Calculation of Volume of Gas at Different Pressures
If a gas at 25.0°C occupies 2.5 liters at a pressure of 3.50 atm, what will be its volume at a pressure of 1.75 atm?
If a gas at 25.0°C occupies 2.5 liters at a pressure of 3.50 atm, what will be its volume at a pressure of 1.75 atm?
Answer:
The final volume of the gas is 5 liters.
Explanation:
Let suppose that the gas experiences an isothermal process and is an ideal gas. Hence, volume is inversely proportional to pressure, that is:
\[P_{1} \cdot V_{1} = P_{2} \cdot V_{2}\]
Where:
- \(P_{1}\), \(P_{2}\) - Initial and final pressure, in atmospheres.
- \(V_{1}\), \(V_{2}\) - Initial and final volume, in liters.
Given that \(P_{1} = 3.50 atm\), \(V_{1} = 2.5 L\), and \(P_{2} = 1.75 atm\), we can calculate the final volume of the gas using the formula:
\[V_{2} = \frac{P_{1}}{P_{2}} \cdot V_{1}\]
\[V_{2} = 5 L\]
Therefore, the final volume of the gas at a pressure of 1.75 atm is 5 liters.