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Standard XII

Chemistry

Relating Translational KE and T

The kinetic e...

Question

The kinetic energy of $N$ molecules of $O_{2}$ is $x$ joule at $- 123^{o} C$ . Another sample of $O_{2}$ at $27^{o} C$ has a kinetic energy of $2 x$ . The later sample contains ____________ molecules of $O_{2}$ .

N

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N / 2

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2 N

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3 N

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Solution

The correct option is A $N$
As we know, $K . E . = \frac{3}{2} n R T$
Now,
$x = \frac{3}{2} n R T = \frac{3}{2} \times \frac{N}{N_{A}} \times R \times 150$ ---- 1
$2 x = \frac{3}{2} R T = \frac{3}{2} \times \frac{N^{'}}{N_{A}} \times R \times 300$ ---- 2

From eqn. 1 and 2 we get,

$N^{'} = N$

So, later sample contains $N$ molecules of $O_{2}$

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The kinetic energy of N molecules of O2 is x joule at −123oC. Another sample of O2 at 27oC has a kinetic energy of 2x. The later sample contains ____________ molecules of O2.

The correct option is A NAs we know, K.E.=32nRT Now,x=32nRT=32×NNA×R×150 ---- 12x=32RT=32×N′NA×R×300 ---- 2From eqn. 1 and 2 we get,N′=NSo, later sample contains N molecules of O2

The kinetic energy of $N$ molecules of $O_{2}$ is $x$ joule at $- 123^{o} C$ . Another sample of $O_{2}$ at $27^{o} C$ has a kinetic energy of $2 x$ . The later sample contains ____________ molecules of $O_{2}$ .