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In 2.00 min, $29.7 \mathrm{mL}$ of He effuse through a small hole. Under the same conditions of pressure and temperature, $10.0 \mathrm{mL}$ of a mixture of $\mathrm{CO}$ and $\mathrm{CO}_{2}$ effuse through the hole in the same amount of time. Calculate the percent composition by volume of the mixture.

$$\begin{array}{l}\% \mathrm{CO} \text { by volume }=54.4 \% \\\% \mathrm{CO}_{2} \text { by volume }=45.6 \%\end{array}$$

Chemistry 101

Chapter 5

Gases

University of Central Florida

University of Kentucky

University of Toronto

Lectures

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 we have a Graham's law of effusion problem. Um, the ratio of the, uh Moeller masses or or molecular masses is equal to the square of the ratio of the, uh, effusion speeds. And so we tested the infusion speed for helium, and it was 29 points of mill leaders in two minutes. And for a mixture of CEO and CO. Two was 10 milliliters in two minutes. And so notice that we've got the ah, helium and the denominator on one side and the numerator on the left to their inverse to each other. The A carbon compound CEO and carbon dioxide will have a greater mass, but it will have the lower speed Aziz we see here. And so the ratio of the speeds is almost 32.97 The square of that ratio is 8.82 that is equal to the ratio. Uh, the, um the massive of one of these average massive one of these carbon oxygen molecules over the mass of a helium molecule, which is the same as the ratio of there molar masses. So now multiplying both sides by the molar mass of the helium. I get the molar mass of the carbon compound. That CEO stands for both of the carbon oxygen compounds. Ah, is this factor times the mass, uh, the, uh of the helium. And again, this factor comes from the square of the ratio of disputes to take the ratio at which the ratio of the speed at which the healing diffuses divided by the speed at which the ah carbon oxygen mixture diffuses carbon monoxide, carbon dioxide and then square that multiplied by the molar mass of the helium. And you've got the average mass averaged for the number of molecules of CEO, which has ah Muller Massive 28 carbon dioxide, which has a miller massive 44. Some percent of that mixture is the carbon monoxide X and 100 minus exits. The rest of it, which is carbon dioxide and so multiplying the molar masses times their percentages should give the average molar mass tubs 100%. And when I solved through, I get 54% 54.4% carbon monoxide, 45.6% Carbon dioxide

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