Which of the following is TRUE or FALSE
Equal volumes of different gases under similar conditions of temperature and pressure contain equal number of molecules.

Answer

To determine whether the statement "Equal volumes of different gases under similar conditions of temperature and pressure contain equal number of molecules" is TRUE or FALSE, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Statement**: We need to analyze the claim that equal volumes of different gases at the same temperature and pressure contain the same number of molecules.

2. **Recall the Ideal Gas Law**: The ideal gas law is given by the equation:
\[ PV = nRT \]
where:
- \( P \) = pressure
- \( V \) = volume
- \( n \) = number of moles
- \( R \) = universal gas constant
- \( T \) = temperature

3. **Set Up for Two Gases**: Let's consider two different gases, Gas A and Gas B. According to the problem, both gases are at the same pressure and temperature and occupy equal volumes. Therefore, we can denote:
- For Gas A: \( P_1 = P \), \( V_1 = V \), \( T_1 = T \)
- For Gas B: \( P_2 = P \), \( V_2 = V \), \( T_2 = T \)

4. **Calculate Moles for Each Gas**:
- For Gas A:
\[ n_1 = \frac{P_1 V_1}{RT_1} = \frac{PV}{RT} \]
- For Gas B:
\[ n_2 = \frac{P_2 V_2}{RT_2} = \frac{PV}{RT} \]

5. **Compare the Number of Moles**: Since both gases have the same pressure, volume, and temperature:
\[ n_1 = n_2 \]
This means that the number of moles of Gas A is equal to the number of moles of Gas B.

6. **Relate Moles to Molecules**: The number of molecules (\( N \)) is related to the number of moles (\( n \)) by Avogadro's number (\( N_A \)):
\[ N = n \times N_A \]
Since \( n_1 = n_2 \), it follows that:
\[ N_1 = N_2 \]
This indicates that the number of molecules in equal volumes of different gases under the same conditions is indeed equal.

7. **Conclusion**: Therefore, the statement is TRUE.

### Final Answer:
**The statement is TRUE.**