Physical chemistry
This distribution curve has several important features. There are no molecules with zero energy and only a few with very high energies. There is also no maximum energy for molecules – the curve in Fig 1 approaches zero asymptotically at high energy. The most probable energy of a molecule corresponds to the maximum of the curve as indicated in Fig 2. Fig 2 Most probable and average energies
Number of molecules
Emp is the most probable – energy and E is the average energy
Emp
– E
Energy
Effect of temperature variation on the Maxwell–Boltzmann curve
Number of molecules
If the temperature of the sample is increased from T1 to T2, the average energy of the molecules increases, and the most probable energy of the molecules increases. The spread of energies also increases and the shape of the distribution curve changes as shown in Fig 3. For a fixed sample of gas, the total number of molecules is unchanged so the area under the curve remains constant (see also Collins Student Support Materials: A-Level year 1 – Inorganic and Relevant Physical Chemistry, section 3.1.6). The curve for the higher temperature, T2, is broader, has a lower peak and, apart from at the origin, is always to the right of the lower temperature curve, T1 T1
T2
Fig 3 Distribution of energies at two temperatures
The area under each curve, however, is the same because this represents the total number of molecules
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