Chemistry Help 2?

Question

Consider a mixture of air and gasoline vapor in a cylinder with a piston. The original volume is 30. cm3. If the combustion of this mixture releases 885 J of energy, to what volume will the gases expand against a constant pressure of 665 torr if all the energy of combustion is converted into work to push back the piston?

Answer 1

Let final vol. = v

So, P(v-30) = 885

Now just substitute P in N/m^2 and 30cm3 = 30*10^-6 m3

Answer 2

One cool trick to remember is that each side of the ideal gas law (PV and nRT) is in units of energy. If you pick the right units, you can get joules.

So you know that PV, pressure times volume, is in units of energy. You have a value for energy: +885 J added to your system. So either pressure or volume will increase. Since the pressure is constant at 665 torr, the only thing that can increase is the volume. So you're looking for the additional volume.

Since PV = E, then V = E/P. Additional volume = additional energy / constant pressure. So take 885 J / 665 torr, and convert units appropriately until you can get it into cc's, and then add your original 30 cc's back. (If you're confused about units, convert your torr into pascals, another SI unit. 1 J / 1 Pa = m^3. Then you can downsize cubic meters into cubic centimeters.)