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General Chemistry Gas Laws CE 541

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What Are Gas Laws The gas laws are a set of laws that describe the relationship between thermodynamic temperature (T), pressure (P) and volume (V) of gases thermodynamic temperaturepressurevolumegasesthermodynamic temperaturepressurevolumegases

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Boyle's Law Boyle's law (sometimes referred to as the Boyle Mariotte law) is one of the gas laws. gas lawsgas laws It states that For a fixed mass of ideal gas at fixed temperature, the product of pressure and volume is a constant. temperaturepressurevolume temperaturepressurevolume

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The mathematical expression for Boyle's law is: where: P is the pressure of the gas P is the pressure of the gaspressure V is volume of the gas V is volume of the gasvolume k is a constant, and has units of force times distance k is a constant, and has units of force times distance

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Value of k is computed from measurements of volume and pressure for a fixed quantity of gas. Value of k is computed from measurements of volume and pressure for a fixed quantity of gas. The equation says that, after forcing the volume V of the fixed quantity of gas to increase, keeping the gas at the initially measured temperature, the pressure P must decrease proportionally. Conversely, reducing the volume of the gas increases the pressure. The equation says that, after forcing the volume V of the fixed quantity of gas to increase, keeping the gas at the initially measured temperature, the pressure P must decrease proportionally. Conversely, reducing the volume of the gas increases the pressure. Boyle's law is commonly used to predict the result of introducing a change, in volume and pressure only, to the initial state of a fixed quantity of gas. The "before" and "after" volumes and pressures of the fixed amount of gas, where the "before" and "after" temperatures are the same (heating or cooling will be required to meet this condition), are related by the equation: Boyle's law is commonly used to predict the result of introducing a change, in volume and pressure only, to the initial state of a fixed quantity of gas. The "before" and "after" volumes and pressures of the fixed amount of gas, where the "before" and "after" temperatures are the same (heating or cooling will be required to meet this condition), are related by the equation: P after V after = P before V before P after V after = P before V before In practice, this equation is solved for one of the two "after" quantities to determine the effect that a change in the other "after" quantity will have. For example: In practice, this equation is solved for one of the two "after" quantities to determine the effect that a change in the other "after" quantity will have. For example: P after = P before V before / V after P after = P before V before / V after

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Charles's law Charles's law is one of the gas laws. gas lawsgas laws It states that At constant pressure, the volume of a given mass of an ideal gas increases or decreases by the same factor as its temperature (in kelvins) increases or decreases.

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The mathematical expression for Charles's law is: where: V is the volume of the gas V is the volume of the gasvolume T is the temperature of the gas (measured in kelvins) T is the temperature of the gas (measured in kelvins)temperaturekelvinstemperaturekelvins k is a constant k is a constant

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To maintain the constant, k, during heating of a gas at fixed pressure, the volume must increase. Conversely, cooling the gas decreases the volume. The exact value of the constant need not be known to make use of the law in comparison between two volumes of gas at equal pressure: To maintain the constant, k, during heating of a gas at fixed pressure, the volume must increase. Conversely, cooling the gas decreases the volume. The exact value of the constant need not be known to make use of the law in comparison between two volumes of gas at equal pressure: In simpler form, as the temperature increases the volume of the gas increases. In simpler form, as the temperature increases the volume of the gas increases.

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Gay-Lussac's law Gay-Lussac's law, known as the law of combining volumes. It states that At constant volume, the pressure of a fixed mass of a given gas is directly proportional to the Kelvin temperature.

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The mathematical expression for Gay-Lussac's law is: where: P is the pressure of the gas. P is the pressure of the gas.pressure T is the temperature of the gas (measured in kelvins). T is the temperature of the gas (measured in kelvins).temperature k is a constant. k is a constant.constant

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This law holds true because temperature is a measure of the average kinetic energy of a substance; as the kinetic energy of a gas increases, its particles collide with the container walls more rapidly, thereby exerting increased pressure. kinetic energykinetic energy For comparing the same substance under two different sets of conditions, the law can be written as:

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Combined gas law The combined gas law is a gas law which combines Charles's law, Boyle's law, and Gay- Lussac's law. In each of these laws, pressure, temperature, and volume, respectively, must remain constant for the law to be true. In the combined gas law, any of these properties can be found mathematically. gas lawCharles's lawBoyle's lawGay- Lussac's lawpressure temperaturevolumegas lawCharles's lawBoyle's lawGay- Lussac's lawpressure temperaturevolume The law states that The product of the volume of a gas and its pressure over the temperature is equal to a constant.

