Two natural gas storage tanks, with volumes
of 1.5 x 104 and 2.2 x 104L, are at the same
temperature. The tanks are connected by
pipes that equalize their pressures. What
fraction of the stored natural gas is in the
larger tank?
I have no idea how to go about this. Thank you!
Two ways: the long way and the short way.
The long way.
PV = nRT
n = PV/RT. Pressure and T are not specified but you can make a convenient number like 1 atm for P and 273 for T. Solve for n in each, add them together for total n, then take the ratio of each to the total. The actual number of moles you obtain is a fictitious number (since you used a fictitious value for P and T) but the ratio is what you want.
The short way:
Avogadro's Law says that equal volumes of gases contain the same number of molecules of gas as long as both are at the same P and T.
So add 2.2 and 1.5 (you can dispense with the 10^4) = 3.7, then 1.5/3.7= ?? and 2.2/3.7 = ??
To find the fraction of the stored natural gas in the larger tank, you need to compare the volumes of the two tanks. Here's how you can solve this problem:
Step 1: Determine the total volume of both tanks.
Add the volumes of the two tanks to find the total volume. In this case, the total volume would be 1.5 x 104 L + 2.2 x 104 L.
Step 2: Calculate the fraction of the larger tank.
Divide the volume of the larger tank by the total volume to find the fraction of the gas in the larger tank.
For example, let's say the larger tank has a volume of 2.2 x 104 L and the total volume is 3.7 x 104 L. Divide 2.2 x 104 L by 3.7 x 104 L.
2.2 x 104 L ÷ 3.7 x 104 L = 0.594
So, approximately 59.4% of the stored natural gas is in the larger tank.
Note: If you have the specific values for the volumes of the tanks, you can substitute those values into the calculation to get an exact fraction.
I hope this explanation helps! Let me know if you have any further questions.