Calculating the New Volume of a Syringe Based on Pressure Changes
Understanding Boyle's Law
Boyle's Law states that the pressure and volume of a gas are inversely proportional at constant temperature. This means that as one variable increases, the other variable decreases, and vice versa.
The Problem:
A 25.0 mL syringe is filled with air until the pressure inside the syringe reaches 0.942 atm. If you wanted the air inside the syringe to exert a pressure of 1.546 atm, what must be the new volume of the syringe in mL?
The Solution:
To find the new volume of the syringe, we can use Boyle's Law. The equation for Boyle's Law is: P1V1 = P2V2, where P1 and V1 are the initial pressure and volume, and P2 and V2 are the final pressure and volume.
Given:
- Initial pressure (P1) = 0.942 atm
- Initial volume (V1) = 25.0 mL
- Final pressure (P2) = 1.546 atm
Let's substitute these values into the equation and solve for the new volume (V2):
0.942 atm * 25.0 mL = 1.546 atm * V2
Dividing both sides of the equation by 1.546 atm:
15.0 mL = V2
Therefore, the new volume of the syringe would be 15.0 mL.
A 25.0 mL syringe is filled with air until the pressure inside the syringe reaches 0.942 atm. If you wanted the air inside the syringe to exert a pressure of 1.546 atm, what must be the new volume of the syringe in mL? The new volume of the syringe would be 15.0 mL. Explanation: To find the new volume of the syringe, we can use Boyle's Law. Boyle's Law states that the pressure and volume of a gas are inversely proportional at constant temperature. The equation for Boyle's Law is P1V1 = P2V2, where P1 and V1 are the initial pressure and volume, and P2 and V2 are the final pressure and volume. Given: Initial pressure (P1) = 0.942 atm Initial volume (V1) = 25.0 mL Final pressure (P2) = 1.546 atm Let's substitute these values into the equation and solve for the new volume (V2): 0.942 atm * 25.0 mL = 1.546 atm * V2 Dividing both sides of the equation by 1.546 atm: 15.0 mL = V2 Therefore, the new volume of the syringe would be 15.0 mL.