**Boyle’s Law**

Boyle took a volume of gas, V_{1}, at a certain pressure, P_{1}, and recorded both values. He would then take the same sample, keeping the temperature and number of moles constant, changing the volume, V_{2}, of the gas and recording the new pressure, V_{2}. He noticed that the product of the two values, pressure and volume, always equaled a constant.

P_{1}V_{1} = k

P_{2}V_{2} = k

Taking the next step, Boyle set these equations equal to one another and discovered that the pressure and volume relationship was predictable.

P_{1}V_{1} = P_{2}V_{2}

Remember for this to be true, the temperature and number of moles of the gas samples must be held constant.

What this equation implies is that pressure and volume have an inverse relationship at constant temperature. As the pressure rises, the volume decreases. When the pressure drops, the volume decreases. When you graph these variables, you will find a Pressure vs. Volume graph develops two asymptotes as the pressure could never equal zero and neither could volume. If you graph Pressure vs. 1/Volume you will find the linear relationship you would expect.

**Example:**

200mL of a gas at 100kPa is compressed to 100mL. What’s the new pressure?

**Answer:**

Let’s start with Boyle’s Law and then solve for our unknown, the new pressure P_{2}.

P_{1}V_{1} = P_{2}V_{2}

(P_{1}V_{1})/V_{2} = P_{2}

Plugging our values into the equation we get:

(100kPa)(200mL)/(100mL) = P_{2}

200kPa= P_{2}

Does this answer make sense? Sure. The volume shrank, indicating that there is more pressure compressing the gas. The new volume is half, so the pressure must have doubled. This agrees exactly with our calculations.

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