):
`n_(1) xx 2 + n_(2) xx 4 = 5`
`(n_(1) + 2 n_(2)) = 2.5`
Solving Eqs. (i) and (ii), `n_(1) = 0.74, n_(2) = 0.88`
Hence `(m_(H))/(m_(He)) = (0.74 xx 2)/(0.88 xx 4) = (1.48)/(3.52) rarr 2 : 5`
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Knowledge Check

  • A vessel of volume 20L contains a mixture of hydrogen and helium at temperature of 27^(@)C and pressure 2 atm. The mass of mixture is 5g. Assuming the gases to be ideal, the ratio of mass of hydrogen to that of helium in the given mixture will be

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    `1:2`
    B
    `2:3`
    C
    `2:1`
    D
    `2:5`

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    B
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  • A vessel contains a mixture of nitrogen of mass 7 g and carbon dioxide of mass 11 g at temperature 290 K and perssure 1 atm.Find the density of the mixture.

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