Containers A and B have same gases. Pressure, volume and temperature of A are all twice that of B, then the ratio of number of molecules of A and B are:Correct answer is '2'. Can you explain this answer?

Question

Answer

Explanation:

To solve this problem, let's consider the ideal gas law which states that:

PV = nRT

Where,
P = pressure
V = volume
n = number of moles of gas
R = ideal gas constant
T = temperature

Since containers A and B have the same gases, the gas constant (R) and temperature (T) will be the same for both containers.

Step 1:

Let's assume that container B has a volume Vb, pressure Pb, and number of molecules Nb.

Step 2:

According to the problem, container A has twice the volume and pressure of container B. So, the volume of container A will be 2Vb and the pressure will be 2Pb.

Step 3:

Now, let's assume that container A has a number of molecules Na.

Step 4:

Using the ideal gas law, we can write the equations for containers A and B as follows:

For container A:
(2Pb)(2Vb) = NaRT

For container B:
PbVb = NbRT

Step 5:

Dividing the equation for container A by the equation for container B, we get:

(2Pb)(2Vb)/(PbVb) = Na/Nb

4Vb/Vb = Na/Nb
4 = Na/Nb

Step 6:

Therefore, the ratio of the number of molecules in containers A and B is 4:1.

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