Given:
Rate of diffusion of SO2 = 20 units
Time taken for diffusion of SO2 = 60 seconds

To find:
Volume of O2 diffused in 30 seconds

Approach:
We know that the rate of diffusion is inversely proportional to the square root of the molar mass of the gas. Therefore, the ratio of the rates of diffusion of two gases is given by the square root of the ratio of their molar masses.

Let's assume the molar mass of SO2 as M1 and the molar mass of O2 as M2.

From the given information, we can write the following equation:
Rate of diffusion of SO2 / Rate of diffusion of O2 = √(M2/M1)

We need to find the volume of O2 diffused in 30 seconds, which is directly proportional to the rate of diffusion.

Let's assume the volume of O2 diffused in 30 seconds as V.

From the above equation, we can write another equation:
Rate of diffusion of SO2 / Rate of diffusion of O2 = Volume of SO2 diffused / Volume of O2 diffused

Now, let's substitute the given values into the equations and solve for the volume of O2 diffused in 30 seconds.

Calculation:
Rate of diffusion of SO2 = 20 units
Time taken for diffusion of SO2 = 60 seconds
Rate of diffusion of O2 = ?
Volume of SO2 diffused = ?
Volume of O2 diffused = V
M1 = molar mass of SO2
M2 = molar mass of O2

Using the equation:
Rate of diffusion of SO2 / Rate of diffusion of O2 = √(M2/M1)

20 / Rate of diffusion of O2 = √(M2/M1)

Rate of diffusion of O2 = 20 / √(M2/M1)

Now, we know that the rate of diffusion is directly proportional to the volume of gas diffused.

Using the equation:
Rate of diffusion of SO2 / Rate of diffusion of O2 = Volume of SO2 diffused / Volume of O2 diffused

20 / Rate of diffusion of O2 = Volume of SO2 diffused / V

Volume of O2 diffused = V = (20 / Rate of diffusion of O2) * Volume of SO2 diffused

V = (20 / (20 / √(M2/M1))) * Volume of SO2 diffused

V = √(M2/M1) * Volume of SO2 diffused

Now, we need to find the ratio of the molar masses of O2 and SO2.

Molar mass of O2 = 32 g/mol
Molar mass of SO2 = 64 g/mol

M2/M1 = 32/64 = 1/2

Substituting this value into the equation:

V = √(1/2) * Volume of SO2 diffused

V = (√1 / √2) * Volume of SO2 diffused

V = (1 / √2) * Volume of SO2 diffused

Given that the volume of SO2 diffused in 60 seconds is 20 units, we can write:

Volume of SO2 diffused = 20

V = (1 / √2) * 20

V = (1