A spherical balloon of volume 5 litre is to be filled up with `H_2` at NTP from a cylinder of 6 litre volume containing the gas at 6 atm at `0^@C`.The no of balloons that can be filled up is :

Explanation

To solve the problem, we need to determine how many spherical balloons of volume 5 liters can be filled with hydrogen gas from a cylinder containing the gas at a higher pressure. We will use the principles of gas laws, specifically Boyle's Law, to find the answer.

### Step-by-Step Solution:

1. **Understand the Given Information:**
- Volume of one balloon (V_balloon) = 5 liters
- Volume of the cylinder (V_cylinder) = 6 liters
- Pressure in the cylinder (P_cylinder) = 6 atm
- Temperature = 0°C (which is equivalent to 273 K)
- At Normal Temperature and Pressure (NTP), the pressure (P_NTP) = 1 atm.

2. **Use Boyle's Law:**
Boyle's Law states that for a given mass of gas at constant temperature, the product of pressure and volume is constant. Mathematically, it can be expressed as:
\[ P_1 V_1 = P_2 V_2 \]
Where:
- \( P_1 \) = initial pressure (6 atm)
- \( V_1 \) = initial volume (6 liters)
- \( P_2 \) = final pressure (1 atm)
- \( V_2 \) = final volume (unknown)

3. **Substituting the Values:**
Substitute the known values into the equation:
\[ 6 \, \text{atm} \times 6 \, \text{liters} = 1 \, \text{atm} \times V_2 \]
\[ 36 = V_2 \]
Therefore, the volume of hydrogen gas available at NTP is 36 liters.

4. **Calculate the Usable Volume:**
Since the cylinder has a volume of 6 liters, we need to find out how much of the 36 liters can actually be used for filling the balloons:
\[ \text{Usable Volume} = V_2 - V_cylinder = 36 \, \text{liters} - 6 \, \text{liters} = 30 \, \text{liters} \]

5. **Determine the Number of Balloons:**
To find the number of balloons that can be filled, divide the usable volume by the volume of one balloon:
\[ \text{Number of Balloons} = \frac{\text{Usable Volume}}{V_{balloon}} = \frac{30 \, \text{liters}}{5 \, \text{liters}} = 6 \]

### Final Answer:
The number of balloons that can be filled is **6**.