Question

question 3: shown here are 2 connected flasks; the volume and the pressure of the gas in each flask, before the stopcock valve is opened, is shown below each flask. after the valve between the two flasks is opened and the gases have time to mix completely, what is the total pressure inside the entire system in torr? assume temperature is constant and that the tube connecting the two flasks has negligible volume. a. 955 torr b. 760 torr c. 292 torr d. 1200 torr e. 195 torr

Explanation:

Step1: Convert pressure of \(N_2\) to torr

We know that \(1\ atm = 760\ torr\).
For \(N_2\), \(P_{N_2}=2.50\ atm\).
Using the conversion factor \(P = 2.50\times760\ torr\)
\(P_{N_2}=1900\ torr\)

Step2: Use Boyle's law for each gas

Boyle's law is \(P_1V_1 = P_2V_2\).
For \(N_2\): \(V_1 = 50.0\ mL\), \(V_2=(50.0 + 75.0)\ mL=125.0\ mL\), \(P_1 = 1900\ torr\)
By \(P_2=\frac{P_1V_1}{V_2}\), we have \(P_{N_2,\text{final}}=\frac{1900\times50.0}{125.0}=760\ torr\)
For \(Ar\): \(V_1 = 75.0\ mL\), \(V_2 = 125.0\ mL\), \(P_1=325\ torr\)
By \(P_2=\frac{P_1V_1}{V_2}\), we have \(P_{Ar,\text{final}}=\frac{325\times75.0}{125.0}=195\ torr\)

Step3: Calculate total pressure

According to Dalton's law of partial pressures \(P_{total}=P_{N_2,\text{final}}+P_{Ar,\text{final}}\)
\(P_{total}=760 + 195=955\ torr\)

Answer:

A. 955 torr