Ideal Gas Law

Do you remember the values for STP? Chemists have figured out how to calculate the number of gas particles in a sample of gas if they know temperature, volume, and pressure of the gas sample. At STP, 1 mole of gas occupies a volume of 22.4 Liters

If two gas samples have the same pressure, temperature, and volume, they contain the same number of particles, even if you are comparing two different types of gases. This is AVAGADRO’S LAW

Think-Pair-Share: What 4 gas laws have we learned so far? Simple gas laws: Charles, Boyle, and Gay- Lussack’s help us to relate temperature, pressure, and volume. Combined Gas Law: Combines all 3 simple gas laws into one. Thinking back to the PHET simulation, which variable do the above laws not account for?  Amount of gas!

Ideal Gas Law The ideal gas law relates pressure, volume, temperature, and number of moles It was derived by using the combined gas law to compare a gas under ideal conditions Under ideal conditions… …there are no intermolecular forces between gases …gas particles have no volume

Here is how the Ideal Gas Law was derived. 1)Start with the combined gas law (keeps the amount of gas unchanged during the experiment) 2) While the combined gas law equation assumes the amount of gas is constant, n— mol of gas—could be added to the equations on both sides. P 1 V 1 = P 2 V 2 T 1 T 2 P 1 V 1 = k nT 1

Here is how the Ideal Gas Law was derived. 3) OR: Compare a gas (subscript 1) to 1 mole of another gas (subscript ** STP… P= 1 atm or Kpa V= 22.4 L FOR ONE MOLE T= 273 K …thus it is: per mol (on the bottom) 4) The values ( L∙atm)/(mol∙K) and ( L∙KPa)/(mol ∙K) become the universal gas constant (R). This constant stays the same for all gases, but varies depending on the unit of pressure. P 1 V 1 = P 2 V 2 T 1 T 2 P 1 V 1 = P 2 V 2 nT 1 nT 2

Here is how the Ideal Gas Law was derived. 5)We can re-write the equation by substituting “R” for the constant value. 6)Since “R” was calculated using ideal conditions for 1 mole of gas, add another variable “n” to represent number of moles. 7)Re-arrange the equation to move T out of the denominator into the numerator. P 1 V 1 = R T 1 P 1 V 1 = nR T 1 PV = nRT

The Ideal Gas Law If unit for pressure is: 1)Atmosphere (atm), R= ( L∙atm)/(mol ∙K) 2)KiloPascals (KPa), R= ( L∙KPa)/(mol ∙K)

Using the ideal gas law, you can calculate volume, pressure, temperature, or number of molecules (moles) when given any three of the variables. Example: How many moles of air are in a 0.5L breath on top of Mount Everest when the pressure is 0.33 atm and the temperature is 254K?

Example: How many moles of air are in a 0.5L breath on top of Mount Everest when the pressure is 0.33 atm and the temperature is 254K? First, identify your variables: P = V = T = R = 0.33 atm 0.5 L 254 K (L∙atm)/(mol ∙K)

Example: How many moles of air are in a 0.5L breath on top of Mount Everest when the pressure is 0.33 atm and the temperature is 254K?

Now you try… 1)At what pressure (in atmospheres) would mole of nitrogen gas at 23.0 °C occupy 8.90 L? (0.410 atm)

Now you try… 2) What mass of CO 2 is needed to fill an 80.0 L tank to a pressure of atm at 27.0°C? (21.4 kg)

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