Consider the plot below, which shows the relative number of gas particles with a particular speed. The container with "A" and the container with "B" are distinct, but connected by a valve (initially closed) that can be opened to allow the gases to mix.

Based on your understanding of the Maxwell-Boltzmann equation, which of the following statements is TRUE?

Question

Consider the plot below, which shows the relative number of gas particles with a particular speed.  The container with "A" and the container with "B" are distinct, but connected by a valve (initially closed) that can be opened to allow the gases to mix.

Based on your understanding of the Maxwell-Boltzmann equation, which of the following statements is TRUE?

BlackTom AI · Accepted Answer

We begin by restating the setup: two distinct containers, A and B, hold gases with their own MB speed distributions. The valve is closed initially, and we are asked about what happens when it is opened, considering Maxwell–Boltzmann behavior.
Option 1: None of the others is true. This would be selected if every other statement were clearly false. To evaluate that, we must examine each of the other claims in turn rather than assuming all are incorrect.
Option 2: If the two containers were at the same temperature and the valve were opened, the two curves would merge into one average curve, with a similar shape. This hinges on the fact that equal temperatures lead to equal translational energy distributions characterized by the same MB form parameter (temperature) for each gas. When mixing occurs at equal T, energy is redistributed until a common temperature is reached; the velocity (or speed) distributions for each species become MB distributions at that common temperature. The total speed distribution of the mixture is a weighted sum of the two MB distributions (weighted by mole or particle fractions). If the temperatures are equal, this combined distribution resembles an average of the two original curves and retains the general MB shape, differing mainly by the weights and the specific mass-dependent spread. In other words, the two curves do not remain isolated; they superimpose into a single, temperature-adjusted mixture distribution with a shape that remains MB-like, governed by the shared temperature.
Option 3: If A and B have the same molar mass, then A is at a higher temperature. This is not implied by equal molar masses. Temperature and mass influence the MB distribution differently: equal molar masses do not force one container to be hotter than the other; the temperature is an independent parameter. Therefore this statement is not necessarily true.
Option 4: If the two containers were at the same temperature then the plot would look the same, even if the gases were allowed to mix together by opening the valve. This ignores the fact that mixing two different gases changes the overall speed distribution to a sum of two MB distributions with the same temperature but potentially different mass-dependent spreads. Therefore, the combined distribution would differ in shape (as a weighted sum) from either original curve alone, so this claim is not correct in general.
Option 5: If the two containers are at the same temperature then molecule B is more massive than molecule A. Mass alone does not determine temperature equality; equal temperatures do not imply a mass ordering. The statement asserts a relationship between mass and temperature that is not warranted by the given setup, making it incorrect.

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