Gaseous compound Q contains only xenon and oxygen. When 0.100 g of Q is placed in a 50.0-mL steel vessel at 0 °C the pressure is 0.229 atm. (b) When the vessel and its contents are warmed to 100 °C, Q decomposes into its constituent elements. What is the total pressure, and what are the partial pressures of xenon and oxygen in the container?

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Hi everyone. This problem reads Xenon tetra fluoride is a gaseous compound that only contains flooring and xenon a 100 mL steel vessel filled with 1000.283 g of xenon tetra fluoride has a pressure of 0.178 atmospheres at zero degrees Celsius. Xenon tetra fluoride breaks down into its component parts. When the vessel is heated up to 117 degrees Celsius. What are the partial pressures of xenon and flooring in the container as well as the total pressure. So the question that we want to answer here is the partial pressures of xenon and flooring as well as the total pressure. Okay, because we're dealing with gasses here, we want to write out our reaction, Okay, So as we write out our reaction, we see that xenon Tetra fluoride breaks down into xenon gas plus fluoride gas. Okay. And what we want to do here is calculate the total amount of moles. Okay. And so we need to write out the ideal gas law and the ideal gas law is pressure times volume is equal to the total number of moles times gas constant. R times temperature. So because we want to calculate the total moles, we need to isolate the variable end. So let's go ahead and divide both sides by R. T. And when we do that we get n which is our moles is equal to P. V. Over R. T. So for us to calculate our total moles, let's go ahead and write out what's given in the problem. So P represents pressure and we're told the pressure is 0.178 atmospheres V is volume. We're told that the volume is milliliters. Okay, Are is a gas constant and that is 0.8 to 06 leaders. Atmosphere over mole kelvin And T is temperature. And in the problem we're told the temperature is 0°C. So looking at our our constant, we see the units that we need, we see that the volume is in leaders and the temperature is in Kelvin. So we need to convert our volume and our temperature. Okay. So we need to convert our middle leaders to leaders. Okay. And so in one leader there's 1000 ml. And so our volume is 0.1 leaders. And for our temperature we need to add 273 to get it in Kelvin. So we have 273 Kelvin. Alright, so now that we have all of our our units, let's go ahead and plug in our values. So we get 0. Atmospheres time. 0.1 leaders over 0.8 to Leaders, atmosphere over mole Calvin times 273 Calvin. So our total moles. Once we do this calculation is 0. moles. So this is our total number of moles. However, we want to calculate the total number of moles after decomposition. Alright, so let's go ahead and right here after decomposition. We want to know how many moles of xenon tetra fluoride and how many moles of fluoride. Okay. Or we want to know how many moles of xenon and how many moles of flooring that's in the container. So we're going to start off with what we're given. All right. So we just solved for the total moles. So that's going to be our starting point. Okay, so we have 0. moles total moles of xenon tetra fluoride. Our goal here is to go from moles of xenon tetra fluoride, two moles of xenon. And we're going to do the same thing for flooring. We're going to go from moles of xenon tetra fluoride to Mosul flooring. So let's go ahead and figure this out for both. Okay, so we want to go from moles of xenon toucher fluoride, two moles of xenon. So we're going to look at the mole to mole ratio. Looking at our balanced equation, we see that for every one mole of xenon tetra fluoride consumed, one mole of xenon gas is produced. So this is a 1 to 1 mole ratio. So we're right back here for every one mole of xenon toucher fluoride consumed, one mole of xenon gas is produced. So our units of moles of xenon tetra fluoride cancel. And we're left with moles of xenon. Once we do this calculation, we get 0. moles of xenon. So let's go ahead and do the same thing but figure out our moles of flooring gas. So we're going to start off with our total moles 0. moles of xenon tetra fluoride. And we want to go from moles of xenon tetra fluoride. two moles of flooring gas. Okay, so let's go ahead and do this. All right. So when we look at our equation, we see for every one mole of xenon tetra fluoride consumed two moles of flooring gas is produced. So our moles of Xenon touch of fluoride cancel. And we're left with moles of flooring gas. When we do this calculation we get 0. moles of flooring gas. Okay, so now that we know the amount of moles that we have for each after decomposition, we can use the ideal gas law again, PV equals N R T. Now we're going to solve for the partial pressures for both. Okay, so the variable that we want to isolate is the pressure. So let's go ahead and divide both sides by volume and we're going to get pressure is equal to N R. T over V. This is what we're going to use to solve for partial pressure. So our partial pressure for Xenon is going to equal N R T over V. Okay, so we just saw for our moles of xenon. And we said that our modes of Xenon is zero moles times R is 0.8 to 06 leaders. Atmosphere over mole kelvin. And our temperature is Now we're going to look at the temperature afterwards after decomposition. We're told that the temperature is 117°C. So we need to take 100 degrees Celsius, 117° C. Excuse Me. So, we're going to take 117°C. And remember we're going to add 273. Okay. And then this is going to be divided by the volume which is 0.1 leaders. All right. So once we do this calculation, we get the pressure of Xenon gas is equal to 0. atmospheres. Okay, so that's our first answer. Okay. And we're going to calculate the partial pressure of our flooring gas. Okay, So our partial pressure for our flooring gas. If we look at the multiple ratio, we see that it's going to equal two times the partial pressure of our xenon gas. So we're going to take two times the value. We just calculated for Xenon which is 0.2543 atmospheres. And we're going to get that the partial pressure of our flooring gas is equal to 0. atmospheres. Okay, so that's the partial pressure for our flooring gas. And lastly it asked for the total partial pressure. So our total partial pressure is going to equal the sum of these two. Okay, so we're going to write p total Is equal to the partial pressure of our xenon gas plus the partial pressure of our flooring gas. So this is going to equal 0. atmospheres plus 0.5086 atmospheres. And we'll see that P total Is equal to 0.76 - nine atmospheres. Okay, so that is our final answer for everything in this problem. Those are the partial pressures of xenon and flooring in the container as well as the total pressure. That is the end of this problem. I hope this was helpful.

Verified Solution

Key Concepts

Ideal Gas Law

Decomposition Reactions

Dalton's Law of Partial Pressures