Question

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

Short answer

Boyle's Law: Pressure is inversely proportional to volume at constant temperature. Charles's Law: Volume is directly proportional to temperature in Kelvins at constant pressure. Avogadro's Law: Volume is directly proportional to the number of moles of gas at constant temperature and pressure.

Step-by-step solution

Summarizing Boyle's Law

Boyle's Law describes the relationship between the pressure and volume of a gas held at a constant temperature. It states that the pressure of a given mass of gas is inversely proportional to its volume, as long as temperature remains constant. Mathematically, this is represented as: \( P \propto \frac{1}{V} \) or \( PV = k \), where P is the pressure, V is the volume, and k is a constant.

Summarizing Charles's Law

Charles's Law describes the relationship between the volume and temperature of a gas at constant pressure. It states that the volume of a given amount of gas is directly proportional to its temperature on the Kelvin scale. The mathematical form of Charles's Law is: \( V \propto T \) or \( \frac{V}{T} = k \), where V is the volume, T is the temperature in Kelvins, and k is a constant.

Summarizing Avogadro's Law

Avogadro's Law states that the volume of a gas at a given temperature and pressure is directly proportional to the number of moles of the gas present. This means that equal volumes of gases, at the same temperature and pressure, contain the same number of molecules. It is expressed mathematically as: \( V \propto n \) or \( \frac{V}{n} = k \), where V is the volume, n is the number of moles, and k is a constant.

Key concepts

Boyle's Law

Picture yourself pressing on a closed, air-filled syringe. As you push, you notice it gets harder to compress the air. Boyle's Law explains this phenomenon, providing insight into how pressure and volume of a gas are related when you keep temperature stable. To understand it in daily life, think of diving deep into the ocean; as the depth increases, water pressure rises and the volume of air in a diver's lungs decreases. This inverse relationship is symbolized mathematically as \( P \propto \frac{1}{V} \) or \( PV = k \), which simply means if you increase pressure, the volume decreases, as long as temperature doesn't change.

When solving problems using Boyle's Law, remember to always use the same units for pressure and volume and expect to see results that show this inverse proportionality. For instance, if you double the pressure exerted on the gas, the volume should, theoretically, reduce by half.

Charles's Law

Have you ever observed a hot air balloon rise as it's heated? Charles's Law offers an explanation for this intriguing occurrence. It describes the direct relationship between the volume of a gas and its temperature when pressure is held constant. The science behind it is simple: heat a gas, and its volume expands; cool it down, and the volume shrinks. This is because gas particles move more energetically at higher temperatures, thus requiring more space. We express this as \( V \propto T \), or \( \frac{V}{T} = k \), meaning that if the temperature (measured in Kelvins) doubles, so does the volume, given that pressure doesn't change.

Using Charles's Law in calculations, it's key to convert temperature to Kelvin, where absolute zero (0 K) is the total absence of thermal energy. Also, as with any gas law, consistency in units is crucial. Through this law, we can predict how gases will behave under different temperatures—like predicting how much a balloon will expand on a hot day.

Avogadro's Law

Have you ever wondered why balloons of the same size contain the same amount of air, regardless of where they are? This consistent behavior of gases is described by Avogadro's Law. The law states that under the same conditions of temperature and pressure, equal volumes of gases contain an equal number of molecules. It reveals a direct proportionality between the volume of gas (V) and the number of moles of gas (n) as shown in the equation \( V \propto n \) or \( \frac{V}{n} = k \). This means that if you have a certain volume of a gas with 1 mole of particles, doubling the number of moles to 2 while keeping temperature and pressure constant will also double the volume.

Practically, this law allows chemists to use gases to determine molecular weights and quantify chemical reactions. Just recall that to apply Avogadro's law, the temperature and pressure conditions must not change and that the volume and number of moles are directly proportional to each other.