Table of Contents

**What is Boyle-Mariotte's law?**

Boyle-Mariotte's law can be stated as follows:

*At constant temperature, the volume of a gas mass is inversely proportional to the pressure.*

p_{1}·V_{1} = p_{2}·V_{2}

**Boyle-Mariotte experiment**

It answers the question **what happens to the volume and pressure of an ideal gas when we keep the temperature constant?**

Boyle-Mariotte observed that volume and pressure are inversely proportional quantities; the p·V product remains constant for the same temperature.

p·V = cte

p_{1}·V_{1} = p_{2}·V_{2}

Thus, if the volume decreases, the frequency of collisions with the walls increases, and therefore, the pressure increases:

fig-1

**Solved exercises on Boyle-Mariotte's law**

1) Butane cylinders, made of aluminum, have a volume of 13 L and contain 6 kg of butane gas at a pressure of 8 atm. Part of this butane gas is liquefied, but assuming that all the butane gas is in gas form.

What pressure would the same gas have in a traditional 26.1 L capacity cylinder at the same temperature?

**Solution:**

p_{1} = 8 atm; V_{1} = 13 L; V_{2} 26.1 L

p_{1}·V_{1} = p_{2}·V_{2}

(8 atm)·(13 L) = p_{2} · (26.1 L) ⇒ p_{2} = (8 atm·13 L)/(26.1 L) = 4 atm

**Limitations on Boyle-Mariotte's law**

Gases that perfectly comply with Boyle's and Charles and Gay Lussac's laws are called ideal gases.

In principle, such gases do not exist. However, the ideal gas model is a valid approximation for the description of real gases in two situations:

- When at high temperatures
- When at low pressures

Real gases, at pressures and temperatures close to ambient (1 atm and 25ºC), act as ideals.

For these conditions we can relate the pressure, volume and temperature of a gas quantity by means of the equation of state of ideal gases pV=nRT

This hypothesis is very useful to study the behavior when they are far from a change of state, but fails when the gas is close to liquefaction or sublimation.

In these cases, the interactions between the gas molecules are no longer negligible, nor is the volume they occupy.