Gas Law Calculations Bernoullis Principle Boyles Law Fast

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Gas Law Calculations Bernoulli’s Principle Boyle’s Law Fast moving fluids… create low pressure P

Gas Law Calculations Bernoulli’s Principle Boyle’s Law Fast moving fluids… create low pressure P 1 V 1 = P 2 V 2 Avogadro’s Law Add or remove gas Manometer Charles’ Law V 1 = V 2 T 1 = T 2 Combined P 1 V 1 = P 2 V 2 T 1 = T 2 PV = n. RT Big = small + height Graham’s Law Gay-Lussac P 1 = P 2 T 1 = T 2 Ideal Gas Law Density P 1 = P 2 T 1 D 1 = T 2 D 2 diffusion vs. effusion Dalton’s Law Partial Pressures 1 atm = 760 mm Hg = 101. 3 k. Pa R = 0. 0821 L atm / mol K PT = P A + P B

History of Science Gas Laws Gay-Lussac’s law Dalton announces his atomic theory Boyle’s law

History of Science Gas Laws Gay-Lussac’s law Dalton announces his atomic theory Boyle’s law 1650 Charles’s law 1700 Mogul empire in India (1526 -1707) Avagadro’s particle Number theory 1750 1800 Constitution of the United States signed United States Bill of Rights ratified Latin American countries gain independence (1791 - 1824) Herron, Frank, Sarquis, Schrader, Kulka, Chemistry, Heath Publishing, 1996, page 220 1850 U. S. Congress bans importation of slaves Napoleon is emperor(1804 - 12) Haiti declares independence

Scientists • Evangelista Torricelli (1608 -1647) – Published first scientific explanation of a vacuum.

Scientists • Evangelista Torricelli (1608 -1647) – Published first scientific explanation of a vacuum. – Invented mercury barometer. • Robert Boyle (1627 - 1691) – Volume inversely related to pressure (temperature remains constant) • Jacques Charles (1746 -1823) – Volume directly related to temperature (pressure remains constant) • Joseph Gay-Lussac (1778 -1850) – Pressure directly related to temperature (volume remains constant)

Apply the Gas Law • The pressure shown on a tire gauge doubles as

Apply the Gas Law • The pressure shown on a tire gauge doubles as twice the volume of air is added at the same temperature. Avogadro’s principle • A balloon over the mouth of a bottle containing air begins to inflate as it stands in the sunlight. Charles’ law • An automobile piston compresses gases. • • An inflated raft gets softer when some of the gas is allowed to escape. Avogadro’s principle A balloon placed in the freezer decreases in size. Charles’ law • A hot air balloon takes off when burners heat the air under its open end. • When you squeeze an inflated balloon, it seems to push back harder. Boyle’s law • A tank of helium gas will fill hundreds of balloons. Boyle’s law • Model: When red, blue, and white ping-pong balls are shaken in a box, the effect is the same as if an equal number of red balls were in the box. Dalton’s law Boyle’s law Charles’ law

Gas Law Problems A gas occupies 473 cm 3 at 36°C. Find its volume

Gas Law Problems A gas occupies 473 cm 3 at 36°C. Find its volume at 94°C. CHARLES’ LAW GIVEN: T V V 1 = 473 cm 3 T 1 = 36°C = 309 K V 2 = ? T 2 = 94°C = 367 K WORK: P 1 V 1 T 2 = P 2 V 2 T 1 (473 cm 3)(367 K)=V 2(309 K) V 2 = 562 cm 3 Courtesy Christy Johannesson www. nisd. net/communicationsarts/pages/chem

Gas Law Problems A gas occupies 100. m. L at 150. k. Pa. Find

Gas Law Problems A gas occupies 100. m. L at 150. k. Pa. Find its volume at 200. k. Pa. BOYLE’S LAW GIVEN: P V WORK: P 1 V 1 T 2 = P 2 V 2 T 1 V 1 = 100. m. L P 1 = 150. k. Pa V 2 = ? P 2 = 200. k. Pa (150. k. Pa)(100. m. L)=(200. k. Pa)V 2 = 75. 0 m. L Courtesy Christy Johannesson www. nisd. net/communicationsarts/pages/chem

Gas Law Problems A gas occupies 7. 84 cm 3 at 71. 8 k.

Gas Law Problems A gas occupies 7. 84 cm 3 at 71. 8 k. Pa & 25°C. Find its volume at STP. COMBINED GAS LAW GIVEN: P T V WORK: P 1 V 1 T 2 = P 2 V 2 T 1 V 1 = 7. 84 cm 3 P 1 = 71. 8 k. Pa T 1 = 25°C = 298 K V 2 = ? P 2 = 101. 325 k. Pa T 2 = 273 K (71. 8 k. Pa)(7. 84 cm 3)(273 K) =(101. 325 k. Pa) V 2 (298 K) V 2 = 5. 09 cm 3 Courtesy Christy Johannesson www. nisd. net/communicationsarts/pages/chem

Gas Law Problems A gas’ pressure is 765 torr at 23°C. At what temperature

Gas Law Problems A gas’ pressure is 765 torr at 23°C. At what temperature will the pressure be 560. torr? GAY-LUSSAC’S LAW GIVEN: P T P 1 = 765 torr T 1 = 23°C = 296 K P 2 = 560. torr T 2 = ? WORK: P 1 V 1 T 2 = P 2 V 2 T 1 (765 torr)T 2 = (560. torr)(309 K) T 2 = 226 K = -47°C Courtesy Christy Johannesson www. nisd. net/communicationsarts/pages/chem