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The mathematical expression for the combined law is: where: p is the pressure. p is the pressure. V is the volume. V is the volume. T is the temperature (measured in kelvin in SI units). T is the temperature (measured in kelvin in SI units).kelvinSIkelvinSI k is a constant k is a constant

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For comparing the same substance under two different sets of conditions, the law can be written as: We can however remove n (number of moles of the gas) from the equation because it is constant when changing only the conditions, to make: The addition of Avogadro's law to the combined gas law yields the ideal gas law. Avogadro's lawideal gas lawAvogadro's lawideal gas law

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Ideal Gas Law The ideal gas law is the equation of state of a hypothetical ideal gas. equation of stateideal gasequation of stateideal gas The state of an amount of gas is determined by its pressure, volume, and temperature according to the equation: stategasstategas where where P is the pressure [Pa], P is the pressure [Pa],pressure V is the volume [m 3 ], V is the volume [m 3 ],volume n is the amount of substance of gas [mol], n is the amount of substance of gas [mol],amount of substanceamount of substance R is the gas constant m 3 · Pa · K -1 · mol -1, and R is the gas constant m 3 · Pa · K -1 · mol -1, andgas constantgas constant T is the temperature in kelvins [K]. T is the temperature in kelvins [K].temperaturekelvinstemperaturekelvins

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The ideal gas constant (R) is dependent on what units are used in the formula. The value given above, , is for the SI units of pascal-cubic meters per mole-Kelvin. Another value for R is L atm per mol -Kelvin ideal gas constantideal gas constant The ideal gas law is the most accurate for monatomic gases and is favored at high temperatures and low pressures. It does not factor in the size of each gas molecule or the effects of intermolecular attraction.

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A sample of chlorine gas weighs 1.31 g at STP. Calculate the volume this sample of chlorine would occupy under the following new conditions: 3.20 atm and 0.0 C Example

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Solution Calculate the moles of Cl 2 from 1.31 grams = moles Cl 2 Calculate the moles of Cl 2 from 1.31 grams = moles Cl 2 Check the temperature and convert to Kelvin if necessary: K = C = = 273 K Check the temperature and convert to Kelvin if necessary: K = C = = 273 K Check the pressure given and convert to atmospheres unit. Pressure is already in atmospheres, 3.20 atm Check the pressure given and convert to atmospheres unit. Pressure is already in atmospheres, 3.20 atm Use the value of R = liter-atm/mole-K Use the value of R = liter-atm/mole-K Using the PV = nRT plug in the moles, temperature, pressure, and R and solve for the Volume in liters V = nRT / P = ( moles) ( liter-atm / mol-K) (273 K) / 3.20 atm = liters Using the PV = nRT plug in the moles, temperature, pressure, and R and solve for the Volume in liters V = nRT / P = ( moles) ( liter-atm / mol-K) (273 K) / 3.20 atm = liters

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You try this: A sample of chlorine gas weighs 1.31 g at STP. Calculate the volume this sample of chlorine would occupy under the following new conditions: 760 torr and C

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Solution Calculate the moles of Cl 2 from 1.31 grams = moles Cl 2 Check the temperature and convert to Kelvin if necessary: K = C = = 250 K Check the pressure given and convert to atmospheres unit.Pressure is in torr units and 1 atm = 760 torr units so 760 torr 1 atm / 760 torr = 1 atm Use the value of R = liter-atm/mole-K Using the PV = nRT plug in the moles, temperature, pressure, and R and solve for the Volume in liters V = nRT / P = ( moles) ( liter-atm / mol-K) (250 K) / 1 atm = liters

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Dalton's Law In chemistry and physics, Dalton's law (also called Dalton's law of partial pressures) states that the total pressure exerted by a gaseous mixture is equal to the sum of the partial pressures of each individual component in a gas mixture. chemistryphysics pressuregaseous partial pressureschemistryphysics pressuregaseous partial pressures

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Mathematically, the pressure of a mixture of gases can be defined as the summation: Where P 1, P 2, and P 3 represent the partial pressure of each component. It is assumed that the gases do not react with each other. react

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Add partial pressures: P= 1 n 1 RT/V P= 2 n 2 RT/V P = (P 1 + P 2 = ((n 1 + n 2 )( RT/V) Add moles of each substance: n = n+ 1 n 2 P = (nRT/V = ((n 1 +n 2 ) )RT/V(

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Henry s Law In chemistry, Henry's law is one of the gas laws. It states that: chemistrygas lawschemistrygas laws At a constant temperature, the amount of a given gas dissolved in a given type and volume of liquid is directly proportional to the partial pressure of that gas in equilibrium with that liquid. At a constant temperature, the amount of a given gas dissolved in a given type and volume of liquid is directly proportional to the partial pressure of that gas in equilibrium with that liquid. partial pressure partial pressureOR The Solubility of a Gas in a Liquid is Directly Proportional to the Partial Pressure of the Gas above the Liquid. The Solubility of a Gas in a Liquid is Directly Proportional to the Partial Pressure of the Gas above the Liquid.

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The Law can be represented by: Where C equal = concentration of gas dissolved in the liquid at equilibrium P gas = partial pressure of the gas above the liquid K H = Henry s law constant for the gas at the given temperature

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Graham s Law The Law states that: The rate of diffusion of a gas is inversely proportional to the square root of its molecular weight The rate of diffusion of a gas is inversely proportional to the square root of its molecular weight

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The Law can be represented by: Where t = time required for diffusion MW = Molecular Weight So A and B are gas A and gas B, respectively

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