Describe how temperature ($T$) shifts the distribution curve of molecular speeds.
Describe how molar mass ($M$) affects the broadness and peak of the curve.
Visualize the fraction of particles possessing enough Activation Energy ($E_a$) to react.
Key Equations
\( v_{rms} = \sqrt{\frac{3RT}{M}} \)
Arrhenius (Reaction Rate):
\( k = A e^{-E_a/RT} \)
Why It Matters
Temperature is a macroscopic measure of average kinetic energy. However, individual molecules move at a wide variety of speeds. A reaction only occurs when colliding molecules surpass the $E_a$ threshold.
Probability Density Function $f(v)$ vs Speed $v$
$V_{rms}$ (Root-Mean-Square)515 m/s
Molecules $\ge E_a$ Threshold5.2%
Temperature ($T$) 300 K
Molar Mass ($M$) 28 g/mol ($N_2$)
Activation Energy ($E_a$ Velocity) 800 m/s
Rule of Thumb: Notice that the area under the curve is ALWAYS constant ($100\%$ of particles). If the curve flattens and stretches to the right, the peak probability must drop.
Quick Quiz
Why does an increase in Temperature dramatically increase the rate of reaction?