Question

rms speed of so2 molecule at 400k is equal to RMS speed of ch4 at

Answer 1

See this and check whether it is correct or not

Answer 2

Given:

The RMS speed of SO₂ at 400 K = The RMS speed of CH₄ at some temperature T

To Find:

The temperature T

Solution:

The RMS speed of SO₂ at 400 K is equal to the RMS speed of CH₄ at 100 K.

The RMS or the root mean square speed of gas of molecular mass M at temperature T is given by the formula:

Vrms = $\sqrt{\frac{3RT}{M} }$

Here, R is the universal gas constant

Since R and 3 are constants,

⇒ Vrms ∝ √(T/M)    - (1)

The molecular mass of SO₂ = 1 X Molecular mass of S + 2 X Molecular mass of O

= 32 + 2 X 16

= 64g

Similarly, the molecular mass of CH₄ =  1 X Molecular mass of C + 4 X Molecular mass of H

= 12 + 4 X 1

= 16g

Substituting in relation 1,

Vrms of SO₂ ∝ √(400/64)

and

Vrms of CH₄ ∝ √(T/16)

Dividing the above two proportionalities,

$\frac{Vrms of SO_2}{Vrms of CH_4} =\sqrt{\frac{400X16}{64XT} }$

= √(100/T)

Since according to the question Vrms of SO₂ = Vrms of CH₄

⇒ √T = √100

or T = 100 K