Question

at 300 C, Vrms of H2 is same as Vrms of O2 at T (in kelvin)​

Answer 1

Find the temperature at which oxygen molecules would have the same rms speed as hydrogen molecules at 300K.

The value of temperature (T) is 4800 K.

Given:

At 300 k, Vrms of H2 is the same as Vrms of O2 at T (In kelvin).

To Find:

The value of temperature (T).

Solution:

To find the temperature T we will follow the following steps:

As we know,

According to the kinetic theory of gases molecules in gas has different kinetic energy as they move at different speed and their speed depends upon the temperature and mass. But some molecules have the most probable speed some move by average energy and some by root mean square speed.

So,

The formula for root mean square velocity =

$\sqrt{ \frac{3rt}{m} }$

So,

Velocity is directly proportional to temperature and inversely proportional to mass.

$\frac{t1}{m1} (for \: h2) = \frac{t2}{m2} (for \: O2)$

According to the question:

T1 = 300 k

t2 = T

The molecular mass of hydrogen gas = m1 = 2 g

The molecular mass of oxygen gas = m2 = 32g

Now,

Putting values we get,

$\frac{300}{2} = \frac{T}{32}$

$T = \frac{300}{2} \times 32 = 300 \times 16 = 4800K$

Henceforth, the value of temperature (T) is 4800K.

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