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An equimolar mixture of $\mathrm{H}_{2}$ and $\mathrm{D}_{2}$ effuses through an orifice (small hole) at a certain temperature. Calculate the composition (in mole fractions) of the gases that pass through the orifice. The molar mass of $\mathrm{D}_{2}$ is $2.014 \mathrm{g} / \mathrm{mol}$.

$$x_{\mathrm{H}_{2}}=0.587 ; x_{\mathrm{D}_{2}}=0.413$$

Chemistry 101

Chapter 5

Gases

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05:03

In physics, a gas is one of the three major states of matter (the others being liquid and solid). A gas is a fluid that does not support tensile stress, meaning that it is compressible. The word gas is a neologism first used by the early 17th-century Flemish chemist J.B. van Helmont, based on the Greek word ("chaos"), the simplest of all the elemental forms of matter.

04:46

In physics, thermodynamics is the science of energy and its transformations. The three laws of thermodynamics state that energy can be exchanged between physical systems as heat and work; that the total energy of a system can be calculated by adding up all forms of energy in the system; that energy spontaneously flows from being localized to becoming dispersed, spread out, or uniform; and that the entropy of an isolated system not in equilibrium will tend to increase over time, approaching a maximum value at equilibrium.

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so Graham's law for diffusion and effusion. I like to use it in the, uh, squared for him rather than the square root form, and it says that the ratio of the speed squared will be equal to the inverse of the ratio of the masses. And so, if B is the deuterium, ah, then the massive deuterium is about to, and that means a is hydrogen and its mass well. A ratio of 21 H two has a massive two and D two has a massive poor. Anyway, it's a 2 to 1 ratio for the masses. Ah, and so then multiplying both sides by the square of the That's the root mean square speed, the square of the speed of the D two. That's also the infusion rate Ah, and then taking the square root of both sides at this point to get the ratio than you come up with. The speed at which the hydrogen is if using, is 1.41 times the speed at which the deuterium is diffusing. And so for every 100 molecules of deuterium that moved through the hole through which the leaking occurs. 141 of hydrogen will go through. And so the mole fraction of hydrogen is 1.4 1/2 0.41 about 0.5 87 and the rate for the wealthy a mole fraction for the hydrogen deuterium based on the rate is 1.0 0/2 0.41 or about 0.413

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