Introduction:
In order to determine the temperature at which the root mean square velocity (Urms) of SO2 is equal to the average speed of O2 at 27 degrees Celsius, we need to apply the principles of kinetic theory of gases. This theory states that the average kinetic energy of gas molecules is directly proportional to the temperature of the gas.

Understanding Urms and Average Speed:
Before proceeding, let's understand the concepts of Urms and average speed.

- Urms (Root Mean Square Velocity): It is the measure of the typical speed of gas molecules in a sample. It is calculated using the formula:
Urms = sqrt(3RT/M)
where R is the gas constant, T is the temperature in Kelvin, and M is the molar mass of the gas.

- Average Speed: It is the average of the speeds of all the gas molecules in a sample. It is calculated using the formula:
Average Speed = sqrt(8RT/πM)

Determining the Temperature:
To find the temperature at which Urms of SO2 equals the average speed of O2 at 27 degrees Celsius, we need to equate the two formulas mentioned above and solve for T.

1. Convert the temperature of 27 degrees Celsius to Kelvin:
T (Kelvin) = 27 + 273.15 = 300.15 K

2. Substitute the values into the formulas for Urms and average speed:
Urms(SO2) = sqrt(3RT/M(SO2))
Average Speed(O2) = sqrt(8RT/πM(O2))

3. Equate the two expressions and solve for T:
sqrt(3RT/M(SO2)) = sqrt(8RT/πM(O2))

4. Square both sides of the equation to eliminate the square roots:
3RT/M(SO2) = 8RT/πM(O2)

5. Cancel out the common terms and rearrange the equation:
M(O2)/M(SO2) = 8/3π

6. Substitute the molar masses of O2 and SO2:
32/64 = 8/3π

7. Simplify the equation and solve for π:
π = 8/6 = 4/3

8. Substitute the value of π back into the equation to find the temperature:
32/64 = 8/3(4/3)
1/2 = 8/12
1/2 ≠ 2/3

Conclusion:
After solving the equation, we find that the temperature at which the Urms of SO2 is equal to the average speed of O2 at 27 degrees Celsius cannot be determined. The molar masses of SO2 and O2 do not satisfy the equation, indicating that the temperatures at which their Urms and average speeds are equal do not coincide.