A flask at room temperature contains exactly equal amounts...

A flask at room temperature contains exactly equal amounts (in moles) of nitrogen and xenon. \begin{equation} \begin{array}{l}{\text { a. Which of the two gases exerts the greater partial pressure? }} \\ {\text { b. The molecules or atoms of which gas have the greater average }} \\ {\text { velocity? }} \\ {\text { c. The molecules of which gas have the greater average kinetic }} \\ {\text { energy? }} \\ {\text { d. If a small hole were opened in the flask, which gas effuses }} \\ {\text { more quickly? }}\end{array} \end{equation}

A flask at room temperature contains exactly equal amounts (in moles) of nitrogen and xenon.
\begin{equation}
\begin{array}{l}{\text { a. Which of the two gases exerts the greater partial pressure? }} \\ {\text { b. The molecules or atoms of which gas have the greater average }} \\ {\text { velocity? }} \\ {\text { c. The molecules of which gas have the greater average kinetic }} \\ {\text { energy? }} \\ {\text { d. If a small hole were opened in the flask, which gas effuses }} \\ {\text { more quickly? }}\end{array}
\end{equation}

Key Concepts

Graham's Law of Effusion

Graham's law of effusion states that the rate of effusion of a gas is inversely proportional to the square root of its molar mass. This means that, under identical conditions, lighter gases effuse more rapidly than heavier gases because their molecules move faster on average. Consequently, in a situation where a small hole is opened in a container, the lighter gas will escape the container at a quicker rate than the heavier gas.

Maxwell-Boltzmann Distribution and Molecular Speeds

The Maxwell-Boltzmann distribution describes the spread of speeds among gas molecules in a sample. The root-mean-square speed, which is a measure of the average molecular speed, depends on the mass of the gas molecules, being given by the expression sqrt(3RT/M). Lighter molecules, such as nitrogen, will have a higher average (and RMS) speed compared to heavier molecules like xenon when measured at the same temperature.

Kinetic Molecular Theory and Average Kinetic Energy

According to kinetic molecular theory, at a given temperature all gases have the same average kinetic energy per molecule, given by (3/2)kT. This is because temperature is a measure of the average kinetic energy, regardless of the mass of the gas molecules. Therefore, under identical conditions, molecules of both nitrogen and xenon possess the same average kinetic energy.

Ideal Gas Law and Partial Pressures

The ideal gas law (PV = nRT) relates pressure, volume, temperature, and the number of moles of gas. In a mixture containing equal moles of different gases at the same temperature and volume, each gas contributes equally to the overall pressure. Thus, the partial pressure of each gas is directly related to its number of moles, independent of the gas's identity, resulting in equal partial pressures for each gas in the mixture.

Transcript

00:01 Question 82.

00:04 A flask at room temperature contains exactly equal amount in mole of nitrogen and xenon.

00:15 So you can say more of nitrogen equals to more of zero.

00:24 And then the first question asks, which of the gases exert is greater pressure pressure? so which of the gas is exactly the pressure? because they have equal mode it will exact equal pressure pressure you know if you want to calculate partial pressure you will take let's say partial pressure of nitrogen is going to be more ratio of nitrogen multiplied by total pressure and more than the ratio of nitrogen will be more of nitrogen over total mode that is mold of nitrogene n2 plus more of z -a than total pressure partial pressure of xenon will be more ratio of xenon more fraction of genome by the partial pressure which will be more of xenom over more of nitrogen plus more of you know, partial pressure.

02:07 We don't need to do any capital because we know that all of nitrogen that already wrote here equals to more of, you know, so the way have equal, they will equal pressure pressure.

02:30 This is a deep part which molecule atom of regard how the, the greater average velocity.

02:41 So to find average, velocity i will use the formula for finding root mean square velocity you root mean square velocity that is u rm is a kind of afraid velocity so u rm is equals 3 r t divide 5 n a times f this is abogados number this is the mass of one particle and it's going to be equal to 3 rt divided by m where m equals to molar mass where m is equal to mulam so this kind of equation sometimes we don't really need to do some calculation we just need to look at the formula and see the follow and just you don't really need the exact answer so i will do root main square if i let me calculate for for nitrogen urms with a square root of 3rt divided by the molar mass of nitrogen will be 14 times to that is 28 gram per move i can confirm it to kilogram or whatever let me just write 28 so for zeno you are a mess with this carot of 3 r2 divided by zeno when i check my i'm checking my priority table okay the personal the mulla mass is 131 .291 131.

05:26 Point to nine so because the denominator here is lower so for nitrogen we have a yeah this is lower it's like less let's assume you have something like two divided by one and two defined by 30 so this is two this is like zero point something this is lower so nitrogen has higher afric velocity.

06:22 Nitrogen has higher afresh velocity.

06:31 And the next part which is afresh kinetic energy.

06:40 See, afrika kinetic energy...

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