Assume that you have 1.00 g of nitroglycerin in a 500.0-mL
steel...

Question

Assume that you have 1.00 g of nitroglycerin in a 500.0-mL 
steel container at 20.0 °C and 1.00 atm pressure. An explosion 
occurs, raising the temperature of the container and its 
contents to 425 °C. The balanced equation is 
4 C3H5N3O91l2¡ 
12 CO21g2 + 10 H2O1g2 + 6 N21g2 + O21g2 
(c) What is the pressure in atmospheres inside the container 
after the explosion according to the ideal gas law?

Accepted Answer

Hi everyone. This problem reads. Consider a situation where 1.50 g of ice, a sorbet die nitrate is present in a 350 ml steel container at 21°C and one atmosphere of pressure. The temperature of the container and its contents is increased by an explosion to 437°C. The equation that balances is the following. According to the ideal gas law. What is the atmospheric pressure inside the container after the explosion? So we want to know what the atmospheric pressure is after the explosion. Using the ideal gas law. So let's go ahead and write down the ideal gas law. It is PV equals N. R. T pressure times volume is equal to the number of most times gas constant r times temperature. And here we're interested in the atmospheric pressure. So we need to isolate this variable by dividing both sides by volume. So we're going to get the pressure is equal to N R T over V. Okay, so N represents the number of moles. So we need the total number of moles. So this is going to be the moles of gas from the ice. A sorbet di nitrate plus the moles of air. Okay, so let's start off by calculating the total number of moles. Okay, so we have 1.50 g of ice. A sorbet die nitrate. That's what we're starting with. Okay, so 1.50 g and we want to go from grams of ISIS or by day nitrate, two moles of ISIS or by day nitrate. So we're going to need its molar mass. Alright, so we have 1.50 g. Now write down C six H eight N 208. Okay, so we want to go from grams of this. Two moles of this. So in one mole We'll calculate the molar mass using our periodic table and the Molar mass is 236. g. Okay, so once we do this, we'll see that our units of grams cancel and we're left with moles. So this equals 0. moles. Okay, of surviving nitrate. Okay, so this is the moles of it. But we want to know the moles of gas. Okay. So what we're going to do is take this value that we just solved for and go from moles of ISIS or by day nitrate, two moles of gas from us or by day nitrate. So let's rewrite the value here. So we have 0. moles. And we want to go from moles to moles of gas. So we need to know how many moles of gas there are. So we need to look at our equation. Okay, so in our, in our equation, excuse me, we're going to look at the products, how many moles of gas product do we have? So we see we have six moles of carbon dioxide. We have four moles of H 20 gas and one mole of Nitrogen gas. Okay, so we need to take the total moles of that. So the total moles is 11 moles of gas. Okay, so we'll write that as our conversion and one mole of. So so ride that nitrate. There is 11 moles of gas. All right. So we see here that moles of ISIS or by die nitrate cancel. And now we're left with moles of gas. So let's do this calculation. And when we do that, we get 0. moles of gas. So now that we know how many moles of gas we have. We need to know how many moles of air we have because we're trying to calculate the total moles. And for our ideal gas law. So we're going to calculate the total moles of air and we're going to do that by using and we're going to rearrange our ideal gas law so that we're solving for N. Which is moles. So we get N. Is equal to P. V over R. T. Okay, so Pressure is one atmospheres volume. We need to convert male leaders two leaders By dividing by 1000. So we get time. 0.35 leaders and this is over gas constant R which is 0.8 to 06 leaders, atmosphere over mole Calvin times temperature. Okay, our temperature we're going to take 21°C and add 273. Okay, so That temperature, because we need the temperature in Kelvin comes out to Kelvin. So our moles of air comes out to 0. moles of air. So now that we know are moles of gas and we know our molds of air, we can calculate the total moles. So n total is going to equal the sum of those two. So our moles of gas is 0.69872. Let's move this down plus our moles of Air. So this is moles gas plus 0.14. Excuse me? 0. moles of air. So our total most is equal to zero 084382 moles. Okay, so let's go ahead and just bring down our ideal gas law that we rearrange. So we have P is equal to N. R. T over V. Okay, so P is equal to N. R. T over V. For N. We were trying to calculate the total moles which we just did. So let's go ahead and plug that in for N. So we have 0. four three 82 moles times R R gas constant 0. leaders atmosphere over mole Calvin. And the temperature is so we want to know The temperature inside the container after the explosion. So we need to use the temperature that's given when the temperature that was increased. Okay, so we see that it increased to 437°C. So we need to convert 437°C to Kelvin. And we're going to do that by adding 273. So that means our temperature is going to be 73 plus 2 73. Okay. And this is all over the volume and our volume is ml that we're going to convert to leaders. So 0.35 leaders. Okay, so let's go ahead and do this calculation. And when we do that, we get our pressure is equal to atmospheres. Okay, this is the final answer. And this is going to be the atmospheric pressure inside the container after the explosion. That's it for this problem. I hope this was helpful.

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