An important part of chemistry today is understanding the kinetics and reactions of gases. Over the past several hundred years, chemistry with gases has been studied extensively, and from this research, several laws have been developed. One of the more well known laws is Avogadro's law, which is a law that relates the volume of a gas with the number of moles contained. Although the law sounds complex, it can be understood quite simply, and when placed in context with the other main gas laws (Boyle's law and Charles's law), it forms the basis of all that we know about gas chemistry today.
As previously stated, Avogadro's law relates the volume of a gas with the number of moles of said gas. The law states that the relationship between the two is direct and linear. Essentially, this means that when the number of moles increases by a set amount, the volume of the gas will also increase by a set amount (providing that the temperature and pressure of the gas is kept constant). Therefore, a formula between the two can be written, V=kn, where V is volume, n is the number of moles, and k is a constant. This law is relatively common sense, as it merely states that the more gas you have, the more space it's going to take up.
So why is this law important? At first glance, it seems so obvious that a law shouldn't even be assigned with it. Its main applicability comes from its combination with Boyle's law and Charles law. The former is a law that inversely relates volume and pressure, and the latter is a principle that directly relates temperature and pressure. Essentially, these two laws state that for increased pressure, the volume decreases and the temperature increases for a constant number of moles. These three principles are easily combined in what is called the ideal gas law. This is a formula that relates temperature, volume, pressure, and the number of moles of a gas in one convenient equation: PV=nRT, where R is the gas constant of 0.082058 and n is the number of moles of gas.
This law works because it takes advantage of the three gas laws. It takes into account Boyle's law by putting both pressure and volume on the same side of the equation, implying that they are inversely related. Charles's law is accounted for by placing temperature and pressure on opposite sides of the equation, as they are both directly related. A similar procedure is conducted to account for Avogadro's law by placing volume and moles on opposite sides. The equation is completed by the inclusion of the ideal gas constant, which in situations involving the equation is 0.082058 L*atm/(K*mol).
While Avogadro's law itself is simple, intuitive, and may seem like it has little value, its usefulness is easily seen when combined with the other gas laws; its use is essential in modern gas kinetic calculations.