Question

At what tempreature would ethane molecules have the same r.m.s velocity as methane molecules at 27°C​

Answer 1

Given:

Methane molecules are at 27°C= 300K

To Find:

Temperature of ethane molecules = x =?

Solution:

We know the expression to calculate the r.m.s velocity,

  $v_{r.m.s} = \sqrt{\dfrac{3RT}{M} }$

where, $v_{r.m.s}$ = r.m.s velocity

            R = gas constant

            T = temperature

            M = molecular mass

now, molecular mass of ethane = 30

        molecular mass of methane = 16

Now, according to the question molecules of ethane at x temperature will have the same r.m.s velocity as molecules of methane at 300K

$\sqrt{\dfrac{3Rx}{30} } = \sqrt{\dfrac{3R\times300}{16} }$

squaring both sides

$\dfrac{3RX}{30} = \dfrac{3(300)R}{16}$

solving for x

x = 562.5K

Thus, the temperature of ethane molecules = 562.5K