Question

Summarize each of the simple gas laws (Boyle's law, Charles's law, and Avogadro's law). For each law, explain the relationship between the two variables it addresses and also state which variables must be kept constant.

Short answer

Boyle's law relates pressure and volume inversely at constant temperature and gas amount. Charles's law shows direct proportionality between volume and temperature at constant pressure and gas amount. Avogadro's law says gas volume is directly proportional to the number of moles at constant pressure and temperature.

Step-by-step solution

Summarizing Boyle’s Law

Boyle's Law describes the inverse relationship between the pressure and volume of a gas. Mathematically, it is expressed as: \( P_1V_1 = P_2V_2 \), where \( P \) represents pressure and \( V \) represents volume. For Boyle's law to apply, temperature and the amount of gas must be held constant.

Summarizing Charles’s Law

Charles's Law states that the volume of a gas is directly proportional to its absolute temperature, assuming that the pressure and the amount of gas are constant. The mathematically expression of Charles's law is: \(\frac{V_1}{T_1} = \frac{V_2}{T_2}\), where \( V \) is volume and \( T \) is temperature in Kelvins.

Summarizing Avogadro’s Law

Avogadro's Law asserts that the volume of a gas is directly proportional to the number of moles of gas particles when the pressure and the temperature are constant. This is represented by the equation: \(\frac{V_1}{n_1} = \frac{V_2}{n_2}\), where \( V \) denotes volume and \( n \) denotes the number of moles of gas.

Key concepts

Boyle's Law

Imagine you're holding a balloon and you start to gently squeeze it. What happens to the air inside? It gets compressed, and as a result, the pressure inside the balloon increases while the volume decreases. This simple demonstration is the essence of Boyle's Law, one of the fundamental principles of gas behavior in chemistry.

Boyle's Law specifically states that for a given amount of gas at a constant temperature, the volume of the gas is inversely proportional to its pressure. Mathematically, this relationship is beautifully crystallized in the formula: \( P_1V_1 = P_2V_2 \). Here, if we increase the pressure (\( P \)) on the gas, the volume (\( V \)) must decrease, and vice versa, as long as the temperature and amount of the gas are not changed.

This law is particularly relevant when you are working with closed systems - like our balloon example - where no gas enters or leaves the container. It helps us understand activities ranging from the behavior of gases under the deep sea to how we breathe. Boyle's Law is often used by scuba divers, for instance, to estimate how long an air tank might last under water, making it not just a theoretical law, but one with practical applications.

Charles's Law

Have you ever noticed how a basketball becomes softer in the cold and bouncier when it’s warm? This phenomenon can be explained by Charles's Law. This law relates the volume of a gas to its temperature, showing how gases expand when heated and contract when cooled.

In technical terms, Charles's Law tells us that the volume (\( V \)) of a gas is directly proportional to its absolute temperature (\( T \)), given that the pressure and the amount of gas remain unchanged. We can express this relationship with the equation: \(\frac{V_1}{T_1} = \frac{V_2}{T_2}\). As the temperature of a gas increases, we expect to see a rise in its volume, and as the temperature decreases, its volume falls.

Real-Life Example

Consider a hot air balloon. It rises because the air inside the balloon is heated up, causing it to expand and become less dense than the surrounding air. This is a direct application of Charles's Law, showing how variations in temperature can lead to a change in the gas's volume.

Avogadro's Law

When we add more gas particles, in the form of moles, into a container at a set temperature and pressure, what changes? According to Avogadro's Law, the volume of the gas will increase proportionally with the number of gas particles, or moles. Hence, if you double the number of moles of gas in a balloon, and keep the temperature and pressure constant, the balloon will double in size.

This direct proportionality is captured in the equation \(\frac{V_1}{n_1} = \frac{V_2}{n_2}\), where \( V \) is volume and \( n \) is the number of moles. Avogadro's Law is crucial in explaining why equal volumes of gases, at the same temperature and pressure, contain the same number of particles.

Kitchen Science

If you’ve ever made bread, you've seen Avogadro’s Law in action. Yeast produces gas as it eats the sugars in the dough; this gas increases the volume of the dough, making it rise. This is possible because the gas, regardless of type, always occupies a predictable volume for a given number of particles at a certain temperature and pressure.