Question

If the K.E of hydrogen is 151.91J at the pressure of 1 atmosphere, then its volume is a) 3 litre b) 2 litre c) 1 litre d) 0.5 litre​

Answer 1

Answer:

1Litre.

it is given that, kinetic energy of hydrogen = 151.91 J at pressure of 1 atmosphere.

we have to find its volume.

according to kinetic theory of gases,

kinetic energy of hydrogen is given by, K.E = 3/2 nRT

from gas equation, PV = nRT

so, K.E = 3/2 PV

now, putting K.E = 151.91 J, P = 1atm = 1.013 × 10^5 N/m²

so, 151.91 J = 3/2 × (1.013 × 10^5 N/m²) × V

or, V = (151.91 × 2)/(3 × 1.013 × 10^5) m³

= 99.97 × 10^-5 m³ ≈ 10^-3 m³

we know, 1 m³ = 1000Litres

= 10^-3 × (1000Litres )

= 1Litres

so, volume of hydrogen is 1Litre.

[note : here it is not clear that kinetic is given of hydrogen atom or hydrogen molecules. in this situation we should use hydrogen atom. or if options are given then you should check which one is preferred. ]

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Answer 2

1 Litre

Explanation:

Kinetic Energy of Hydrogen KE = 151.91 J

Pressure P = 1 atm = 1.013 × 10⁵ N/m²

Kinetic Energy of an ideal gas is given by

KE=\frac{3}{2}nRT

but we know that from Ideal Gas Equation

PV=nRT

Therefore, the Kinetic Energy of a gas can be written as

KE=\frac{3}{2}PV

or, V=\frac{2}{3} \times\frac{KE}{P}

Putting the values we get

V=\frac{2}{3} \times\frac{151.91}{1.013\times10^{5}}

or, V=\frac{99.97}{10^{5}} m³

or, V=\frac{99.97}{100} L

or V ≈ 1 Litre

Therefore, the volume of the hydrogen is 1 Litre

Hope this help you