Gas laws
59 flashcards covering Gas laws for the MCAT Chem / Phys / Psych / Soc section.
Gas laws describe the behavior of gases in response to changes in pressure, volume, temperature, and the amount of gas present. For example, if you squeeze a balloon, its volume decreases while the pressure inside increases—this follows Boyle's Law. Other key laws include Charles's Law, which links volume and temperature, and the Ideal Gas Law, which combines these factors into a single equation. These principles are fundamental in chemistry and physics, helping us understand everything from weather patterns to how engines work, and they form the basis for more complex topics in science.
On the MCAT, gas laws frequently appear in the Chemical and Physical Foundations section, often as passage-based questions or standalone problems requiring calculations or conceptual understanding. You'll encounter traps like forgetting to convert units (e.g., from Celsius to Kelvin) or assuming gases behave ideally under all conditions. Focus on mastering the relationships between variables, applying laws to biological contexts like respiration, and practicing problem-solving to handle multi-step questions efficiently.
Remember to always check your units before plugging numbers into equations.
Terms (59)
- 01
Boyle's Law
Boyle's Law states that for a given amount of gas at constant temperature, the pressure and volume are inversely proportional, meaning that if the volume decreases, the pressure increases, and vice versa.
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Charles's Law
Charles's Law indicates that for a fixed amount of gas at constant pressure, the volume is directly proportional to its absolute temperature in Kelvin, so increasing the temperature expands the gas volume.
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Gay-Lussac's Law
Gay-Lussac's Law describes that for a given amount of gas at constant volume, the pressure is directly proportional to its absolute temperature, meaning higher temperature results in higher pressure.
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Avogadro's Law
Avogadro's Law states that equal volumes of different gases at the same temperature and pressure contain an equal number of moles, implying that volume is directly proportional to the number of moles for a gas.
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Ideal Gas Law
The Ideal Gas Law, expressed as PV = nRT, relates pressure, volume, number of moles, the gas constant, and absolute temperature for an ideal gas, assuming no interactions between molecules.
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Combined Gas Law
The Combined Gas Law combines Boyle's, Charles's, and Gay-Lussac's Laws into one equation, P1V1/T1 = P2V2/T2, allowing calculation of changes in pressure, volume, and temperature for a fixed amount of gas.
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Dalton's Law of Partial Pressures
Dalton's Law states that in a mixture of non-reacting gases, the total pressure is the sum of the partial pressures of each individual gas, which is the pressure each gas would exert if it alone occupied the container.
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Graham's Law of Effusion
Graham's Law describes that the rate of effusion of a gas is inversely proportional to the square root of its molar mass, meaning lighter gases effuse faster than heavier ones under the same conditions.
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Kinetic Molecular Theory
Kinetic Molecular Theory explains gas behavior by assuming gas molecules are in constant random motion, collide elastically, and have negligible volume compared to the container, leading to properties like pressure from molecular impacts.
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Standard Temperature and Pressure
Standard Temperature and Pressure (STP) is defined as 0 degrees Celsius and 1 atmosphere, where one mole of an ideal gas occupies 22.4 liters, serving as a reference point for gas measurements.
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Root Mean Square Speed
Root Mean Square Speed is the average speed of gas molecules in a sample, calculated as the square root of (3RT/M), where R is the gas constant, T is temperature, and M is molar mass, indicating molecular kinetic energy.
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Mean Free Path
Mean Free Path is the average distance a gas molecule travels between collisions, depending on the molecule's size and the number of molecules per unit volume, and it increases with lower pressure or density.
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Van der Waals Equation
The Van der Waals Equation, (P + a/n²V²)(V - nb) = nRT, modifies the Ideal Gas Law to account for intermolecular forces and molecular volume in real gases, providing a more accurate description at high pressures.
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Real Gas Behavior
Real Gas Behavior deviates from the Ideal Gas Law due to intermolecular attractions and finite molecular volumes, becoming significant at high pressures or low temperatures where gases do not behave ideally.
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Compressibility Factor
The Compressibility Factor, Z, is defined as PV/nRT for a gas, where Z equals 1 for an ideal gas; for real gases, Z varies based on conditions, indicating deviations from ideal behavior.
