Question

consider the flask diagramed below.
2.00 l h₂
505 torr
1.00 l n₂
0.255 atm
(a) what are the final partial pressures of h₂ and n₂ after the stopcock between the two flasks is opened? (assume the final volume is 3.00 l.)
partial pressure of h₂ = torr
partial pressure of n₂ = torr
(b) what is the total pressure (in torr)?
total pressure = torr

Explanation:

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

Since \(1\ atm = 760\ torr\), for \(N_2\) with \(P_1 = 0.255\ atm\), we use the conversion formula \(P_{torr}=P_{atm}\times760\).
\(P_{N_2 - initial\ in\ torr}=0.255\times760 = 193.8\ torr\)

Step2: Use Boyle's law (\(P_1V_1 = P_2V_2\)) for \(H_2\)

Boyle's law states that for a given amount of gas at constant temperature \(P_1V_1=P_2V_2\). For \(H_2\), \(V_1 = 2.00\ L\), \(P_1=505\ torr\), \(V_2 = 3.00\ L\).
We solve for \(P_2\): \(P_{H_2}=\frac{P_1V_1}{V_2}=\frac{505\times2.00}{3.00}\approx337\ torr\)

Step3: Use Boyle's law (\(P_1V_1 = P_2V_2\)) for \(N_2\)

For \(N_2\), \(V_1 = 1.00\ L\), \(P_1 = 193.8\ torr\), \(V_2=3.00\ L\)
Using \(P_2=\frac{P_1V_1}{V_2}\), we get \(P_{N_2}=\frac{193.8\times1.00}{3.00}=64.6\ torr\)

Step4: Calculate the total pressure

According to Dalton's law of partial pressures \(P_{total}=P_{H_2}+P_{N_2}\)
\(P_{total}=337 + 64.6=401.6\approx402\ torr\)

Answer:

• Partial pressure of \(H_2 = 337\) torr
• Partial pressure of \(N_2 = 64.6\) torr
• Total pressure \(= 402\) torr