Chemical explosions are characterized by the instantaneous release of large quantities of hot gases, which set up a shock wave of enormous pressure (up to 700,000 atm) and velocity (up to 20,000 mi/h). For example, explosion of nitroglycerin 1C3H5N3O92 releases four gases, A, B, C, and D:
n C3H5N3O91l2¡a A1g2 + b B1g2 + c C1g2 + d D1g2
Assume that the explosion of 1 mol (227 g) of nitroglycerin releases gases with a temperature of 1950 °C and a volume of 1323 L at 1.00 atm pressure.
(d) When gases C and D were passed through a hot tube of powdered copper, gas C reacted to form CuO. The remaining gas, D, was collected in a third 500.0-mL flask and found to have a mass of 0.168 g and a pressure f 223 mm Hg at 25 °C. How many moles each of C and D were present, and what are their likely identities?

Question

Accepted Answer

Hi everyone. This problem reads at high temperatures, ammonium nitrate undergo spontaneous explosion that can have a detonation velocity of up to 6000 mph. The equation shown is proposed as the predominant detonation reaction, wherein three gasses, X, y and Z are released, assume that when one mole of ammonium nitrate explodes, 624 liters of gas is at 1900 degrees Celsius and one atmosphere pressure is released considering the following analysis done when 10.5 moles of ammonium nitrate undergoes explosion And we have 1, 2 and three analysis. Okay, so the question is asking us to calculate the molds of X, Y and Z present and determine their identities. So this is what we want to determine. We're going to calculate the molds of X, Y and Z present and determine their identities. So let's go through the problem and take a look at what we're given. Okay, so we know we have one mole of ammonium nitrate. Okay? And We have 0.0050 moles of ammonium nitrate. And then with the analysis given, we have 250 ml flask, we have negative 15°C and we have 483 mm of mercury. And we also have 250 millimeter flask. We have 1.401 g and 374 millimeters of mercury at 27 degrees Celsius. So this is some information that we just want to highlight as some of our Gibbons. Okay, so the first step that we're going to want to do with this problem in order to calculate the molds of X, Y and Z. We need to calculate the two total moles of gas released for one mole of ammonium nitrate. So this first thing that we highlighted here, this one mole of ammonium nitrate. We're going to calculate the total moles of gas released from it. And the way that we're going to do that is we're going to use the ideal gas law PV equals N. R. T. And so because we want to calculate total moles that is represented by N. So let's go ahead and isolate that variable by dividing both sides by R. T. So we get N. Which is the number of moles is going to equal P V pressure times volume over r gas constant times T temperature. Okay, so in the problem we know that the temperature is 1900°C. That's what we Underlined for that one mole of ammonium nitrate. It's 1900°C. So let's go ahead and highlight that in the same color. So we need to convert that temperature to kelvin. Okay, because our gas constant R is in the unit of kelvin. Alright, so temperature is equal to 1900 degrees Celsius plus 273. That's how we go from, It's 273.15. Excuse me. So this is how we go from C to Kelvin. So once we do that calculation, our temperature in Kelvin is going to equal 2173. Kelvin. Okay, and we know what the pressure is, We know what the volume is. R gas constant, R is a constant and we know what the temperature is. So let's go ahead and plug in all of our values. Okay, so the pressure is one atmosphere. Okay? The volume is 624. No leaders. Okay or excuse me? Leaders. 624 leaders. So we can go ahead and highlight that as well. And this is all over R times T R is the gas constant. We should have memorized 0.8 to leader times atmosphere over more times Calvin. Okay. And our temperature we converted to 2,173. Kelvin. Okay, so once we do that calculation we get N is equal to 3.50 moles of gasses. Okay, so that is the total moles of gas is released for one mole of ammonium nitrate. So that was step one, Step two is now we're going to calculate the total moles of gas is released for 0.005 moles of ammonium nitrate. So that is where we see that Right here. So this 0.005 moles of ammonium nitrate. Now we're going to calculate the total moles of gas is released from that. Alright, so Under our 3.50 more gasses, I'm going to write this is the total moles for one mole of ammonium nitrate. Okay, so now we're going to calculate the total moles from 0.005. Alright, so we're going to have and total is equal to So we're going to start off with that 0. moles of ammonium nitrate. And we want to go from moles of ammonium nitrate, two moles of gas is okay, so we're going to use that conversion that we just solved for. Okay, because we needed to know the molds of gasses so now we know that in one mole of ammonium nitrate there's 3.5 moles of gas is so that's the conversion we're going to use so and one more of ammonium nitrate, there is 3. moles of gas is okay, so making sure our units cancel properly here, you can see that our molds of ammonium nitrate cancel and we're left with moles of gas is okay, so once we do that calculation we get 0. more of gasses. Okay, so this is the Alright underneath total malls four 0. moles of ammonium nitrate. Alright, so now what we're going to do is we're going to calculate the molds of remaining gasses. Alright, so this is step three so I write the numbers, so this was step one, let me write it in a different color. Okay, alright, it in black. This is step one. This was step two. Now step three is going to be to calculate the moles of remaining gasses and those remaining gasses are why? And z. So we're going to calculate the moles for that and we're going to use the same equation. So n is equal to P V over R. T. Okay, so the temperature now we're going to go to Part one. So the