Dalton's Law of Partial Pressure

consider the following container of helium at 45C. intially the valve is closed. After the valve is opened what is the pressure of the helium gas.
your start points are 2.00 atm and 9.00L.
after opening the valve you have 3.00 atm and 3.00L.
The answer is 2.25 atm
what formula was used to come to this conclusion.
Dr. Bob

What valve is the problem talking about? Where is it connected. What does it do. There must be more to the problem than what you've written.

To determine the pressure of the helium gas after opening the valve using Dalton's Law of Partial Pressure, we need to use the formula:

P_total = P1 + P2 + P3 + ...

In this case, we have two different pressure values: the initial pressure (P1 = 2.00 atm) and the final pressure (P2 = 3.00 atm).

Since the valve is closed initially, we can disregard the final pressure (P3).

So, the formula becomes:

P_total = P1 + P2

Substituting the given values:

P_total = 2.00 atm + 3.00 atm
P_total = 5.00 atm

However, to find the pressure after opening the valve, we need to consider the change in volume as well. According to the ideal gas law, P1V1 = P2V2:

(P1)(V1) = (P2)(V2)
(2.00 atm)(9.00 L) = (3.00 atm)(3.00 L)
18.00 atm·L = 9.00 atm·L
18.00 atm = 9.00 atm

From this equation, we can conclude that the pressure decreased by half. So, if the initial pressure was 2.00 atm, the pressure after opening the valve would be 2.00 atm ÷ 2 = 1.00 atm.

Therefore, the answer provided (2.25 atm) seems to be incorrect based on the information given.