"The M-B curves for isotopes are nearly identical because mass difference is small relative to absolute mass. However, the effusion rate depends on the inverse square root of mass. Over many stages, this tiny difference in the distribution's average velocity accumulates into measurable separation." Part 6: Common Extension Question 5 – The Effect of a Vacuum Question: The M-B distribution assumes molecules are independent (ideal gas). If you remove half the molecules (create a vacuum), does the distribution shape change? Why or why not? Answer Key Reasoning This is a trick question to test if students confuse distribution with total number .
| Extension Topic | Does M-B Curve Change? | What Changes the Rate? | | :--- | :--- | :--- | | Increase Temperature | Yes (Flattens, shifts right) | Higher fraction > (E_a) | | Add Catalyst | No | (E_a) decreases (threshold moves left) | | Reduce Pressure/Vacuum | No | Total collisions decrease, but distribution shape same | | Heavier Isotope | Yes (Peak shifts left) | Lower average speed reduces collision frequency |
Effusion rate depends on the average speed ((v_avg = \sqrt\frac8RT\pi M)). The small difference in mass leads to a small difference in average speed. "The M-B curves for isotopes are nearly identical
No, the shape does not change.
Use this guide to facilitate discussion, not just to provide answers. The power of POGIL is in the argument—let the students defend why the tail matters more than the peak. If you remove half the molecules (create a
"The fraction of molecules with sufficient energy is exquisitely sensitive to temperature because (E_a / RT) appears in the exponent. A 100K increase reduces the exponent magnitude, yielding a 150-fold increase in reactive collisions." Part 5: Common Extension Question 4 – Isotopes and Effusion Question: Consider two isotopes: (^235\textUF_6) and (^238\textUF_6) at the same temperature. Draw their M-B distributions. Why is the difference in average speeds small, but the difference in effusion rates significant? Answer Key Reasoning This connects the M-B distribution to Graham's Law of Effusion.
At the same (T), ( \frac12 m v^2 ) is constant on average. Heavier molecules ((^238\textUF_6)) have a lower most probable speed. The two curves overlap significantly but are shifted. | Extension Topic | Does M-B Curve Change
"A catalyst does not alter the Maxwell-Boltzmann distribution (the curve does not change). It lowers the activation energy threshold, so a larger fraction of the existing molecules have sufficient energy to react. Temperature changes the shape of the distribution curve itself." Part 4: Common Extension Question 3 – Fractional Distribution Calculations Question: Given that the fraction of molecules with kinetic energy greater than (E_a) is roughly ( e^-E_a / RT ), explain why a reaction with (E_a = 50 \text kJ/mol) proceeds very slowly at 300K but rapidly at 400K. (Use (R = 8.314 \text J/mol·K)). Answer Key Reasoning Students must perform a qualitative calculation to see the exponential effect.