If for an ideal gas with 2 litres volume, pressure was increased by 0.25 atm then volume became 555 ml. At what initial pressure was the gas present?

Options

A. 0.096 mm Hg
B. 0.96 mm Hg
C. 73 mm Hg
D. 73 atm

Answer

To find the initial pressure of the gas, we can use the ideal gas law and the relationship between pressure and volume. We will apply Boyle's Law, which states that for a given amount of gas at constant temperature, the product of pressure and volume is constant.

### Step-by-Step Solution:

1. **Identify the Given Values:**
- Initial volume \( V_1 = 2 \, \text{liters} = 2000 \, \text{ml} \)
- Final volume \( V_2 = 555 \, \text{ml} \)
- Increase in pressure \( \Delta P = 0.25 \, \text{atm} \)

2. **Set Up the Pressure Relationship:**
- Let the initial pressure be \( P_1 \).
- The final pressure \( P_2 \) after the increase is given by:
\[ P_2 = P_1 + 0.25 \, \text{atm} \]

3. **Apply Boyle's Law:**
- According to Boyle's Law:
\[ P_1 \times V_1 = P_2 \times V_2 \]
- Substituting the known values:
\[ P_1 \times 2000 = (P_1 + 0.25) \times 555 \]

4. **Expand and Rearrange the Equation:**
- Expanding the right side:
\[ 2000 P_1 = 555 P_1 + 0.25 \times 555 \]
- Rearranging gives:
\[ 2000 P_1 - 555 P_1 = 0.25 \times 555 \]
- This simplifies to:
\[ (2000 - 555) P_1 = 0.25 \times 555 \]

5. **Calculate the Values:**
- Calculate \( 2000 - 555 = 1445 \):
\[ 1445 P_1 = 0.25 \times 555 \]
- Calculate \( 0.25 \times 555 = 138.75 \):
\[ 1445 P_1 = 138.75 \]
- Now, solve for \( P_1 \):
\[ P_1 = \frac{138.75}{1445} \approx 0.096 \, \text{atm} \]

6. **Convert to mmHg:**
- To convert atm to mmHg, use the conversion factor \( 1 \, \text{atm} = 760 \, \text{mmHg} \):
\[ P_1 \approx 0.096 \times 760 \approx 73 \, \text{mmHg} \]

### Final Answer:
The initial pressure of the gas was approximately **73 mmHg**.