Answer
See explanation below.
Work Step by Step
First, let's convert all the pressures to the same units:
(0.456 atm) (760 torr/atm) = 346.6 torr
(25 kPa) (7.5 torr/kPa) = 187.5 torr
To solve the problem, we use both Boyle's Law and Dalton's Law. When the stopcocks are opened, the volume of the gases are increased, and their pressures are decreased. (Boyle's Law). However, these individual partial pressures sum to the total pressure in the system (Dalton's Law). It does not matter if the gases are the same or different, we can still handle them as partial pressures.
The total volume of the system after the stopcocks are opened is:
1.0 L + 1.5 L + 2.0 L = 4.5 L
After the stopcocks are opened, the partial pressure of the gas from the first container is found by Boyle's law:
P1 V1 = P2 V2;
(185 torr) (1.0 L) = P (4.5 L);
P = 41.1 torr
Similarly, for the gas in the second container:
(346.6 torr) (1.5 L) = P (4.5 L);
P = 115.5 torr
For the gas in the third container:
(187.5 torr) (2.0 L) = P (4.5 L);
P = 83.4 torr
So the final total pressure is (by Dalton's Law):
41.1 torr + 115.5 torr + 83.4 torr = 240.0 torr
