Samples of Neon and helium are placed in separate containers connected by a pinched rubber tube. There is 5.00 liters of neon at a pressure of 634 mm Hg in the first container. The second container has 3.00 liters of helium at 522 mm Hg. When the clamp is removed from the rubber tube and the gases are allowed to mix, what is the partial pressure of each gas and the total pressure of the gas mixture?

To determine the partial pressure of each gas and the total pressure of the gas mixture, we need to apply the principles of Dalton's law of partial pressures. Dalton's law states that the total pressure exerted by a mixture of gases is equal to the sum of the partial pressures of each individual gas.

Let's break down the problem step by step:

Step 1: Convert the given pressures to a common unit.
Since the pressure units are different (mm Hg for neon and helium), we need to convert them to a common unit. In this case, we can convert both pressures to atmospheres (atm) since it is a commonly used unit in gas calculations.
1 atm = 760 mm Hg

Pressure of neon:
634 mm Hg * (1 atm / 760 mm Hg) = 0.83421 atm (rounded to five decimal places)

Pressure of helium:
522 mm Hg * (1 atm / 760 mm Hg) = 0.68684 atm (rounded to five decimal places)

Step 2: Apply Dalton's law to calculate the partial pressures and the total pressure of the mixture.

Partial pressure of neon (P_neon):
P_neon = Total pressure of the mixture * (Volume of neon / Total volume)

Partial pressure of helium (P_helium):
P_helium = Total pressure of the mixture * (Volume of helium / Total volume)

Total pressure of the mixture:
Total pressure = P_neon + P_helium

Using the given information:
Volume of neon = 5.00 liters
Volume of helium = 3.00 liters

Total volume = Volume of neon + Volume of helium
Total volume = 5.00 liters + 3.00 liters = 8.00 liters

Now we can substitute the values into the formulas:

P_neon = Total pressure * (5.00 L / 8.00 L)
P_helium = Total pressure * (3.00 L / 8.00 L)

But we don't know the total pressure yet. To find the total pressure, we can rearrange the equations and solve for total pressure (P_total):

P_total = P_neon + P_helium

Substituting the partial pressure formulas:

P_total = (Total pressure * (5.00 L / 8.00 L)) + (Total pressure * (3.00 L / 8.00 L))

Step 3: Solve for the unknown, which is the total pressure.

Let's solve for P_total:

P_total = (Total pressure * 0.625) + (Total pressure * 0.375)

To simplify the equation, combine like terms:

P_total = Total pressure * (0.625 + 0.375)

P_total = Total pressure * 1.0

Now, we isolate the Total pressure term:

P_total = P_total

Therefore, the total pressure (P_total) will be the same as the total pressure of the mixture.

Step 4: Calculate the partial pressures and the total pressure.

To calculate the partial pressure of each gas, we can use the equation derived earlier:

Partial pressure of neon (P_neon) = Total pressure * (5.00 L / 8.00 L)
Partial pressure of helium (P_helium) = Total pressure * (3.00 L / 8.00 L)

To find the total pressure, we can use the given information:

Total pressure = 0.83421 atm + 0.68684 atm

Total pressure = 1.52105 atm (rounded to five decimal places)

So, the partial pressure of neon is 0.41761 atm (rounded to five decimal places), and the partial pressure of helium is 0.32044 atm (rounded to five decimal places). The total pressure of the gas mixture is 1.52105 atm (rounded to five decimal places).