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# Boyle's Law Calculator

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Boyle's law states that the pressure of the gas at fixed temperature is inversely related to its volume.
Mathematically,
$P\propto$ $\frac{1}{V}$

$P$ = $\frac{k}{V}$

$PV = k$

where,
P = pressure of gas,
V = volume of gas,
k = constant.

Suppose the initial pressure of gas is $P_{i}$ and volume is $V_{i}$. If there is a change, the pressure and volume changes to $P_{f}$ and $V_{f}$. Boyle's Law can be expressed as,
$P_{i}V_{i}=P_{f}V_{f}$

where,
$P_{i}$ = Initial Pressure
$P_{f}$ = Final Pressure
$V_{i}$ = Initial Volume
$V_{f}$ = Final Volume.

## Steps

Step 1 : Read the problem and note the given values in the problem.

Step 2 : Plug in the values into the Boyle's law formula, $P_{i}V_{i}=P_{f}V_{f}$ and get the desired parameter value.

## Problems

Below are some of the problems based on Boyle's Law .

### Solved Examples

Question 1: A 40 L gas at a pressure of 0.80 atm is allowed to inflate until the pressure falls to 0.25 atm. What is the new volume, if the temperature is constant.
Solution:

Step 1: Given:$P_{i}$ = 0.80 atm
$P_{f}$ = 0.25 atm
$V_{i}$ = 40 L
$V_{f}$ = ?

Step 2: $P_{i}V_{i}=P_{f}V_{f}$

$V_{f}$=$\frac{P_{i} \times V_{i}}{P_{f}}$

$V_{f}$=$\frac{0.80 atm \times 40 L}{0.25 atm}$

$V_{f}=128 L$

Therefore, New volume of gas is 128 L.

Question 2: A 5 L gas is at a pressure of 1.50 atm. Determine the pressure obtained when the volume is 8.2 L?
Solution:

Step 1: Given:$P_{i}$ = 1.50 atm
$P_{f}$ = ?
$V_{i}$ = 5 L
$V_{f}$ = 8.2 L

Step 2: $P_{i}V_{i}=P_{f}V_{f}$

$P_{f}$=$\frac{P_{i} \times V_{i}}{V_{f}}$

$P_{f}$=$\frac{1.50 atm \times 5 L}{8.2 L}$

$P_{f}=0.91 atm$

Therefore, Pressure of gas is 0.91 atm.