How can we use Boyle's law to determine the pressure of compressed gas in a syringe?
Boyle's Law states that the pressure of a gas is inversely proportional to its volume, as long as the temperature remains constant. When a gas is placed in a syringe and the volume is reduced by pressing the plunger, we can use Boyle's law to calculate the new pressure of the compressed gas.
Boyle's Law Formula
Boyle's Law formula can be expressed as:
\[P_1V_1=P_2V_2\]
Where:
- \(P_1\) = Initial pressure of the gas
- \(V_1\) = Initial volume of the gas
- \(P_2\) = Final pressure of the gas
- \(V_2\) = Final volume of the gas
Given Data
The data provided in the problem are:
- Initial volume, \(V_1 = 5.0 \ mL\)
- Initial pressure, \(P_1 = 127 \ mm \ Hg\)
- Final volume, \(V_2 = 2.4 \ mL\)
- Pressure of the compressed gas (to be calculated), \(P_2 = ?\)
Calculating the Pressure
Substitute the given values into Boyle's Law formula:
\[127 \times 5 = P_2 \times 2.4\]
\[635 = 2.4P_2\]
\[P_2 = \frac{635}{2.4}\]
\[P_2 = 264.58 \ mm \ Hg\]
Therefore, the pressure of the compressed gas in the syringe is 264.58 mm Hg.