If the initial conditions of a gas are 1 atm and 3.15 L, what will be the resulting volume if the pressure changes to 3.5 atm at the same temperature?

Steps to Solve

1. Identify the variables

Start by identifying the variables in the problem using Boyle's Law:

• P1: Initial pressure
• V1: Initial volume
• P2: Final pressure
• V2: Final volume

2. Write the Boyle's Law equation

The formula for Boyle's Law is:

$$ P_1 V_1 = P_2 V_2 $$

This means that the product of the initial pressure and volume is equal to the product of the final pressure and volume.

3. Rearrange the equation to solve for $V_2$

To find the new volume ($V_2$), rearrange the equation:

$$ V_2 = \frac{P_1 V_1}{P_2} $$

This formula allows you to calculate the final volume based on the initial pressure and volume, and the final pressure.

4. Substitute known values

Insert the known values for $P_1$, $V_1$, and $P_2$ into the rearranged equation. For example, if $P_1 = 2 , \text{atm}$, $V_1 = 4 , \text{L}$, and $P_2 = 1 , \text{atm}$:

$$ V_2 = \frac{2 , \text{atm} \times 4 , \text{L}}{1 , \text{atm}} $$

5. Calculate the final volume

Perform the calculation to find $V_2$:

$$ V_2 = \frac{8 , \text{L}}{1} = 8 , \text{L} $$

The result gives you the new volume of the gas after the change in pressure.