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Ideal Gas Law

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Combining Relationships Science often relies on a controlled experiment. Science often relies on a controlled experiment. Hold all variables fixed except oneHold all variables fixed except one Measure change in another propertyMeasure change in another property Gas laws were each made with all but two properties constant. Gas laws were each made with all but two properties constant. Combine those three laws into a single relationship. Combine those three laws into a single relationship.

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Counting Atoms Adding atoms increases the volume of a gas. Adding atoms increases the volume of a gas. Twice the air in a balloon doubles the volume Twice the air in a balloon doubles the volume Constant pressure and temperatureConstant pressure and temperature Try a relationship: Try a relationship: + =

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Mass Independent Density is mass divided by volume. Density is mass divided by volume. Mass in an equation can be converted to densityMass in an equation can be converted to density PV=amT becomes P = a TPV=amT becomes P = a T Experimentally a would vary for each type of gas Experimentally a would vary for each type of gas Constant is the same if the number of molecules N is counted instead of the mass m. Constant is the same if the number of molecules N is counted instead of the mass m.

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Ideal Gas Law I The equation of state links pressure, volume, temperature, and amount of gas. The equation of state links pressure, volume, temperature, and amount of gas. This is an ideal gas law, since real gases may vary slightly. This is an ideal gas law, since real gases may vary slightly.

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Boltzmanns Constant The constant k applies to all gases. The constant k applies to all gases. Its called Boltzmanns constant. Its called Boltzmanns constant. k = 1.38 x 10 -23 J/Kk = 1.38 x 10 -23 J/K Dimension links temperature and energyDimension links temperature and energy

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The Mole Boltzmanns constant has a very small value. Boltzmanns constant has a very small value. There are a vast number of atoms in a macroscopic systemThere are a vast number of atoms in a macroscopic system Define a fundamental unit to count large numbersDefine a fundamental unit to count large numbers The mole (mol) is a unit of amount. The mole (mol) is a unit of amount. Number of carbon-12 atoms in 12.00 gNumber of carbon-12 atoms in 12.00 g Amount of molecules equal to Avogadros numberAmount of molecules equal to Avogadros number N A = 6.022 x 1023N A = 6.022 x 1023

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Ideal Gas Law II The amount of gas can be measured in moles. The amount of gas can be measured in moles. n = N / N An = N / N A R is the universal gas constant R is the universal gas constant R = N A kR = N A k R = 8.314 J / mol-KR = 8.314 J / mol-K

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Mole Size Standard temperature and pressure (STP) is 0 C and 1 atm = 1.013 x 10 5 Pa. Standard temperature and pressure (STP) is 0 C and 1 atm = 1.013 x 10 5 Pa. What is volume of one mole? What is volume of one mole? Convert temperature to K. T = 0 + 273.15 = 273.15 K Use the molar form of the ideal gas law. V = nRT/P Substitute values: V = (1.000 mol)(8.314 J/mol- K)(273.15 K) / (1.013 x 10 5 Pa) V = 2.242 x 10 -2 m 3 = 22.42 L next

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Molar Volume Avogadro’s Law: Equal volumes of gas at the same temperature and pressure contain equal numbers of particles. But the mass is different!!!

Molar Volume Avogadro’s Law: Equal volumes of gas at the same temperature and pressure contain equal numbers of particles. But the mass is different!!!

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