`5 L` of nitrogen measured at `750 mm` have to be compressed into an iron cylinder of `1 L` capacity. If temperature is kept constant, calculate the pressure in atmospheres required to do so.

Explanation

To solve the problem, we will use Boyle's Law, which states that for a given mass of gas at constant temperature, the product of pressure and volume is constant. The formula is given by:

\[ P_1 V_1 = P_2 V_2 \]

Where:
- \( P_1 \) = initial pressure
- \( V_1 \) = initial volume
- \( P_2 \) = final pressure
- \( V_2 \) = final volume

### Step-by-Step Solution:

1. **Identify the Given Values**:
- Initial volume, \( V_1 = 5 \, \text{L} \)
- Final volume, \( V_2 = 1 \, \text{L} \)
- Initial pressure, \( P_1 = 750 \, \text{mmHg} \)

2. **Convert Initial Pressure from mmHg to atm**:
To convert mmHg to atm, use the conversion factor:
\[ 1 \, \text{atm} = 760 \, \text{mmHg} \]
Therefore, we convert \( P_1 \):
\[ P_1 = \frac{750 \, \text{mmHg}}{760 \, \text{mmHg/atm}} \approx 0.9868 \, \text{atm} \]

3. **Apply Boyle's Law**:
Rearranging Boyle's Law to find \( P_2 \):
\[ P_2 = \frac{P_1 V_1}{V_2} \]

4. **Substitute the Values**:
Substitute \( P_1 \), \( V_1 \), and \( V_2 \) into the equation:
\[ P_2 = \frac{(0.9868 \, \text{atm})(5 \, \text{L})}{1 \, \text{L}} = 4.934 \, \text{atm} \]

5. **Final Result**:
Rounding to two decimal places, the final pressure \( P_2 \) required to compress the nitrogen gas into a 1 L cylinder is approximately:
\[ P_2 \approx 4.93 \, \text{atm} \]

### Summary:
The pressure required to compress 5 L of nitrogen at 750 mmHg into a 1 L cylinder at constant temperature is approximately **4.93 atm**.