Gas Laws Summary - Lecture notes 1 PDF

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Gas Laws Summary 1/Volume vs. Pressure

1/V

Volume vs. Pressure

Boyle's Law (1662): Provided the temperature is held constant, the Volume of a gas is inversely related to its Pressure. V

Mathematically: P x V = k (a constant); or P1V1 = P2V2

Dalton's Law (1766): The total pressure of a mixture of gases is P P equal to the sum of the partial pressures of each gas. The partial pressure of the gas is directly related to the proportion of that gas in the mixture by particle count (mole fraction, Χ z = moles of gas z / moles of total gas) Mathematically: Ptotal = pA + pB + pc + … ; a lower case "p" indicates a partial pressure. = ΧAPtotal + Χ BPtotal + ΧAPtotal +… Avogadro's Law (1776): Equal volumes of gas at the same temperature and pressure contain equal numbers of moles of gas molecules (n). Although Avogadro himself never actually determined the value that bears his name (6.022 x 1023 mol-1), it was this law that provided the insight needed for Dalton to formulate his relative masses for the elements which led to the mole concept.

Mathematically: V = kn or V/n= k (a constant); or V1/n1 = V2/n2 Charles' Law (1802): Provided the pressure is held constant, the Volume of a gas is directly related to its Temperature Mathematically: V = kT or V/T= k (a constant); or V1/T1 = V2/T2 Pressure vs. Temperature

Volume

Volume vs. Temperature

"Absolute Zero" -273.15 °C

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Temperature (deg. C)

Gay-Lussac's Law (1808), also Amonton’s Law (late 1600’s): Provided the volume is held constant, the Pressure of a gas is directly related to its Temperature (Note: Amonton preceded Gay-Lussac by over 100 years, but worked with a gas mixture (air) since pure gas samples were not available at the time)

"Absolute Zero" -273.15 °C

Mathematically: P = kT or P/T= k (a constant) or P1/T1 = P2/T2 -400

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Temperature (deg. C)

COMBINED GAS LAW: The product of the pressure and the volume of a gas divided by the temperature of the gas is equal to a constant. Kelvin temperatures must be used. The combined gas law is the combination of Boyle’s, Charles’, and Gay-Lussac’s Laws and is used when it isn’t possible to keep one of the PVT variables constant during a process Can be used to calculate the new pressure, volume, or temperature of a gas provided that sufficient information is known AND provided that the system is closed and there is no change in the amount of gas present (number of moles). Mathematically: PV/T = k (a constant)

or

P1V1/T1 = P2V2/T2

IDEAL GAS LAW (Claperyon 1834): The product of the pressure and the volume of a gas divided by the temperature of the gas is equal to number of moles of gas (n) present times the universal gas constant (R). Results from the combination of the combined gas law and Avogadro's Law. Holds for any gas that behaves ideally (see Kinetic-Molecular Theory of Gases). The gas constant, R, was originally determined empirically (by experiment), but it was later shown that the Ideal Gas Law could be derived from the microscopic scale using kinetic molecular theory. Mathematically: PV/T = nR (n = number of moles of gas, R = 0.0821 (L•atm)/(mol•K)) Usually written as: PV = nRT Can also be used to track changes in both conditions and number of moles: (P1V1)/(n1T1) = (P2V2)/(n2T2) = R...