Solve Chemistry Gas Problem: Pressure in System When Stopcocks Open

[Grapz]

Homework Statement

The apparatus shown consists of three bulbs connected by stopcocks. What is the pressure inside the system when the stopcocks are opened? Assume that the lines connnecting the bulbs have zero volume and that the termperature remains constant.

CO_2 - Pressure : 2.13 atm , Volume = 1.5 L
H_2 : Pressure = 0.861 atm, Volume = 1.00 L
Ar : Pressure = 1.15 atm , volume = 2.00 L

Homework Equations

The equation i used was Daltons partial gas equation

P1 + p2 + p3 = ptotal

The Attempt at a Solution

so i just did 2.13 + 0.861 + 1.15

But the answer is 1.414 atm.

i dont' know what to do

 

[eli64]

that would be too easy of course

hint: P1V1 = P2V2

what is V2 or V(total)?

 

[Blueshift5]

.



To solve this problem, we can use the ideal gas law equation, PV = nRT, where P is pressure, V is volume, n is the number of moles, R is the gas constant, and T is the temperature. Since the temperature remains constant, we can use the simplified form of the equation, PV = constant.

First, we need to calculate the total number of moles in the system. To do this, we can use the ideal gas law equation for each gas:

For CO2:
n = (PV)/(RT) = (2.13 atm * 1.5 L)/(0.0821 L*atm/mol*K * 298 K) = 0.116 moles

For H2:
n = (PV)/(RT) = (0.861 atm * 1.00 L)/(0.0821 L*atm/mol*K * 298 K) = 0.034 moles

For Ar:
n = (PV)/(RT) = (1.15 atm * 2.00 L)/(0.0821 L*atm/mol*K * 298 K) = 0.092 moles

Now, we can use the ideal gas law equation to calculate the total pressure in the system:
PTotal = (nTotal * RT)/VTotal = [(0.116 + 0.034 + 0.092) * 0.0821 L*atm/mol*K * 298 K]/(1.5 L + 1.00 L + 2.00 L) = 0.784 atm

Therefore, the pressure inside the system when the stopcocks are opened is 0.784 atm. This is different from the answer of 1.414 atm that you calculated by simply adding the individual pressures. This is because when the stopcocks are opened, the gases will mix and the total volume will increase, leading to a decrease in pressure.

I hope this helps you understand how to solve this type of problem using the ideal gas law equation. Remember to always check your units and make sure they are consistent throughout the calculations.