Identify the correct labels of A, B and C in the following graph from the options given below : Root mean square speed (Vrms) ; most probable speed (Vmp); Average speed (Vav)
CRMS > CAvg > CMPS
This graph shows the distribution of molecular speeds in a gas at a given temperature. The curve is not symmetric; it peaks at a certain speed and has a tail towards higher speeds. Three important speeds are marked: A (leftmost peak), B (middle), and C (rightmost).
For any gas at a given temperature, the three characteristic speeds always follow this order:
This means the Most Probable Speed (Vmp) is the smallest, followed by the Average Speed (Vav), and the Root Mean Square Speed (Vrms) is the largest.
The peak of the distribution curve (its highest point) corresponds to the Most Probable Speed (Vmp). This is the speed possessed by the largest number of molecules. Therefore, point A, which is at the peak of the curve, must be Vmp.
Since Vrms is the largest speed, it will be the farthest to the right on the speed axis. Therefore, point C must be Vrms.
By process of elimination, the remaining point B in the middle must be the Average Speed (Vav).
We have determined:
Now, let's find which option matches this conclusion: A – Vmp ; B – Vav ; C – Vrms
The correct labeling is: A – Vmp ; B – Vav ; C – Vrms
These speeds are calculated using the following formulae (where R is the gas constant, T is the temperature, and M is the molar mass of the gas):
Most Probable Speed:
Average Speed:
Root Mean Square Speed:
The distribution has a longer "tail" towards higher speeds. This asymmetry means the average is pulled to a value higher than the most probable value. The RMS speed, which squares the values before averaging, is even more sensitive to these higher speeds and thus is the largest of the three.