Let's examine this gas mixing problem. We have Flask Q containing 5 cubic decimeters of helium at 12 kilopascals pressure, and Flask R containing 10 cubic decimeters of neon at 6 kilopascals pressure. When these flasks are connected at constant temperature, we need to find the final equilibrium pressure.
To solve this problem, we apply Boyle's Law and the ideal gas law. At constant temperature, the number of moles of each gas remains constant. We calculate the moles of helium using its pressure and volume, and similarly for neon. The total moles is the sum of both gases, and the final pressure is determined by dividing total moles times RT by the total volume of 15 cubic decimeters.
Now let's calculate the solution step by step. We use the conservation principle that the final pressure times total volume equals the sum of each gas's pressure times its volume. Substituting our values: final pressure times 15 equals 12 times 5 plus 6 times 10, which gives us 60 plus 60 equals 120. Dividing 120 by 15, we get 8 kilopascals as our final pressure.
Here we can visualize the gas mixing process. Before connection, Flask Q contains helium at 12 kilopascals and Flask R contains neon at 6 kilopascals. When the flasks are connected, the gases mix and redistribute throughout the combined volume. The final equilibrium state shows both gases uniformly distributed at the calculated pressure of 8 kilopascals.
Our final answer is 8 kilopascals, which corresponds to option A. We can verify this result: 12 times 5 plus 6 times 10 equals 120, and 120 divided by 15 gives us 8 kilopascals. This makes physical sense because although the simple average of the pressures would be 9 kilopascals, Flask R has twice the volume of Flask Q, so the final pressure is weighted more toward the lower pressure of 6 kilopascals, resulting in 8 kilopascals.