Question

The ratio of rates of diffusion of gases X and Y is $1:5$ and that of Y and Z is $1:6$ . The ratio of rate of diffusion of Z and X is :
A. $1:30$
B. $1:6$
C. $30:1$
D. $6:1$

Answer 1

Hint: We know that gas particles have a tendency to diffuse because they have kinetic energy . The rate of diffusion is faster at high temperature as particles of gases have greater kinetic energy. Gases move from high concentration regions to low concentration regions. We can calculate the rate of diffusion by the formula ,rate of diffusion= amount of gas passing through an area unit of time.

Complete answer:
In the problem here it is given that the rate of diffusion of gas X and Y is 1: 5 and that of Y and Z is 1:6. Let assume that the rate of diffusion of X ,Y and Z are respectively \[{r_x},{r_y},{r_z}\] .
Now $\dfrac{{{r_x}}}{{{r_y}}} = \dfrac{1}{5}$ …….. equation (i)
       $\dfrac{{{r_y}}}{{{r_z}}} = \dfrac{1}{6}$ ………. equation (ii)
In the further process of getting the answer now we have to do some mathematical calculation so now we will multiply equation (i) and equation (ii).
$\dfrac{{{r_x}}}{{{r_y}}} \times \dfrac{{{r_y}}}{{{r_z}}} = \dfrac{1}{5} \times \dfrac{1}{6}$
$\dfrac{{{r_x}}}{{{r_z}}} = \dfrac{1}{{30}}$
Thus the ratio of diffusion of X gas to Z gas.

So the ratio of rate of diffusion of Z and X is $30 :1$, option C is the correct answer of this question.

Note: We know about the term diffusion which is a t movement of atoms or molecules from high concentration to low concentration .we have approached this problem easily as there is given in the problem that the ratio of rates of diffusion of gases X and Y is $1:5$ and that of Y and Z is $1:6$ so by doing some mathematical calculation we have found out the ratio of rate of diffusion between Z and X.