Gas laws concerning pressure & temp.

[Agent M27]

Homework Statement

Suppose an aerosol can contains a residual pressure of 755mm Hg and a temperature of 25*c. What would the pressure be if the can was heated to 1155*c?

Homework Equations

P₁xV₁=P₂xV₂

V$$\propto$$T

The Attempt at a Solution

I began by converting the 755mm Hg to atm, .993atm. I then converted the temperatures to 298 kelvins & 1428 kelvins. I honestly do not know where to take this problem from here. The above equations I gave deal with temperature & pressure seperately so I need to find some way of combining them. All I need is a nudge, I can take it from there. Thanks in advance.

Joe

 

[Gunthi]

hint: Ideal gas law

 

[Agent M27]

I originally tried that one but I am missing both V & n, volume & number of moles. I looked a little deeper and my book and found Gay-Lussac's Law, $$\frac{P_{1}}{T_{1}}$$=$$\frac{P_{2}}{T_{2}}$$. Using simple algebra I got 4.76 ATM. Thanks for your help.

 

[Gunthi]

I originally tried that one but I am missing both V & n, volume & number of moles. I looked a little deeper and my book and found Gay-Lussac's Law, $$\frac{P_{1}}{T_{1}}$$=$$\frac{P_{2}}{T_{2}}$$. Using simple algebra I got 4.76 ATM. Thanks for your help.

You can deduce that equality from the ideal gas law, because the gas is in a can that you can consider as a body that doesn't expand or contract, and so the volume is constant, on the other hand the quantity of gas in the can also remains constant (you didn't let any gas in or out). So, PV=nrT <=> P/T=nr/V=cte and you get the Gay-Lussac's Law.

This law is very general, you don't need to memorize all the possible combinations, just consider every constraint (V,T,n,P) and see how it varies in the process, if some of them remain constant, then all the others can be calculated from the initial and final conditions.

Glad to help.

 

[DeeNos]

Hello Joe,

You are on the right track with converting the temperature to Kelvin and the pressure to atm. To find the new pressure at 1155°C, you can use the combined gas law equation: P1V1/T1 = P2V2/T2. This equation takes into account the relationship between pressure, volume, and temperature.

First, we need to find the initial volume (V1) of the can. We can use the ideal gas law equation, PV = nRT, where P is the initial pressure (0.993 atm), V is the unknown volume, n is the number of moles (which we can assume to be constant), R is the gas constant, and T is the initial temperature (298 K). Solving for V, we get V1 = (nRT)/P = (n x 0.0821 x 298)/0.993 = 24.7L.

Now, we can plug in the values into the combined gas law equation: (0.993 x 24.7)/298 = (P2 x 24.7)/1428. Solving for P2, we get P2 = (0.993 x 24.7 x 1428)/298 = 47.7 atm.

Therefore, if the can is heated to 1155°C, the pressure inside the can would increase to 47.7 atm.

I hope this helps! Let me know if you have any further questions.

Best,