Question

It takes 36 seconds for 0.01 mole of He to diffuse
through a pinhoie in an effusion apparatus. It takes 144
seconds for 0.02 moles of gas X to diffuse through the
same apparatus. Find the root mean square velocity
of gas X at 25°C. ​

Answer 1

rate of diffusion , $r=\frac{n}{t}\propto \frac{1}{\sqrt{M}}$

where M is molecular mass and n is no of moles of gases,

or, $\frac{t_2}{t_1}=\frac{n_2}{n_1}\sqrt{\frac{M_2}{M_1}}$

here, t1 = 36s, t2 = 144s, n1 = 0.01mol, n2 = 0.02mol, M2 = X and M1 = 4g/mol

so, 144/36 = (0.02/0.01)√{X/4}

or, 4 = 2√{X/4}

or, X = 16g/mol = 16 × 10^-3 Kg/mol

now, Rms velocity = √{3RT/M}

here, R = 25/3, T = 25°C = 298K , M = 16g/mol

so, Rms velocity = √{3 × 25/3 × 298/16 × 10^-3}

= √{25000 × 298/16}

= 215.78 m/s

Answer 2

Answer:

hey bud answer is 215.78