9.2 Relating Pressure, Volume, Amount, and Temperature: The Ideal Gas Law
2 min read•june 25, 2024
The connects pressure, volume, moles, and temperature for gases. It's a powerful tool for predicting how gases behave under different conditions. Understanding this equation helps us solve real-world problems involving gases.
Gas behavior can be explained by the motion of tiny particles. As these particles move faster or collide more often, we see changes in pressure, volume, and temperature. This microscopic view helps us make sense of the macroscopic properties we observe.
The Ideal Gas Law
Application of ideal gas law
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- expressed as [PV = nRT](https://www.fiveableKeyTerm:PV_=_nRT) relates pressure (), volume (), amount of gas in moles (), ( = 0.08206 L·atm/mol·K), and temperature in ()
- Rearrange equation to solve for desired variable (volume: )
- Ensure consistent units when solving problems convert degrees Celsius to Kelvin () and other pressure units (, ) to
- conditions are often used as a reference point for gas behavior calculations
Effects of variable changes on gases
- : (constant temperature and amount) pressure and volume inversely proportional as pressure increases, volume decreases and vice versa
- : (constant pressure and amount) volume and temperature directly proportional as temperature increases, volume increases and vice versa
- : (constant volume and amount) pressure and temperature directly proportional as temperature increases, pressure increases and vice versa
- : (constant pressure and temperature) volume and amount directly proportional as amount of gas increases, volume increases and vice versa
- Dalton's Law of Partial Pressures: In a mixture of gases, the total pressure is the sum of the partial pressures of each gas
Molecular interpretation of gas behavior
- describes gas behavior based on particle motion
- Gas particles in constant, random motion collide with each other and container walls
- Collisions are elastic, no energy lost during collisions
- Average kinetic energy of gas particles proportional to absolute temperature
- Pressure results from gas particles colliding with container walls
- As number of particles or speed increases, frequency and force of collisions increase, resulting in higher pressure
- Temperature measures average kinetic energy of gas particles
- Higher temperatures indicate greater average kinetic energy and faster particle movement
- Volume changes result from changes in distance between gas particles
- As volume increases, particles have more space to move, reducing collision frequency and decreasing pressure
Real gases and deviations from ideal behavior
- deviate from ideal gas behavior due to particle interactions and finite particle size
- quantifies the deviation of real gases from ideal behavior
- of a gas is the volume occupied by one mole of the gas under specific conditions
Key Terms to Review (30)
Amontons’s law: Amontons's law states that the pressure of a gas is directly proportional to its absolute temperature, assuming volume and amount of gas are constant. Mathematically, it is expressed as $P \propto T$ or $P/T = k$ where $k$ is a constant.
Atmospheres: An atmosphere is the layer of gases surrounding a planet or other celestial body that is retained by the body's gravity. It plays a crucial role in the gas pressure and temperature of a planet, which are key factors in the Ideal Gas Law.
Avogadro’s law: Avogadro's law states that the volume of a gas is directly proportional to the number of moles of gas when temperature and pressure are held constant. Mathematically, it can be expressed as $V \propto n$ or $\frac{V}{n} = k$.
Avogadro's Law: Avogadro's Law states that the volume of a gas is directly proportional to the amount of the gas, at constant temperature and pressure. It establishes a connection between the number of gas particles and the volume they occupy, which is a crucial concept in understanding the behavior of gases and the Ideal Gas Law.
Boyle's Law: Boyle's Law is a fundamental principle in the study of gas behavior that describes the inverse relationship between the pressure and volume of a gas at constant temperature. It states that the pressure of a gas is inversely proportional to its volume, meaning that as the volume of a gas increases, its pressure decreases, and vice versa.
Charles' Law: Charles' Law is a fundamental principle in thermodynamics that describes the relationship between the volume and absolute temperature of a gas, assuming the pressure and amount of gas remain constant. It states that the volume of a gas is directly proportional to its absolute temperature.
Charles’s law: Charles's law states that the volume of a gas is directly proportional to its temperature when pressure and the amount of gas are held constant. Mathematically, it is expressed as $V \propto T$ or $\frac{V_1}{T_1} = \frac{V_2}{T_2}$.
Compressibility Factor: The compressibility factor, also known as the compression factor or the gas deviation factor, is a dimensionless quantity that describes the deviation of a real gas from the behavior of an ideal gas. It is used to account for the non-ideal behavior of gases, which arises due to the finite size and intermolecular interactions of gas molecules.
Compressibility factor (Z): The compressibility factor (Z) is a measure of how much the behavior of a real gas deviates from an ideal gas. It is defined as the ratio $Z = \frac{PV}{nRT}$.
Gay-Lussac's Law: Gay-Lussac's Law is a fundamental principle in chemistry that describes the relationship between the pressure and temperature of a gas. It states that the pressure of a gas is directly proportional to its absolute temperature, as long as the volume and amount of the gas remain constant.
Ideal gas constant: The ideal gas constant (R) is a proportionality factor in the ideal gas law equation, $PV = nRT$, which relates the pressure, volume, amount of gas, and temperature. Its value depends on the units used for these variables.
