Two 112-L tanks are filled with gas at 330 K. One contains 5.00 mol of Kr, and the other contains 5.00 mol of O 2 . Considering the assumptions of kinetic–molecular theory, rank the gases from low to high for each of the following properties. (d) Pressure

Alright, so inspect this problem. We have equal masses of 02 gas and H. I. Gas that are in separate containers but they have equal volumes and the same temperature. Which of the statements is truth. We're looking for a true statement. All right, so, the average kinetic energy of the H. I. Molecules is greater than that of 02 molecules. So because we are at the same temperature, both the 02 and H. I. Gas, they're going to have the same kinetic energy. So same average connect energy for both. So this is not true. The average velocity of the H. I. Molecules is greater than that of the 02 molecules. So when we're talking about velocity, we're going to say that the lighter the molecule is the faster is going to move. Okay, now, obviously for that, we just need to take a look at the molar masses of 02 and HI write so 02 oxygen by itself weighs 16 g. Right from the product table, but 16 times two is going to be 32. So smaller masses 32 g per mole. Okay, let's go ahead and compare that to H. I. So, hydrogen weighs 1.01g and um I dine Um I don't have the number. It is going to be 127-02 Or no, just 127 sorry, grams. So when we add that together, we get 100 and 28.1 g per mole. So that is the total molar mass of H. I molecules. So we can see that 02 is actually lighter. Right? So it's going to be moving faster. So it's average velocity is going to be larger. So H. I molecules will have smaller average velocity than that of 02 because 02 is lighter. So it's gonna be faster. So that makes be incorrect. Right? Alright. See the pressure in the H. I container is less than that in the 02 container. So here we need to take a look at the number of moles of each of these. Right? So we don't know the actual masses of 02 or H. I. But we know that they're equal masses. Right? So we can just pick any number. We can say one g, we can say 50 g. So let's say we have 50g of 02 and then we have 50 g of H. I. So it doesn't really matter what amount you pick. But we're just going to go ahead and find out what's the difference in the moles here. So if we go ahead and convert these grams into moles, we already found out the molar masses of each of these molecules. So in one mole Of 02 there are 32 g of 02. That will give me 1.563 moles Of 02. Never realized. You can use any numbers. As long as they're equal masses. Right? So if you picked a different number, it's okay. And then one mole of H I equals to 1 28 point oh one grams. And with this I get .391 moles of H I. Right, So we actually do have more molecules more moles of 02. So more moles of 02 here, which means that the pressure that the 02 is going to be exerting is going to be greater. Right? So the pressure of H of H. I concern is less. Yes, it's less because we have less moles of H. I. And that of 02 is going to be larger. Right? So this is going to be larger pressure. So C is correct. Yes, this one is true. Let's go ahead and take a look at the other ones. Both gasses will have equal pressures. We already said because C is correct. He cannot be correct because the pressure of the 02 container will be greater than that of the H. I container. And there are fewer 02 molecules than H. I molecules. So even though here we calculated the relative amount of moles of each, not the molecules. But if we were to use the avocados number and convert these moles into molecules which we're not going to do, we don't need that. We'll see that basically, you know, the more moles we're starting with the more molecules we're going to have. So because 02 here, we have more moles of it than of H. I. That means 02 will have more molecules, not fewer, but more. Okay, so that is incorrect. So are correct. Choice. Here is option C. Alright, thank you so much for watching.

Ch.10 - Gases: Their Properties & Behavior

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McMurry 8th Edition

Ch.10 - Gases: Their Properties & Behavior

Problem 108d

Chapter 10, Problem 108d

Two 112-L tanks are filled with gas at 330 K. One contains 5.00 mol of Kr, and the other contains 5.00 mol of O₂. Considering the assumptions of kinetic–molecular theory, rank the gases from low to high for each of the following properties. (d) Pressure

Verified step by step guidance

Identify the ideal gas law equation: \( PV = nRT \).

Recognize that both gases are in identical conditions: same volume (112 L), same temperature (330 K), and same number of moles (5.00 mol).

Understand that according to the ideal gas law, pressure \( P \) is directly proportional to the number of moles \( n \), temperature \( T \), and inversely proportional to volume \( V \).

Since both gases have the same \( n \), \( T \), and \( V \), the pressure \( P \) for both gases will be the same.

Conclude that the pressure of Kr and O₂ are equal, so they are ranked equally for pressure.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Kinetic-Molecular Theory

Kinetic-molecular theory explains the behavior of gases in terms of particles in constant motion. It posits that gas pressure results from collisions of gas molecules with the walls of their container. The speed and frequency of these collisions are influenced by temperature and the number of gas particles, which are crucial for understanding how different gases exert pressure.

Ideal Gas Law

The ideal gas law, represented as PV = nRT, relates the pressure (P), volume (V), number of moles (n), gas constant (R), and temperature (T) of a gas. This law helps predict how changes in one variable affect the others. In this scenario, since both tanks have the same volume and temperature, the pressure will depend on the type of gas and its molecular characteristics.

Molar Mass and Gas Behavior

Molar mass significantly influences the behavior of gases, particularly their speed and kinetic energy at a given temperature. Lighter gases, like Kr (krypton), will generally have higher average speeds than heavier gases, such as O2 (oxygen). This difference in molecular weight affects the frequency and force of collisions with the tank walls, thereby impacting the pressure exerted by each gas.