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**General Chemistry Gas Laws**

CE 541 General Chemistry Gas Laws

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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

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

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**The mathematical expression for Boyle's law is:**

where: P is the pressure of the gas V is volume of the gas 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.**

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: Pafter Vafter = Pbefore Vbefore 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: Pafter = Pbefore Vbefore / Vafter

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**Charles's law Charles's law is one of the gas 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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**where: The mathematical expression for Charles's law is:**

V is the volume of the gas T is the temperature of the gas (measured in kelvins) 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: 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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**where: The mathematical expression for Gay-Lussac's law is:**

P is the pressure of the gas. T is the temperature of the gas (measured in kelvins). k is a 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. 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. 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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**where: The mathematical expression for the combined law is:**

p is the pressure. V is the volume. T is the temperature (measured in kelvin in SI units). 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.

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**Ideal Gas Law where V is the volume [m3],**

The ideal gas law is the equation of state of a hypothetical ideal gas. The state of an amount of gas is determined by its pressure, volume, and temperature according to the equation: where P is the pressure [Pa], V is the volume [m3], n is the amount of substance of gas [mol], R is the gas constant m3·Pa·K-1·mol-1, and T is the temperature in kelvins [K].

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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 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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Example 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

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**Solution Calculate the moles of Cl2 from 1.31 grams = 0.0184 moles Cl2**

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 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

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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 -23.0 C

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**Solution Calculate the moles of Cl2 from 1.31 grams = 0.0184 moles Cl2**

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.

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**Mathematically, the pressure of a mixture of gases can be defined as the summation:**

Where P1, P2, and P3 represent the partial pressure of each component. It is assumed that the gases do not react with each other.

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**Add partial pressures:**

P=1n1RT/V P= 2n2RT/V P = (P1+ P2 = ((n1+ n 2)( RT/V) Add moles of each substance: n = n+ 1n2 P = (nRT/V = ((n1+n2) )RT/V(

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Henry’s Law In chemistry, Henry's law is one of the gas laws. It states that: “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”. OR “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 Cequal = concentration of gas dissolved in the liquid at equilibrium Pgas = partial pressure of the gas above the liquid KH = 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”

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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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Gas Laws.

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