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Boyle's Law Formula
The formula for Boyle's Law is P1V1 = P2V2 for a fixed amount of gas at constant temperature, allowing prediction of pressure or volume changes when one variable is altered.
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Charles's Law Formula
The formula for Charles's Law is V1/T1 = V2/T2 for a fixed amount of gas at constant pressure, relating volume and absolute temperature to show how volume changes with temperature.
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Gay-Lussac's Law Formula
The formula for Gay-Lussac's Law is P1/T1 = P2/T2 for a fixed amount of gas at constant volume, demonstrating the direct relationship between pressure and absolute temperature.
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Avogadro's Law Formula
The formula for Avogadro's Law is V/n = constant at constant temperature and pressure, meaning volume is directly proportional to the number of moles of gas.
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Ideal Gas Constant
The Ideal Gas Constant, R, is a proportionality constant in the Ideal Gas Law, with a value of 0.0821 L·atm/(mol·K) when pressure is in atm and volume in liters, used to relate gas properties.
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Universal Gas Constant Value
The Universal Gas Constant is 8.314 J/(mol·K), used in the Ideal Gas Law when working with SI units, allowing consistent calculations across different systems of measurement.
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Conditions for Ideal Gas Behavior
Ideal Gas Behavior occurs under low pressure and high temperature, where gas molecules are far apart and move rapidly, minimizing intermolecular forces and molecular volume effects.
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Deviations from Ideal Gas Behavior
Deviations from Ideal Gas Behavior happen when gases are at high pressures or low temperatures, where intermolecular attractions and the actual volume of molecules become significant factors.
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Partial Pressure
Partial Pressure is the pressure that a single gas in a mixture would exert if it occupied the same volume alone at the same temperature, calculated as the mole fraction times the total pressure.
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Total Pressure in a Mixture
Total Pressure in a gas mixture is the sum of the partial pressures of all component gases, as per Dalton's Law, which applies when the gases do not react with each other.
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Mole Fraction
Mole Fraction is the ratio of the number of moles of a specific gas to the total number of moles in the mixture, used to calculate partial pressures in gas mixtures.
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Effusion vs. Diffusion
Effusion is the process where gas molecules pass through a small hole into a vacuum, while diffusion is the mixing of gases due to random molecular motion; Graham's Law applies specifically to effusion rates.
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Graham's Law Formula
Graham's Law Formula states that the rate of effusion of one gas divided by another is equal to the square root of the inverse ratio of their molar masses, used to compare effusion speeds.
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Temperature Scales in Gas Laws
Gas Laws require the use of absolute temperature scales like Kelvin, where zero is absolute zero, to ensure direct proportionality in relationships like those in Charles's and Gay-Lussac's Laws.
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Absolute Zero
Absolute Zero is the theoretical temperature at which the volume of an ideal gas would reach zero, equivalent to -273.15 degrees Celsius or 0 Kelvin, marking the absence of molecular motion.
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Charles's Law and Absolute Temperature
In Charles's Law, volume is proportional to absolute temperature in Kelvin, not Celsius, because only the Kelvin scale starts at absolute zero, avoiding negative values in calculations.
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Gay-Lussac's Law and Pressure-Temperature
Gay-Lussac's Law links pressure directly to absolute temperature at constant volume, emphasizing that pressure increases linearly with temperature above absolute zero.
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Avogadro's Hypothesis
Avogadro's Hypothesis posits that equal volumes of gases at the same temperature and pressure contain the same number of molecules, foundational for understanding gas stoichiometry.
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Law of Combining Volumes
The Law of Combining Volumes states that gases react in volumes that are in simple ratios when measured at the same temperature and pressure, as demonstrated by Gay-Lussac in chemical reactions.
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Pressure-Volume Work
Pressure-Volume Work is the energy transferred when a gas expands or contracts against external pressure, calculated as the integral of P dV, and is a key concept in thermodynamics.
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Adiabatic Processes
Adiabatic Processes occur when no heat is exchanged with the surroundings, so the internal energy of a gas changes only through work, leading to temperature changes during expansion or compression.
