Three containers of the same volume contain three different gases. The masses of the molecules are m₁, m₂ and m₃ and the numbers of molecules in their respective containers are N₁, N₂ and N₃. The gas pressures are P₁, P₂ and P₃. The gases are now mixed and put in one of the containers. The pressure P of the mixture will be:
Options

Question

Three containers of the same volume contain three different gases. The masses of the molecules are m₁, m₂ and m₃ and the numbers of molecules in their respective containers are N₁, N₂ and N₃. The gas pressures are P₁, P₂ and P₃. The gases are now mixed and put in one of the containers. The pressure P of the mixture will be:

Options

G1 Physics · Accepted Answer

Step 1: For each ideal gas initially at the same temperature and in volume V, PᵢV = NᵢkBT. Step 2: After mixing the gases in a container of the same volume V at the same temperature, total number of molecules is N₁ + N₂ + N₃. Step 3: Thus PV = (N₁ + N₂ + N₃)kBT = (P₁ + P₂ + P₃)V. Step 4: Cancel V: P = P₁ + P₂ + P₃ (Dalton’s law of partial pressures). Final answer: (C).