The , however, are where the magic happens. These questions push students to connect the molecular distribution to macroscopic observables like reaction rates, temperature dependence, and catalysis.
Using ( v_p = \sqrt\frac2RTM ) — but here we use ( R = 8.314 , J/(mol·K) ) and mass in kg/mol. Molar mass of soccer ball = ( 0.43 , kg \times 6.022 \times 10^23 = 2.59 \times 10^23 , kg/mol ). The , however, are where the magic happens
Students often mistakenly think the peak simply moves right and up. In reality, because the total area (number of molecules) is constant, the curve must "spread out." To maintain the same area, the curve must flatten. Mathematically, the most probable speed ( v_p = \sqrt\frac2RTM ) increases with T. However, the peak height is proportional to ( \frac1\sqrtT ), meaning it drops as temperature rises. Question 3: The Activation Energy (Ea) Barrier Prompt: Draw a vertical line on the M-B distribution representing the activation energy (Ea). For a reaction at 300 K, the fraction of molecules with energy > Ea is represented by the tail area. If you increase the temperature to 350 K, does the area of the tail (E > Ea) increase or decrease? Molar mass of soccer ball = ( 0
The area under the Maxwell-Boltzmann distribution curve represents the total number of molecules (N) in the system. The problem states we are comparing the same sample of gas at two different temperatures. While the shape of the curve flattens and broadens at higher temperatures, the total count of molecules does not change. Therefore, the area under both curves must be identical. Question 2: The Shift of the Peak Prompt: As temperature increases, what happens to the peak of the curve? Why does this violate a simple "shift to the right" explanation? Mathematically, the most probable speed ( v_p =
[ v_p = \sqrt\frac2(8.314)(300)2.59 \times 10^23 \approx \sqrt1.93 \times 10^-20 \approx 1.39 \times 10^-10 , m/s ]
Below, we provide a detailed answer key and, more importantly, the reasoning behind the answers for typical POGIL extension questions. Question 1: The Area Under the Curve Prompt: Compare two curves on the same graph: Curve A (T1 = 300 K) and Curve B (T2 = 400 K). The area under Curve A is 100 units. What is the area under Curve B? Explain.