Two flasks of equal volumes have been joined by a narrow tube of negligible volume. Initially both the flasks are 300 K and totally 9 mole of gas is present. One of the flasks is then placed in a thermostat at 600K. How many moles of gas is present in hot bulb.

Answer

To solve the problem, we will follow these steps:

### Step 1: Understand the System
We have two flasks of equal volume connected by a narrow tube. Initially, both flasks are at 300 K, and there are a total of 9 moles of gas present.

### Step 2: Define Variables
Let:
- \( n_1 \) = moles of gas in Flask 1 (initially at 300 K)
- \( n_2 \) = moles of gas in Flask 2 (initially at 300 K)

From the problem, we know:
\[ n_1 + n_2 = 9 \]

### Step 3: Apply the Ideal Gas Law
Since the flasks are at constant volume and pressure, we can use the relationship from the ideal gas law:
\[ PV = nRT \]
At constant volume and pressure, we can say that:
\[ nT = \text{constant} \]
This implies that the number of moles is inversely proportional to temperature:
\[ n \propto \frac{1}{T} \]

### Step 4: Set Up the Ratio
Since Flask 1 is at 300 K and Flask 2 is heated to 600 K, we can set up the ratio of moles:
\[ \frac{n_1}{n_2} = \frac{T_2}{T_1} = \frac{600}{300} = 2 \]
This means:
\[ n_1 = 2n_2 \]

### Step 5: Solve the Equations
Now we have two equations:
1. \( n_1 + n_2 = 9 \)
2. \( n_1 = 2n_2 \)

Substituting the second equation into the first:
\[ 2n_2 + n_2 = 9 \]
\[ 3n_2 = 9 \]
\[ n_2 = 3 \]

Now substituting back to find \( n_1 \):
\[ n_1 = 2n_2 = 2 \times 3 = 6 \]

### Step 6: Conclusion
The number of moles of gas present in the hot flask (Flask 2) at 600 K is:
\[ n_2 = 3 \]

### Final Answer
**The number of moles of gas present in the hot bulb is 3 moles.**

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