Three bulbs are connected by tubing, and the tubing is evacuated. The volume of the tubing is 32.0 mL. The first bulb has a volume of 78.0 mL and contains 2.72 atm of argon, the second bulb has a volume of 250 mL and contains 2.83 atm of neon, and the third bulb has a volume of 37.0 mL and contains 8.24 atm of hydrogen. If the stopcocks (valves) that isolate all three bulbs are opened, what is the final pressure of the whole system in atm?

Question

Three bulbs are connected by tubing, and the tubing is evacuated. The volume of the tubing is 32.0 mL. The first bulb has a volume of 78.0 mL and contains 2.72 atm of argon, the second bulb has a volume of 250 mL and contains 2.83 atm of neon, and the third bulb has a volume of 37.0 mL and contains 8.24 atm of hydrogen. If the stopcocks (valves) that isolate all three bulbs are opened, what is the final pressure of the whole system in atm?

So I know that you have to use PV=PV, but how would you do it with three different bulbs? I mean, how would you get the volume of the whole system?

The following procedure provides a crude method of determining the molar mass of a volatile liquid. A liquid of mass 0.0171 g is introduced into a syringe and the end is capped (sealed). The syringe is transferred to a temperature bath maintained at 62.7 oC, and the liquid vaporizes. As the liquid vaporizes the plunger is pushed out. At equilibrium, the plunger reads 6.81 mL of gas. Atmospheric pressure is 740. mmHg. What is the approximate molar mass of the compound (in g/mol)?

Okay for this one I would us V/T=V/T, but why do they mention atmospheric pressure/how does it play into solving the problem?

Thanks in advance!

Answer 1

For #1, the volume of the entire system is volume bulb 1 + volume bulb 2 + volume bulb 3 + 32 mL (for the tubing).

Answer 2

To go further on #1, I would use PV = nRT and convert those volumes and pressures to mols = n. The add all the moles together and the volumes together and use PV = nRT to solve for P. You don't have a T but you can make up a T and keep it constant.

Answer 3

To find the final pressure of the whole system in the first question, you can use the principle of partial pressures and the ideal gas law.

First, use the ideal gas law equation PV = nRT to find the number of moles (n) of each gas in the system. Rearrange the equation to solve for n: n = PV / RT.

For the first bulb:
n1 = (2.72 atm) * (0.078 L) / [(0.0821 L*atm/mol*K) * Temperature]

For the second bulb:
n2 = (2.83 atm) * (0.250 L) / [(0.0821 L*atm/mol*K) * Temperature]

For the third bulb:
n3 = (8.24 atm) * (0.037 L) / [(0.0821 L*atm/mol*K) * Temperature]

Next, sum up the total moles of all the gases:
ntotal = n1 + n2 + n3

Finally, use the total moles and the total volume (which is the sum of the volumes of all three bulbs plus the tubing volume) to find the final pressure using the ideal gas law again:
Ptotal = (ntotal * R * Temperature) / (Vtotal)

Here, Vtotal = V1 + V2 + V3 + Vtubing, where Vtubing is the volume of the tubing.

For the second question, the atmospheric pressure is mentioned because it is the external pressure acting on the system. The gas inside the syringe pushes against this external pressure. To solve the problem, you'll need to work with the difference between the pressure inside the syringe and the atmospheric pressure.

You can use the combined gas law, which states that P1V1/T1 = P2V2/T2, to relate the initial state (before the vaporization) to the final state (at equilibrium).

In this case, P1 is the pressure inside the syringe, V1 is the volume of the gas at equilibrium (6.81 mL = 0.00681 L), T1 is temperature of the bath in Kelvin (62.7 + 273 = 335.7 K), P2 is the atmospheric pressure (740 mmHg), and T2 is the same as T1.

Rearrange the equation to solve for P1: P1 = (P2 * V2 * T1) / (V1 * T2)

Plug in the known values and solve for P1. Once you have P1, you can rearrange the ideal gas law equation PV = nRT, solve for n (number of moles), and finally calculate the molar mass by dividing the mass of the compound by the number of moles.