If the initial pressures of the H2 and N2 in the flasks in the figure below were instead 350. torr and 160. torr, respectively, what would be the final pressure after the stopcock is opened?

Left side of stopcock= 2.00L H2
Right side of stopcock= 1.00L N2

I would use PV = nRT and solve for n for H2 flask. So the same for N2 flask. You have no T listed but you can make up a T (and keep it the same throughout). Then add n1 + n2 and use PV = nRT again with total mols and total volume, solve for P.

A shorter route is to use
P1V1 = P2V2 and convert pH2 from 2L @ 350 mm to 3L at ? P.
Do the same for converting pN2 from 1L @ 160 mm to 3L @ ?P. Then add pH2 + pN2 = Ptotal. You will get the same answer either way.

To determine the final pressure after the stopcock is opened, we can use the concept of partial pressures and the ideal gas law.

First, let's calculate the moles of H2 and N2 in the flasks:
Number of moles of H2 = (pressure of H2 / total pressure) * volume of H2
Number of moles of N2 = (pressure of N2 / total pressure) * volume of N2

Given:
Pressure of H2 = 350. torr
Pressure of N2 = 160. torr
Volume of H2 = 2.00 L
Volume of N2 = 1.00 L

Calculating the number of moles:
Number of moles of H2 = (350. torr / (350. torr + 160. torr)) * 2.00 L
Number of moles of N2 = (160. torr / (350. torr + 160. torr)) * 1.00 L

Now, let's assume ideal gas behavior and combine the moles of both gases and the volumes of both flasks since they mix when the stopcock is opened:
Total moles = moles of H2 + moles of N2
Total volume = volume of H2 + volume of N2

Now, we can use the ideal gas law equation PV = nRT to find the final pressure:
(Pressure of H2 + Pressure of N2) * Total Volume = Total moles * R * T

Since the volume is constant and the temperatures are not given, we can assume they remain constant. Consequently, the equation simplifies to:
(Pressure of H2 + Pressure of N2) = Total moles * R * T / Total Volume

Assuming standard temperature and pressure (STP) as T = 273 K and R = 0.0821 L.atm/mol.K, we can substitute these values and calculate the final pressure:
Final Pressure = (Pressure of H2 + Pressure of N2) * Total Volume / (Total moles * R * T)

By plugging in the values from the given data, we can find the final pressure after opening the stopcock.