The Combined Gas Law (This “gas law” comes from “combining” Boyle’s, Charles’, and Gay-Lussac’s

The Combined Gas Law (This “gas law” comes from “combining” Boyle’s, Charles’, and Gay-Lussac’s law) P = pressure (any unit will work) V = volume (any unit will work) T = temperature (must be in Kelvin) 1 = initial conditions 2 = final conditions

A gas has volume of 4. 2 L at 110 k. Pa. If temperature

A gas has volume of 4. 2 L at 110 k. Pa. If temperature is constant, find pressure of gas when the volume changes to 11. 3 L. P 1 V 1 T 1 = P 2 V 2 T 2 P 1 V 1 = P 2 V 2 110 k. Pa (4. 2 L) = P 2 (11. 3 L) P 2 = 40. 9 k. Pa (temperature is constant) (substitute into equation)

Original temp. and vol. of gas are 150 o. C and 300 dm 3.

Original temp. and vol. of gas are 150 o. C and 300 dm 3. Final vol. is 100 dm 3. Find final temp. in o. C, assuming constant pressure. T 1 = 150 o. C + 273 = 423 K P 1 V 1 T 1 = P 2 V 2 V 1 T 2 T 1 = V 2 300 dm 3 T 2 423 K = 100 dm 3 T 2 Cross-multiply and divide 300 dm 3 (T 2) = 423 K (100 dm 3) - 132 o. C T 2 = 141 K K - 273 = o. C

A sample of methane occupies 126 cm 3 at -75 o. C and 985

A sample of methane occupies 126 cm 3 at -75 o. C and 985 mm Hg. Find its volume at STP. T 1 = -75 o. C + 273 = 198 K P 1 V 1 T 1 = P 2 V 2 985 mm Hg (126 cm 3) T 2 198 K = 760 mm Hg (V 2) 273 K Cross-multiply and divide: 985 (126) (273) = 198 (760) V 2 = 225 cm 3

Density of Gases Density formula for any substance: For a sample of gas, mass

Density of Gases Density formula for any substance: For a sample of gas, mass is constant, but pres. and/or temp. changes cause gas’s vol. to change. Thus, its density will change, too. ORIG. VOL. If V (due to P NEW VOL. or T ), then… D Density of Gases Equation: ORIG. VOL. If V (due to P NEW VOL. or T ), then… D ** As always, T’s must be in K.

Density of Gases Density formula for any substance: For a sample of gas, mass

Density of Gases Density formula for any substance: For a sample of gas, mass is constant, but pres. and/or temp. changes cause gas’s vol. to change. Thus, its density will change, too. Because mass is constant, any value can be put into the equation: lets use 1 g for mass. For gas #1: Take reciprocal of both sides: Substitute into equation “new” values for V 1 and V 2 For gas #2:

A sample of gas has density 0. 0021 g/cm 3 at – 18 o.

A sample of gas has density 0. 0021 g/cm 3 at – 18 o. C and 812 mm Hg. Find density at 113 o. C and 548 mm Hg. T 1 = – 18 o. C + 273 = 255 K P 1 P 2 = T 1 D 1 T 2 D 2 T 2 = 113 o. C + 273 = 386 K 812 mm Hg 548 mm Hg = 255 K (0. 0021 g/cm 3) 386 K (D 2) Cross multiply and divide (drop units) 812 (386)(D 2) = 255 (0. 0021)(548) D 2 = 9. 4 x 10– 4 g/cm 3

A gas has density 0. 87 g/L at 30 o. C and 131. 2

A gas has density 0. 87 g/L at 30 o. C and 131. 2 k. Pa. Find density at STP. T 1 = 30 o. C + 273 = 303 K P 1 P 2 = T 1 D 1 T 2 D 2 131. 2 k. Pa = 303 K (0. 87 g/L) 101. 3 k. Pa 273 K (D 2) Cross multiply and divide (drop units) 131. 2 (273)(D 2) = 303 (0. 87)(101. 3) D 2 = 0. 75 g/L

Find density of argon at STP. m 39. 9 g D = = V

Find density of argon at STP. m 39. 9 g D = = V 22. 4 L 1. 78 g/L 1 mole of Ar = 39. 9 g Ar = 6. 02 x 1023 atoms Ar = 22. 4 L @ STP

Find density of nitrogen dioxide at 75 o. C and 0. 805 atm. D

Find density of nitrogen dioxide at 75 o. C and 0. 805 atm. D of NO 2 @ STP… T 2 = 75 o. C + 273 = 348 K 1 (348) (D 2) = 273 (2. 05) (0. 805) D 2 = 1. 29 g/L

A gas has mass 154 g and density 1. 25 g/L at 53 o.

A gas has mass 154 g and density 1. 25 g/L at 53 o. C and 0. 85 atm. What vol. does sample occupy at STP? Find D at STP. T 1 = 53 o. C + 273 = 326 K 0. 85 (273) (D 2) = 326 (1. 25) (1) D 2 = 1. 756 g/L Find vol. when gas has that density.

Density and the Ideal Gas Law Combining the formula for density with the Ideal

Density and the Ideal Gas Law Combining the formula for density with the Ideal Gas law, substituting and rearranging algebraically: M = Molar Mass P = Pressure R = Gas Constant T = Temperature in Kelvin