Ideal gas law: The Ideal Gas Law is a fundamental equation in chemistry that relates the pressure, volume, temperature, and amount of an ideal gas. It is represented by the formula $PV = nRT$ where $P$ is pressure, $V$ is volume, $n$ is the number of moles, $R$ is the gas constant, and $T$ is temperature.
Ideal Gas Law: The Ideal Gas Law is a fundamental equation that describes the relationship between the pressure, volume, amount, and absolute temperature of a gas. It is a crucial concept in understanding the behavior of gases and their applications in various fields of chemistry.
Kelvin: Kelvin is the base unit of temperature in the International System of Units (SI). It is named after the physicist William Thomson, also known as Lord Kelvin, who was the first to propose an absolute scale of temperature. The Kelvin scale is a fundamental quantity in various areas of chemistry, including measurements, the ideal gas law, collision theory, and the study of spontaneity.
Kelvin (K): Kelvin (K) is the SI unit of thermodynamic temperature. It is one of the seven base units in the International System of Units (SI).
Kinetic molecular theory: The kinetic molecular theory explains the behavior of gases in terms of motion and energy of their molecules. It states that gas particles are in constant, random motion and that the temperature of a gas is proportional to the average kinetic energy of its molecules.
Kinetic Molecular Theory: The kinetic molecular theory is a model that explains the behavior of gases by describing the motion and interactions of gas particles. It provides a framework for understanding the fundamental properties of gases, such as pressure, volume, and temperature, in the context of the microscopic behavior of gas molecules.
KPa: kPa, or kilopascal, is a unit of pressure in the International System of Units (SI). It is a derived unit that represents the force per unit area, and it is commonly used to measure the pressure of gases, liquids, and solids in the context of the Ideal Gas Law.
MmHg: mmHg, or millimeters of mercury, is a unit of pressure commonly used in various scientific contexts, especially in relation to gases. It is defined as the pressure exerted by a column of mercury 1 millimeter high at the standard acceleration due to gravity. This unit is particularly significant in understanding gas behavior under different conditions of temperature and volume, as it relates closely to the concept of pressure in the Ideal Gas Law.
Molar Volume: Molar volume is the volume occupied by one mole of a substance at a given temperature and pressure. It is a fundamental concept in chemistry that relates the amount of a substance to its physical volume and is essential for understanding the behavior of gases, reaction stoichiometry, and the ideal gas law.
P₁/T₁ = P₂/T₂: P₁/T₁ = P₂/T₂ is a fundamental relationship in the study of gas behavior, which states that the ratio of pressure to absolute temperature is constant for a given amount of gas at a fixed volume. This relationship is a key component of the Ideal Gas Law and helps describe how changes in pressure and temperature affect the properties of a gas.
P₁V₁ = P₂V₂: The equation P₁V₁ = P₂V₂ is a fundamental relationship in the study of gases, known as Boyle's law. It describes the inverse proportionality between the pressure and volume of a gas, stating that the product of the initial pressure (P₁) and initial volume (V₁) is equal to the product of the final pressure (P₂) and final volume (V₂) for a given amount of gas at a constant temperature.
Partial Pressure: Partial pressure is the pressure exerted by a specific gas in a mixture of gases. It is the contribution of an individual gas to the total pressure of the system, and it is directly proportional to the mole fraction of that gas in the mixture.
PV = nRT: PV = nRT is the ideal gas law, which describes the relationship between the pressure (P), volume (V), amount of substance (n), and absolute temperature (T) of an ideal gas. This fundamental equation is used to predict the behavior of gases and understand various gas-related phenomena.
R: R is a variable that represents the universal gas constant, a fundamental physical constant that relates the pressure, volume, amount, and temperature of an ideal gas. It is a crucial parameter in the Ideal Gas Law and is used in various calculations involving the behavior of gases.
Real Gases: Real gases refer to the behavior of gases that deviate from the ideal gas model, taking into account the finite size of gas molecules and the attractive and repulsive forces between them. This is in contrast to the idealized behavior described by the Ideal Gas Law, which assumes gas molecules are point-like particles with no volume and no intermolecular interactions.
Standard molar volume: Standard molar volume is the volume occupied by one mole of an ideal gas at standard temperature and pressure (STP), which is 0°C (273.15 K) and 1 atm pressure. It is approximately 22.414 liters.
Standard Temperature and Pressure (STP): Standard temperature and pressure (STP) is a set of conditions used as a reference point to measure and compare the properties of gases. It defines a specific temperature and pressure at which the physical and chemical properties of gases are standardized, allowing for consistent and meaningful comparisons across different situations.
V₁/n₁ = V₂/n₂: The ratio of the volume (V) to the amount of substance (n) is equal between two different states or conditions of a gas. This relationship is a key part of the Ideal Gas Law, which describes the behavior of gases under various conditions of pressure, volume, amount, and temperature.
V₁/T₁ = V₂/T₂: The relationship between the volume and absolute temperature of a fixed amount of an ideal gas, as described by the ideal gas law. This equation states that the ratio of the initial volume (V₁) to the initial absolute temperature (T₁) is equal to the ratio of the final volume (V₂) to the final absolute temperature (T₂).