Question

Two flasks of equal volume connected by a narrow tube (of negligible volume) are at $27{}^\circ C$ and contain 0.70 mole of ${{H}_{2}}$ at 0.5atm pressure. One of the flasks is then immersed into a bath kept at $127{}^\circ C$, while the other remains at $27{}^\circ C$. Calculate the final pressure and the number of moles of ${{H}_{2}}$ in each flask.

Answer 1

Hint: Start by taking an equal number of moles of hydrogen in both the flasks. So, their pressure will be the same. Now, use the ideal gas equation and find the relation between temperature and number of moles in both the flasks. Then you obtain a factor by which the number of moles of hydrogen would increase or decrease. Using that, calculate the number of moles and then cross multiply and calculate the final pressure.

Complete answer:
- The question says, two flasks contain equal volume at 300K and in total contain 0.7 moles of hydrogen at 0.5atm pressure.
- Let us consider, both the flasks A and B contain an equal number of moles initially that is, 0.35moles but the pressure is kept constant.
- Therefore, we get, ${{P}_{A}}={{P}_{B}}$
- Let’s assume if there is a decrease in the number of moles of flask, A then there will be an increase in the number of moles of flask, B and the pressure will remain constant.
- Using the ideal gas equation, PV=nRT, we get,
\[{{n}_{A}}R{{T}_{A}}={{n}_{B}}R{{T}_{B}}\]
- Number of moles is inversely proportional to the temperature. So, if temperature rises, the number of moles will reduce. Let’s say, at 400K, ‘x’ moles are transferred from flask A to B.
\[(0.35+x)300=(0.35-x)400\]
- Therefore, by solving this equation we get, x = 0.05 moles.
- Therefore, when flask A is immersed in water at 400K, 0.05 moles of hydrogen get transferred to flask B, so the number of moles of hydrogen in flask A will be 0.30moles. Similarly, 0.05moles of hydrogen are being added to flask B, therefore the number of moles of hydrogen in flask B will be 0.40moles.
- Now, we need to calculate final pressure. The initial pressure was 0.5atm when the number of moles of hydrogen in a flask was 0.35moles. So, we need to find pressure when the number of moles increases to 0.4moles.
- From the ideal gas equation, we know, pressure is directly proportional to the number of moles.
- Therefore, $\dfrac{{{P}_{1}}}{{{P}_{2}}}=\dfrac{{{n}_{1}}}{{{n}_{2}}}$
\[\dfrac{0.5}{{{P}_{2}}}=\dfrac{0.35}{0.40}\]
- Therefore, ${{P}_{2}}=0.5714$
- Therefore, the final pressure of the gas is 0.5714atm.
- Therefore, the final pressure of the gas is 0.5714atm and the number of moles of ${{H}_{2}}$ in each flask is 0.30moles and 0.40moles.



Note: Remember pressure is directly proportional to temperature and number of moles. Temperature is inversely proportional to the number of moles. Systematically solve this kind of problem to get the answer.