Two flask A and B have equla volumes.Flask A contains hydrogen at 600 K while flask B has same mass of `CH_4` at 300 K.Then choose the correct options.

Options

A. In flask A the molecules move faster than B
B. In flask B the molecules move faster than A
C. Flask A contains greater number of molecules than B
D. Flask B contains greater number of molecules than A

Explanation

To solve the problem step by step, we need to analyze the conditions in both flasks and apply the relevant gas laws and principles.

### Step 1: Identify the gases and their conditions
- Flask A contains hydrogen (H₂) at a temperature of 600 K.
- Flask B contains methane (CH₄) at a temperature of 300 K.
- Both flasks have equal volumes and the same mass of gas.

### Step 2: Determine the molar masses of the gases
- Molar mass of hydrogen (H₂) = 2 g/mol.
- Molar mass of methane (CH₄) = 16 g/mol.

### Step 3: Calculate the number of moles of each gas
Using the formula for the number of moles (n):
\[ n = \frac{\text{mass}}{\text{molar mass}} \]

Since the mass is the same for both gases:
- For hydrogen:
\[ n_H = \frac{m}{2} \]
- For methane:
\[ n_{CH_4} = \frac{m}{16} \]

### Step 4: Compare the number of moles
Since the mass is constant, we can see that:
- The number of moles of hydrogen (n_H) will be greater than the number of moles of methane (n_{CH_4}) because the molar mass of hydrogen is much lower than that of methane.
\[ n_H > n_{CH_4} \]

### Step 5: Calculate the average speed of the molecules
The average speed of gas molecules is given by:
\[ v = \sqrt{\frac{3RT}{M}} \]
Where:
- R = universal gas constant
- T = temperature in Kelvin
- M = molar mass in kg/mol

For hydrogen:
\[ v_H = \sqrt{\frac{3R \cdot 600}{0.002}} \]
For methane:
\[ v_{CH_4} = \sqrt{\frac{3R \cdot 300}{0.016}} \]

### Step 6: Compare the speeds
Since speed is directly proportional to the square root of temperature and inversely proportional to the square root of molar mass, we can deduce:
- Speed of hydrogen will be greater than that of methane because:
\[ \frac{v_H}{v_{CH_4}} = \sqrt{\frac{600 \cdot 0.016}{300 \cdot 0.002}} = \sqrt{\frac{8}{1}} = 2.83 \]
This indicates that hydrogen molecules move faster than methane molecules.

### Conclusion
- **Option A**: In flask A, the molecules move faster than in flask B. (Correct)
- **Option B**: In flask B, the molecules move fast. (Incorrect)
- **Option C**: Flask A contains a greater number of molecules than flask B. (Correct)

Thus, the correct options are A and C.