Question

How many moles of an ideal gas would occupy a 25.0 liter container when the temperature is 22.0° C and the pressure is 646 torr?

Answer 1

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Do you know how to use the ideal gas law?
PV=nRT

Answer 2

If you are a premed like me it helps to know that 1 mole of an ideal gas occupies a volume of 22.4 L at STP (273 K, 760 torr).

How does this help? Well, since each parameter is in proportion, we just have to multiply/divide each parameter by the standard parameter to get the parameter we are looking for. For example, lets say I have a gas at 646 torr, but at 0.9 moles and at a temperature at 2 C (which is 275 K), and we want to find the volume the gas occupies. Now we can just do this:

22.4 L * (275 K/273 K) * (0.9 mol/ 1 mol) * (760 torr/646 torr)

Now, how did I figure out how what goes on top and what goes on bottom? If we think back to PV = nRT, temperature and moles are directly proportional to volume, and pressure and volume are inversely proportional to each other. Therefore, we can figure out if volume will increase if we increase/decrease one of the other parameters, and then multiply/divide accordingly by the direction of each relationship.

Doing what I did above will convert the volume occupied at STP for 1 mol to the volume of occupied at 646 torr, 0.9 moles and 2 C. This doesn't just work for finding volume though, you can use it to find moles, pressure, etc. Just remember PV = nRT and the fact that 1 mol of gas occupy a volume of 22.4 L at STP.

The MCAT loves ideal gas law questions and this should save you some time in the future. I know I didn't solve your problem, but this should give you the method for solving it.