To solve this problem, we can apply Dalton's Law of Partial Pressures, which states that the total pressure exerted by a mixture of non-reacting gases is equal to the sum of the partial pressures of each gas. Since the volumes of the gases are equal and the temperature remains constant, we can directly add the pressures of the two gases to find the resulting pressure when they are allowed to mix.
Understanding the Scenario
We have two gases in separate vessels:
- Gas A: Pressure = 100 mm Hg
- Gas B: Pressure = 300 mm Hg
When these gases are allowed to mix, we need to determine the total pressure in the combined vessel.
Applying Dalton's Law
According to Dalton's Law:
Total Pressure (Ptotal) = PA + PB
Here, PA is the pressure of Gas A, and PB is the pressure of Gas B. Plugging in the values:
Ptotal = 100 mm Hg + 300 mm Hg
Calculating this gives:
Ptotal = 400 mm Hg
Final Result
Therefore, when the two gases mix, the resulting pressure of the mixture will be 400 mm Hg. This corresponds to option (a).
Why This Works
This approach works because the gases do not react with each other, and their individual pressures can be treated independently. The assumption of equal volumes ensures that the number of moles of each gas contributes to the total pressure in a straightforward manner. If the gases had reacted or if their volumes were different, we would need to consider additional factors such as the ideal gas law or stoichiometry of the reaction.
In summary, the key takeaway is that when dealing with non-reacting gases at constant temperature and equal volumes, you can simply add their pressures to find the total pressure in the system. This principle is fundamental in gas behavior and is widely applicable in various scientific fields, including chemistry and physics.
