Gas Pressure Calculation Problem: Decreasing Volume

How to calculate the new pressure inside a gas syringe if the volume is decreased?

Given data:
Volume initial (V1) = 20.0 mL
Pressure initial (P1) = 1.0 atm
Temperature (T) = 20°C

Answer:

The new pressure inside the gas syringe is 2.0 atm.

When solving for the new pressure of a gas in a syringe after the volume has decreased, we can use Boyle's Law which states that the pressure of a gas is inversely proportional to its volume.

First, we need to convert the volume from milliliters to liters. Given that the initial volume (V1) is 20.0 mL, this is equal to 0.02 L.

Next, we use the formula P1V1 = P2V2, where P1 is the initial pressure, V1 is the initial volume, P2 is the final pressure (which we need to find), and V2 is the final volume.

Plugging in the values, we get:

1.0 atm * 0.02 L = P2 * 0.01 L

Solving for P2:

P2 = (1.0 atm * 0.02 L) / 0.01 L

P2 = 2.0 atm