Question

Can someone just tell me what formula to use?

Suppose a 0.10 ml bubble of methane is formed from decaying vegetation that has fallen to an ocean floor 4 miles deep where the temperature is 4 degrees Centigrade and the pressure is 623 atmosphere. Assuming that methane acts like an ideal gas, calculate the volume in milliliters of the bubble when it reaches the ocean surface at 1.0 atmosphere and 20 degrees Centigrade.

Answer 1

This is a PV=nRT question in disguise. We have two situations: the bubble at the ocean floor (1), and the bubble at the surface (2). So:

\[P_{1}V_{1}=n_{1}R_{1}T_{1}\]\[P_{2}V_{2}=n_{2}R_{2}T_{2}\]
Keep in mind though that R is a constant (i.e. R(1)=R(2)). That means we can set these two equations equal to each other:

\[\frac{P_{1}V_{1}}{n_{1}T_{1}}=\frac{P_{2}V_{2}}{n_{2}T_{2}}\]
Also remember that we're dealing with the same amount of methane the entire time (it's whatever amount of methane is trapped in the bubble). So this means n(1)=n(2) and we can take that out of the equation:

\[\frac{P_{1}V_{1}}{T_{1}}=\frac{P_{2}V_{2}}{T_{2}}\]
Now we just have to solve for the unknown. The question gives us V(1), P(1), T(1), P(2), and T(2), so plug in the numbers and solve for V(2)! Don't forget to convert temperatures to Kelvin!

If you have any questions please let me know.

Answer 2

Okay, so I got 6.6 L which is 6,600 ml, and then that's actually 7,000 ml cause of significant figures. Is that correct? This was for a take-home quiz that I've already turned in, but I'm curious cause my friends and I all got different answers.

Answer 3

Hmm that number seems high. Plugging in numbers I get:

\[\frac{623 \times 0.10}{277}=\frac{1.0 \times V}{293}\]
If you solve for V you should get about 66 mL. In the equation above the pressures are in atm, the volumes are in mL, and the temperatures are in K. It looks like you messed up a decimal somewhere.

Answer 4

We were told that PV=nRT problems can only be solved if the volume is in L, so I had to convert and then convert back because the problem wants the answer in mL and the problem has to be done in L cause of R being 0.0821 (L x atm)/(mole x K). So does that make a difference in your problem? (Sorry I can't check for myself, the mobile app/site is finicky.)

Answer 5

You can convert to L and then back and it shouldn't change you answer. If you convert to L, all you're doing is dividing both sides of the equation by 1000 (or MULTIPLYING by 1/1000). If you had to convert to L though, 0.1 mL = 0.0001 L.

If you're using PV=nRT then yes, you might need to use L as your unit for volume if that's your unit for R. But as long as you stay consistent with your units, you will always get the same answer.

You could have solved the problem above by converting to kPA instead of using atm for the same reason. It doesn't work for temperature though, because to go from C to K you need to ADD a constant to one factor, which doesn't cancel out on the other side.

Answer 6

Okay, I guess that makes sense. Thank you! I hope I did okay on the quiz otherwise.

Answer 7

No problem - happy to help! I'm sure you did great :)