Ideal Gas Law
Derivation of the Ideal Gas Law
Gases are a fundamental state of matter. A gas is a collection of molecules that have a significant distance between t…
A gas is simply a dispersed sample of matter that is fluid and expands freely to occupy available space. However, a certain number of gas molecules occupy a specific volume under a defined temperature and pressure. We can describe the behavior of a gas under these parameters using the ideal gas law, which uses the universal gas constant, R, to relate all of these variables.
The universal gas constant is equal to 8.314 joules per mole Kelvin. This equation enables us to understand state relationships in a gaseous system. For example, in a system of constant temperature and pressure, we know that the addition of more moles of gas results in an increase in volume. Similarly, we can look at a system of constant temperature and moles and see that a decrease in volume results in an increase in pressure.
One challenge is that the ideal gas law describes gases behaving ideally. So what do we mean by that? Ideal behavior assumes that first, the molecules themselves are infinitesimally small and essentially have no volume and that the distance between the molecules is significantly larger than the size of the individual molecule.
Second, we assume that the molecules are constantly in motion. Any collisions occurring between the molecules are elastic, and their motion is frictionless, meaning that the molecules do not lose energy. Finally, we assume that there are no intermolecular forces acting between the molecules and their surroundings.
Unfortunately, most gases do not behave ideally. At very low temperature or high pressure, molecules are very close together and slow-moving, so intermolecular interactions are significant. Similarly, gases with a high molecular weight experience increased interactions due to their large size and mass. However, the ideal gas relationship serves as a good approximation in general.
So how do we use the ideal gas law to study the behavior of a gas in the laboratory? Pressure, volume, and temperature are generally more easily measured, but how about moles, and by extension, mass?
One of the simplest ways to measure the mass of a gas is by the Dumas method. To perform this test, a small amount of a volatile compound in its liquid phase is placed inside a Dumas tube, and the tube is then placed in boiling water.
A volatile compound has a high vapor pressure at room temperature. The vapor pressure is the pressure exerted by a vapor in equilibrium with its liquid phase. Thus, a volatile compound with high vapor pressure transitions from liquid to gas rapidly.
When this happens, the newly formed gas forces the air out of the Dumas tube so that it is solely filled with gas. Once the tube is removed from the water bath and left at room temperature, the gas condenses to form a liquid again. Since mass is conserved, we know that the mass of the condensed liquid is equal to the mass of the gas that filled the known volume of the Dumas tube.
In this lab, you'll explore the ideal gas law by using the Dumas Method to determine the molar mass of an unknown volatile substance. You'll then measure the temperature, pressure, and volume of the system and see how much this gas deviates from ideality.
A gas is simply a dispersed sample of matter that is fluid and expands freely to occupy available space. However, a certain number of gas molecules occupy a specific volume under a defined temperature and pressure. We can describe the behavior of a gas under these parameters using the ideal gas law, which uses the universal gas constant, R, to relate all of these variables.
The universal gas constant is equal to 8.314 joules per mole Kelvin. This equation enables us to understand state relationships in a gaseous system. For example, in a system of constant temperature and pressure, we know that the addition of more moles of gas results in an increase in volume. Similarly, we can look at a system of constant temperature and moles and see that a decrease in volume results in an increase in pressure.
One challenge is that the ideal gas law describes gases behaving ideally. So what do we mean by that? Ideal behavior assumes that first, the molecules themselves are infinitesimally small and essentially have no volume and that the distance between the molecules is significantly larger than the size of the individual molecule.
Second, we assume that the molecules are constantly in motion. Any collisions occurring between the molecules are elastic, and their motion is frictionless, meaning that the molecules do not lose energy. Finally, we assume that there are no intermolecular forces acting between the molecules and their surroundings.
Unfortunately, most gases do not behave ideally. At very low temperature or high pressure, molecules are very close together and slow-moving, so intermolecular interactions are significant. Similarly, gases with a high molecular weight experience increased interactions due to their large size and mass. However, the ideal gas relationship serves as a good approximation in general.