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Isothermal Processes
Isothermal Processes maintain a constant temperature for the gas, meaning any work done results in heat exchange to keep the temperature steady, often modeled using Boyle's Law.
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Isobaric Processes
Isobaric Processes keep the pressure constant while allowing volume and temperature to change, following Charles's Law for volume-temperature relationships.
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Isochoric Processes
Isochoric Processes occur at constant volume, so any heat added changes the internal energy and temperature, following Gay-Lussac's Law for pressure-temperature.
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PV Diagram
A PV Diagram plots pressure versus volume for a gas, illustrating processes like isothermal expansion as a hyperbola, helping visualize work done in thermodynamic cycles.
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Work Done in Expansion
Work Done in Expansion is the negative of the integral of pressure with respect to volume, representing the energy a gas uses to push against external pressure during volume increase.
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Heat Capacity at Constant Volume
Heat Capacity at Constant Volume is the amount of heat required to raise the temperature of a gas by one degree without changing its volume, related to the gas's internal energy.
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Heat Capacity at Constant Pressure
Heat Capacity at Constant Pressure is the heat needed to raise the temperature of a gas by one degree at constant pressure, accounting for work done in expansion.
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Joule-Thomson Effect
The Joule-Thomson Effect describes the temperature change of a gas when it expands through a throttle at constant enthalpy, leading to cooling in most gases due to intermolecular forces.
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Critical Point of a Gas
The Critical Point is the temperature and pressure above which a gas cannot be liquefied, regardless of pressure applied, marking the end of distinct gas and liquid phases.
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Supercritical Fluids
Supercritical Fluids exist above the critical point, exhibiting properties of both liquids and gases, such as high density and low viscosity, used in applications like extractions.
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Vapor Pressure
Vapor Pressure is the pressure exerted by a vapor in equilibrium with its liquid or solid phase, depending on temperature and influencing boiling points in gas law contexts.
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Boiling Point and Pressure
Boiling Point is the temperature at which a liquid's vapor pressure equals the surrounding pressure, so it decreases with lower external pressure as per gas laws.
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Clausius-Clapeyron Equation
The Clausius-Clapeyron Equation relates the vapor pressure of a substance to its temperature, expressed as ln(P2/P1) = -ΔHvap/R (1/T2 - 1/T1), for predicting boiling point changes.
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Henry's Law
Henry's Law states that the amount of gas dissolved in a liquid is directly proportional to the partial pressure of that gas above the liquid, explaining gas solubility in blood or water.
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Solubility of Gases
Solubility of Gases in liquids decreases with increasing temperature and increases with pressure, as described by Henry's Law, affecting processes like carbonation.
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Application in Respiration
In respiration, gas laws explain how oxygen and carbon dioxide exchange in the lungs, with partial pressures driving diffusion and Henry's Law governing gas dissolution in blood.
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Alveolar Gas Equation
The Alveolar Gas Equation estimates the partial pressure of oxygen in the alveoli as PAO2 = PIO2 - (PACO2 / R), where R is the respiratory exchange ratio, used in pulmonary physiology.
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Common Trap: Temperature in Kelvin
A common error in gas law problems is using Celsius instead of Kelvin for temperature, as laws require absolute temperature to maintain proportional relationships accurately.
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Strategy for Gas Law Problems
To solve gas law problems, first identify the given variables and the law or equation that applies, then convert units as needed, such as temperature to Kelvin, and solve step by step.
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Example: Boyle's Law Calculation
For example, if a gas at 2 atm and 5 L is compressed to 3 L at constant temperature, the new pressure is 3 atm, calculated using P1V1 = P2V2.
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Example: Charles's Law with Helium Balloon
For instance, a helium balloon with 1 L volume at 300 K expands to 1.2 L when warmed to 360 K at constant pressure, illustrating Charles's Law.
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Real Gas Corrections
Real Gas Corrections adjust for non-ideal behavior using equations like Van der Waals, accounting for molecular attractions and volumes to improve accuracy in calculations.
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Van der Waals Constants
Van der Waals Constants, a and b, are gas-specific values where a accounts for intermolecular forces and b for molecular volume, used in the Van der Waals Equation for real gases.