A stressed chemistry student is hyperventilating into a paper bag. The student stops to wipe his brow after a few breaths, and the bag is at 5.7 KPa and the temperature in the lecture hall is 24 °C. The bag is 0.75L full. The student then goes at it again, and completely fills the bag with air to 1.2L and 7.2KPa. The student panics, and runs out of the lecture hall...when he gets outside, the inflated paper bag explodes. What is the temperature outside?

I posted a response to your first post to the effect that it was unclear as to the meaning of 0.75L full. Exactly what does that mean? Does it mean the bag is 3/4 full? or some other notation.

Yeah and I responded to that and you did not respond to that.

When it gets too far down the list we sometimes don't find it. But that's no reason to post the same question without clarifying it. I'll look for the original question.

OK. I found the original and your explanation really isn't an explanation. From what you wrote, I assume you have copied the question verbatim from your notes/book/homework, whatever and you don't now what the 0.75L full means. No, you don't have two volumes, there is only one and we don't know what it is. The 0.75L full, whatever that means, is supposed to be the way you find the volume of the bag. After you know the volume of the bag you can use (P1V1/T1) = (P2V2/T2). I need to know what the 0.75L full means before I can help. It could mean that the bag is full at 0.75L. Think about the size of bags a stressed out student might blow into. Those could be approximately 750 mL or so.

To solve this problem, we can use the ideal gas law, which states that the pressure, volume, and temperature of a gas are related by the equation: PV = nRT, where P is the pressure, V is the volume, n is the number of moles of gas, R is the ideal gas constant, and T is the temperature in Kelvin.

We can rearrange the equation as T = PV / (nR) to solve for the temperature.

First, let's find the initial number of moles of air inside the paper bag:
To do this, we can use the ideal gas law equation and substitute the given values for the initial condition.
P1 = 5.7 KPa = 5.7 * 1000 Pa (since 1 KPa = 1000 Pa)
V1 = 0.75 L
R = 8.314 J/(mol K) (the ideal gas constant)

Next, we need to convert the pressure to Pascals (Pa) and the volume to cubic meters (m^3) since these are the SI units used in the ideal gas law equation.

P1 = 5.7 * 1000 Pa
V1 = 0.75 * 0.001 m^3 (since 1 L = 0.001 m^3)

Now, we can calculate the number of moles (n1) using the ideal gas law equation:
n1 = (P1 * V1) / (R * T1)

However, we don't know the initial temperature (T1), so we cannot directly solve for the number of moles.

Let's move on to the second condition where the bag is completely filled with air:
P2 = 7.2 KPa = 7.2 * 1000 Pa
V2 = 1.2 * 0.001 m^3

Using the ideal gas law equation, we can calculate the number of moles (n2) using the second set of conditions:
n2 = (P2 * V2) / (R * T2)

Now, we can solve for the ratio of the number of moles:
n2 / n1 = (P2 * V2 * T1) / (P1 * V1 * T2)

Since the same amount of air is trapped inside the bag, the number of moles doesn't change. Therefore, we have:
n2 / n1 = 1

Now, we can rearrange the equation to solve for the temperature outside (T2):
T2 = (P2 * V2 * T1) / (P1 * V1)

Substituting the known values, we have:
T2 = (7.2 * 1000 * 1.2 * 0.001 * T1) / (5.7 * 1000 * 0.75 * 0.001)

The units will cancel out, leaving us with the temperature in Kelvin.

To get the temperature in Celsius, we can convert it by subtracting 273.15 from the temperature in Kelvin.

Now, you can plug in the values for T1 that were given in the problem and calculate T2.