So how do we use the ideal gas law to study the behavior of a gas in the laboratory? Pressure, volume, and temperature are generally more easily measured, but how about moles, and by extension, mass?
One of the simplest ways to measure the mass of a gas is by the Dumas method. To perform this test, a small amount of a volatile compound in its liquid phase is placed inside a Dumas tube, and the tube is then placed in boiling water.
A volatile compound has a high vapor pressure at room temperature. The vapor pressure is the pressure exerted by a vapor in equilibrium with its liquid phase. Thus, a volatile compound with high vapor pressure transitions from liquid to gas rapidly.
When this happens, the newly formed gas forces the air out of the Dumas tube so that it is solely filled with gas. Once the tube is removed from the water bath and left at room temperature, the gas condenses to form a liquid again. Since mass is conserved, we know that the mass of the condensed liquid is equal to the mass of the gas that filled the known volume of the Dumas tube.
In this lab, you'll explore the ideal gas law by using the Dumas Method to determine the molar mass of an unknown volatile substance. You'll then measure the temperature, pressure, and volume of the system and see how much this gas deviates from ideality.
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Q1: What is the ideal gas law and what variables does it relate?
The ideal gas law is a mathematical equation relating pressure, volume, temperature, and moles of gas using the universal gas constant R (8.314 J·K⁻¹·mol⁻¹). This equation enables us to understand state relationships in gaseous systems. For example, at constant temperature and pressure, adding more moles of gas increases volume. It combines several gas laws discovered over centuries into one unified relationship.
Q2: What assumptions does the ideal gas law make about gas molecules?
The ideal gas law assumes gas molecules are infinitesimally small with negligible volume and are significantly separated from each other. Molecules move constantly in frictionless motion, and collisions between them are elastic, meaning no energy is lost. Additionally, no intermolecular forces act between molecules or their surroundings. These assumptions allow the law to predict gas behavior accurately under most laboratory conditions.
Q3: Why do real gases deviate from ideal gas behavior?
Real gases deviate from ideal behavior because their molecules occupy significant volume and experience intermolecular forces. At very low temperatures or high pressures, molecules move slowly and cluster closely together, making intermolecular interactions significant. Gases with high molecular weight also experience increased interactions due to their large size and mass. The Van der Waals equation accounts for these deviations using experimentally determined constants.
Q4: How does the Dumas method use the ideal gas law to find molar mass?
The Dumas method places a volatile liquid in a tube submerged in boiling water, causing it to vaporize and fill the tube with gas. When cooled, the gas condenses back to liquid. Since mass is conserved, the condensed liquid mass equals the original gas mass. By measuring the known volume, temperature, and pressure, you can calculate moles using the ideal gas law and determine the unknown compound's molar mass.
Q5: What is vapor pressure and why is it important for the Dumas method?
Vapor pressure is the pressure exerted by a vapor in equilibrium with its liquid phase. Volatile compounds have high vapor pressure at room temperature, meaning they transition rapidly from liquid to gas. This property is essential for the Dumas method because it ensures the liquid completely vaporizes when heated in boiling water, filling the tube entirely with gas and forcing out all air.
Q6: How do pressure and volume relate in a gas at constant temperature and moles?
At constant temperature and moles, pressure and volume are inversely proportional—when volume decreases, pressure increases proportionally. This relationship, known as Boyle's law, is one of the foundational gas laws combined into the ideal gas law. This inverse relationship helps predict how gas behavior changes when external conditions compress or expand the available space.
Q7: What is the relationship between temperature and pressure in an enclosed gas?
In an enclosed gas at constant volume and moles, pressure is directly proportional to temperature. This relationship, established by Gay-Lussac's law, means that heating a gas increases its pressure proportionally. Conversely, cooling decreases pressure. This direct proportionality is a key component of the ideal gas law and explains why pressurized containers must be kept away from heat sources.