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Three containes of the same volume conta...

Three containes of the same volume contain three different gases. The masses of the molecules are `m_(1), m_(2)` and `m_(3)` and the number of molecules in their respective containers are `N_(1), N_(2)` and `N_(3)`. The gas pressure in the containers are `P_(1), P_(2)` and `P_(3)` respectively. All the gases are now mixed and put in one of the containers. The pressure `P` of mixture will be

A

`p lt (p_(1) + p_(2) + p_(3))`

B

`p = (p_(1) + p_(2) + p_(3))/(3)`

C

`p = p_(1) + p_(2) + p_(3)`

D

`p gt (p_(1) + p_(2) + p_(3))`

Text Solution

AI Generated Solution

The correct Answer is:
To find the pressure \( P \) of the mixture when three different gases are mixed in one container, we can use Dalton's Law of Partial Pressures. Here’s a step-by-step solution: ### Step 1: Understand Dalton's Law of Partial Pressures Dalton's Law 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. ### Step 2: Write the Expression for Total Pressure For the three gases in the containers, we can express the total pressure \( P \) as: \[ P = P_1 + P_2 + P_3 \] where \( P_1 \), \( P_2 \), and \( P_3 \) are the pressures of the individual gases in their respective containers. ### Step 3: Identify the Variables - \( m_1, m_2, m_3 \): Masses of the molecules of the gases - \( N_1, N_2, N_3 \): Number of molecules in their respective containers - \( P_1, P_2, P_3 \): Pressures of the gases in their respective containers ### Step 4: Conclusion The total pressure \( P \) when the gases are mixed in one container is simply the sum of the individual pressures: \[ P = P_1 + P_2 + P_3 \]
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