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UNIT 7 Gas Laws ABClark-Grubb

Elements that exist as gases at STP

Review of Physical Characteristics of Gases Gases assume the volume and shape of their containers. Gases are the most compressible state of matter. Gases will mix evenly and completely when confined to the same container. Gases have much lower densities than liquids and solids.

Important Measurements… Symbol Units Pressure P atm or kPa or mmHg Volume V L or mL or cm3 Temperature T K (K = ºC + 273) Amount n moles Gas Constant R 0.08206 L · atm or 8.31 L · kPa mol · K mol · K

PRESSURE AND VOLUME ARE INVERSELY RELATEDh Boyle’s Law: At Constant temperature (T) & Constant amount of gas (n) PRESSURE AND VOLUME ARE INVERSELY RELATEDh ttp://www.youtube.com/watch?v=J_I8Y-i4Axc

T1 & T2 do not change due to CONSTANT TEMPERATURE A sample of chlorine gas occupies a volume of 946 mL at a pressure of 726 mmHg. What is the pressure of the gas (in mmHg) if the volume is reduced at constant temperature to 154 mL? V1 P1 P2 V2 P1 V1 T2 = P2 V2 T1 T1 & T2 do not change due to CONSTANT TEMPERATURE 726 mmHg x 946 mL = P2 x 154 mL 4460 mmHg = P2 Boyle’s Law

T1 & T2 do not change due to CONSTANT TEMPERATURE A sample of bromine gas occupies a volume of 648 mL at a pressure of 1.23 atm. What is the volume of the gas (in mL) if the pressure is reduced at constant temperature to standard pressure? V1 P1 V2 P2 1.00 atm P1 V1 T2 = P2 V2 T1 T1 & T2 do not change due to CONSTANT TEMPERATURE Find the standard pressure on the chart with the same unit as the given pressure and use it in the problem for P2. 1.23 atm x 648 mL = 1.00 atm x V2 797 mL = V2 Boyle’s Law

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Charles’s Law At constant Pressure and Amount of gas TEMPERATURE AND VOLUME ARE DIRECTLY RELATEDhttp://www.youtube.com/watch?v=xeh86NwQdXA

P1 V1 T2 = P2 V2 T1 *Temperature must always be in Kelvin* A sample of CO gas occupies 3.20 L at 125°C. At what temperature will the gas occupy a volume of 1.54 L if the pressure remains constant? 398 K T2 V2 P1 & P2 do not change due to CONSTANT PRESSURE *Temperature must always be in Kelvin* T1 = 125°C + 273 = 398 K P1 V1 T2 = P2 V2 T1 (3.20 L) T2 = 1.54 L (398 K) T2 = 192 K Charles’s Law

P1 & P2 do not change due to CONSTANT PRESSURE A sample of CO2 gas occupies 6.91 L at 112°C. What volume will the gas occupy when the temp. is raised to 179°C if the pressure remains constant? 385 K V2 V1 T2 452 K P1 & P2 do not change due to CONSTANT PRESSURE T1 = 112°C + 273 = 385 K T2 = 179°C + 273 = 452 K P1 V1 T2 = P2 V2 T1 6.91 L (452 K) = V2 (385 K) 8.11 L = V2 Charles’s Law

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P1 V1 T2 = P2 V2 T1 Combined Gas Law (0.581 atm)(405mL)( 273K) = If the initial volume of a gas was 405 mL at 90.0°C & 0.581 atm, what would the volume be at STP? P1 V2 P2 T2 T1 = 90 + 273 K = 363 K T2 = 273 K P2 = 1.00 atm P1 V1 T2 = P2 V2 T1 (0.581 atm)(405mL)( 273K) = (1.00 atm) V2 (363K) 177 mL = V2

P1 V1 T2 = P2 V2 T1 Combined Gas Law (1.25 atm)(236mL)( 298K) = P2 The initial volume of SO2 was 236 L at 75.0°C & 1.25 atm, what would the pressure be when the volume is raised to 652 L while the temp. is decreased to 25.0°C? P2 V2 T2 T1 = 75 + 273 K = 348 K T2 = 25 + 273 K = 298 K P1 V1 T2 = P2 V2 T1 (1.25 atm)(236mL)( 298K) = P2 (652L) (348K) 0.387 atm = P2

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Ideal Gas Law With the combined gas law, you use three variables: pressure, volume & temperature. It assumes that the amount of gas is constant. The Ideal Gas Law is used to calculate the number of moles of gas The Ideal Gas Law uses a constant in it’s formula. (R)

Ideal Gas Law PV = nRT V = 30.5 L 1.00 atm x V = Remember: n = moles! Change the grams when you need to! n V T P What is the volume (in liters) occupied by 49.8 g of HCl at STP? 49.8 g HCl 1 mole HCl =1.36 mole 36.5 g HCl T = 273 K P = 1.00 atm PV = nRT R = 0.0821 L•atm/mol•K 1.36 mol x 0.0821 x 273 K L•atm mol•K 1.00 atm x V = V = 30.5 L

Ideal Gas Law PV = nRT P = 8.28 atm P x 2.50L = Remember: n = moles! Change the grams when you need to! T P n What is the pressure occupied by 28.0 g of O2 at 15.0°C & 2.50 L? What is the pressure occupied by 28.0 g of O2 at 15.0°C & 2.50 L? V 1 mole O2 28.0 g O2 = 0.875 mole 32.0 g O2 T = 15.0 + 273 = 288 K PV = nRT R = 0.0821 L•atm/mol•K 0.875 mol x 0.0821 x 288 K L•atm mol•K P x 2.50L = P = 8.28 atm

Ideal Gas Law With the combined gas law, you use three variables: pressure, volume & temperature. It assumes that the amount of gas is constant. The Ideal Gas Law is used to calculate the number of moles of gas The Ideal Gas Law uses a constant in it’s formula. (R)