temperature is negative 15°C. Okay, we're going to convert that to Kelvin. The pressure is 483 mm of mercury and the volume is 250 ml. Okay, so we're looking at the analysis in part one and those are the values that we're going to use. All right, so let's go ahead and And plug those values in. But we need to first convert them to the appropriate units. So we know that temperature needs to be in Kelvin. So temperature is negative 15°C. And we're going to add 273.15 to convert it to Kelvin. So when we convert it, it's 258.15 Kelvin. Now for pressure, the pressure for part one of the analysis was mm of mercury. Our unit needs to be an atmosphere. So we need to convert this from mm of mercury to atmospheres. Okay, so that conversion is in one atmosphere, there is 760 of mercury. So we need to make sure our units cancel properly mm of mercury cancel and we're left with atmospheres. So once we do that calculation we get 0. atmospheres. And lastly our volume is given in milliliters. So we have 250 mL. But we need this unit. And leaders, all of the units were converting because our gas constant r. Remember is leaders atmosphere over mole times kelvin. Okay. And so we need everything to match. So we're going to take we're going to use the conversion and one millimeter There is 10 to the -3 leaders. Okay, so we get 0. zero leaders. Okay, so middle leaders cancel and we're left with leaders. Now we have everything that we need to plug in so our pressure is zero. There should be atmospheres. Okay, so we have zero 6355 Atmospheres Times vol, Which is 0.250 leaders over gas constant R Which is 0. Leaders atmosphere over more times kelvin. And the temperature we calculated is 258.15 Kelvin. Okay, so that means N is going to equal our moles is going to equal 0. and this is moles of Y N Z. Okay, so let's write that moles Y and Z. So that's the combined moles for Y and Z. So in order for us to find the moles of X. So now let's go ahead and do that as our next step for we're going to find the moles of X because we know what the moles of Y and Z are. So the malls of X is going to equal our total moles. So end total minus N Y N Z. The number of moles for Y N. Z. So we know what the total moles is. Because we calculated that so we get 0. moles total minus the moles of Y and Z. We just calculated 0. moles. So moles of X is going to equal 0.100. Okay, so let's just bring this down. Okay, so we know what the value is for moles of X. So now we can calculate the moles of remaining gasses. Okay, this is our last step. So when we calculate the moles of remaining gasses, that's us calculating the moles of Z. Okay, so five we're going to calculate moles of remaining gasses which is going to be Z. Okay, so what we're going to do is we're going to do N is equal to P V over R. T. And we're going to look at. So we're going to plug in the last part of the analysis here. Okay, so the last part of the analysis we see that we have a 250 millimeter flask, 1.401 g with a pressure of 374 millimeters of mercury at 27 degrees Celsius. So we're going to go ahead and convert everything to the appropriate units. So temperature Is equal to 27°C. We're going to add 273.15. And so the temperature is 300.15 Kelvin Pressure is given to us in mm of Mercury, mm of Mercury. But we need it and atmospheres. So we need to convert this in one atmosphere there is 760 of mercury. And we're going to cancel our mm of mercury and be left with units of atmosphere. When we do this calculation, we get 0.49- atmospheres volume is 250 mL. We need to convert this to Leaders in one millimeter. There is 10 to the negative three leaders. So middle leaders cancel and we're left with leaders And this is equal to 0.250 L. Okay, so now we've converted everything. So we can go ahead and plug in our values here. And when we plug in our values we get pressure is equal to zero 4921 Atmospheres volume is 0.250 l Over gas constant. R is 0.08206 leaders atmosphere over mole times kelvin times temperature is 300.15 kelvin. So let's go ahead and do this calculation. And when we do this calculation we get the moles of remaining gasses which is C. Is equal to zero point 00500. Okay, and this is going to be moles of Z. Okay, so moles of why? Last step most of why is equal to the total moles of why? And Z minus the moles of Z. Okay, so we get moles of Y is equal to so we know what the molds of Y and Z. Are we calculated that to be 0. moles. And we know what the moles of Z is. That is the last thing we just calculated and it's 0.500 moles. So that means the molds of Y is equal to 0. to 50. Okay, so let's just bring this down modes of y. Okay. And are moles of why is oxygen gas? And it reacted with copper to form copper oxide. Okay, so we identified that it is oxygen gas. The molar mass of Z. We need to calculate and we were given in the problem that it is 0.1401 g. Remember molar masses grams per mole. And we know what the grams is because it was given in the problem and we know what the molds is is because we solved for that. So 0.5 moles. The molar mass of Z is 0.2 g per mole. And if we look at the periodic table, what gas is this? This is nitrogen gas. Okay. So therefore X is most likely water. Okay, So X is most likely H 20. Gas. Okay, So we just calculated everything. So let's go ahead and write out our final answer for everything. Okay, So we said that X, the molds that we calculated for X is 0. moles. And we identified X to be H 20. Gas. Why? We calculated the most to be 0.00-50 moles. And we identified it to be oxygen gas and the moles of Z. We calculated to be zero 0050 moles. And we identified it to be nitrogen gas. So, this is going to be our final answer for this problem. Okay, So we identified, we calculated the moles of X, Y and Z and determined their identities. That is it for this problem. I hope this was helpful

Verified Solution

Key Concepts

Ideal Gas Law

Stoichiometry

Gas Collection and Analysis