# Unit 4 Sections A14a-c In which you will learn about: Combined gas law Dalton’s law Graham’s Law.

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Unit 4 Sections A14a-c In which you will learn about: Combined gas law Dalton’s law Graham’s Law

A14a: Combined Gas Law Combined Gas Law: Used for situations in which only the number of moles is constant. T has to be in Kelvins! ‘Nuff Said

Homework Part 1 1)A 350 cm 3 sample of helium gas is collected at 22.0 o C and 99.3 kPa. What volume would this gas occupy at STP? 2)A sample of neon is collected at 2.7 atm and 12.0 o C. It has a volume of 2.25 L. What would be the volume of this gas at STP? 3) A sample of argon has a volume of 205 cm 3 when its temperature is -44.0 o C and its pressure is 712 mm of Hg. What would be the volume of the argon at STP?

A14b: Dalton’s Law of Partial Pressures Yes, that Dalton. The guy who had that atomic theory thing. When Dalton studied the properties of gases, he found that each gas in a mixture exerts a pressure independently of other gases present. Dalton’s law of partial pressures states that the total pressure of a mixture of gases is equal to the sum of the pressures of all the gases in the mixture. – The portion of the total pressure contributed by a single gas is called its partial pressure. – Partial pressured depends on the number of moles of gas, size of the container, and temperature of the mixture – Partial pressure does NOT depend on the identity of the gas Dalton’s Law: P total = P 1 + P 2 + P 3 +…P n

The Partial Pressure of a Gas A mixture of oxygen (O 2 ), carbon dioxide (CO 2 ), and nitrogen (N 2 ) has a total pressure of 0.97 atm. What is the partial pressure of O 2 if the partial pressure of CO 2 is 0.70 atm and the partial pressure of N 2 is 0.12 atm? P total = 0.97 atm P CO2 = 0.70 atm P N2 = 0.12 atm P O2 = ? P total = P CO2 + P CO2 + P O2 P O2 = P total – (P CO2 + P N2 ) P O2 = 0.97 atm – (0.70 atm + 0.12 atm) = 0.15 atm

Your Turn! (HW Part 2) 4) What is the partial pressure of hydrogen gas in a mixture of hydrogen and helium if the total pressure is 600. mm Hg and the partial pressure of helium is 439 mm Hg? 5) Find the total pressure for a mixture that contains four gases with partial pressures of 5.00 kPa, 4.56 kPa, 3.02 kPa, and 1.20 kPa. 6) Find the partial pressure of carbon dioxide gas in a gas mixture with a total pressure of 30.4 kPa if the partial pressures of the other two gases in the mixture are 16.5 kPa and 3.7 kPa.

A14c: Graham’s Law of Diffusion/Effusion Diffusion: the movement of one material through another from an area of high concentration to an area of lower concentration Effusion: the movement of one material through a small hole from an area of high concentration to an area of lower concentration

Derivation of Graham’s Law Based on KMT – if two gases of differing molar masses are at the same temp, they have the same average kinetic energy (KE) KE = ½ mv 2 where m is molar mass and v is velocity KE A = KE B ½ m A v A 2 = ½ m B v B 2 v A 2 / v B 2 = m B /m A v A /v B = √(m B /m A )

So What Does Graham’s Law Tell Us? First, note that in the formula on the previous slide, the rate of gas A compared to gas B is inversely proportional to the square root of it’s molar mass So, although it’s rate A:rate B, on the other side of the equation is mass B: mass A! Be careful on this! Graham’s law basically says that smaller molecules move faster than bigger molecules

HW Part 3 – Try your best! (sorry, no example problem because it’s too hard to type on PowerPoint – do your best and I’ll do thorough examples in class). 7) Calculate the ratio of effusion rates for nitrogen versus neon. Remember that nitrogen is diatomic! 8) Calculate the ratio of diffusion rates for carbon monoxide versus carbon dioxide. 9) What is the rate of effusion for a gas that has a molar mass twice that of a gas that effuses at a rate of 3.6 mol/min?

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