# Combining the Gas Laws: (The Ideal Gas Equation and the General Gas Equation) The ideal gas equation is a single equation that includes all four gas variables; V, T, P, amount of gas (n). Any gas that obeys this equation is said to be an ideal gas (or perfect gas).

# Example: What is the volume occupied by 13.7 g Cl2 at 45⁰C and 745 mmHg ?

# Solution:

# Example: How many molecules of N2 remained in an ultrahigh vacuum system of 128 mL volume when the pressure is reduced to 5×10-10 mmHg at 25⁰C ? (R=0.0821 L.atm.mol-1.K-1, NA = 6.02×1023)

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# •Ch. 5: Gases

•Dr. Namphol Sinkaset

•Chem 200: General Chemistry I

•I. Chapter Outline

I.Introduction

II.Gas Pressure

III.Gas Laws

IV.Gas Law Problems

V.Dalton’s Law of Partial Pressures

VI.Kinetic-Molecular Theory of Gases

VII.Real Gases

•I. The Unique Gas Phase

•Physical properties of a gas are nearly independent of its chemical identity!

•Gas behavior is markedly different than solid or liquid behavior.

•We look at the origins of equations used to describe gases and then theorize the reasons why gas behavior is so universal.

•II. Pressure

•Pressure is simply a force exerted over a surface area.

•II. Atmospheric Pressure

•Patm is simply the weight of the earth’s atmosphere pulled down by gravity.

•Barometers are used to monitor daily changes in Patm.

•Torricelli barometer was invented in 1643.

•II. Manometers

•In the lab, we use manometers to measure pressures of gas samples.

•II. Units of Pressure

•For historic reasons, we have units such as torr and mm Hg. (Why?)

•The derived SI unit for pressure is N/m2, known as the pascal (Pa).

•Standard conditions for gases (STP) occurs at 1 atm and 0 °C. Under these conditions, 1 mole of gas occupies 22.4 L.

•Note that 1 atm = 760 mm Hg = 760 torr = 101.325 kPa.

•III. Gas Laws

•A sample of gas can be physically described by its pressure (P), temperature (T), volume (V), and amount of moles (n).

•If you know any 3 of these variables, you know the 4th.

•We look at the history of how the ideal gas law was formulated.

•III. Volume and Pressure – Boyle’s Law

•The volume of a gas is inversely related to pressure, i.e. if P increases, V decreases.

•III. Volume and Temperature – Charles’s Law

•The volume of a gas is directly related to its temperature, i.e. if T is increased, V will increase.

•III. The Combined Gas Law

•Boyle’s and Charles’s Laws can be combined into a convenient form.

•III. Volume and Moles – Avogadro’s Law

•The pressure of a gas is directly related to the number of moles of gas, i.e. if n increases, V will increase.

•III. The Ideal Gas Law

•The ideal gas law is a combination of the combined gas law and Avogadro’s Law.

•IV. Gas Law Problems

•There are many variations on gas law problems.

•A few things to keep in mind:

1)Temperature must be in Kelvin

2)If problem involves a set of initial and final conditions, use combined gas law.

3)If problem only gives information for one set of conditions, use ideal gas law.

•IV. Sample Problem

•What’s the final pressure of a sample of N2 with a volume of 952 m3 at 745 torr and 25 °C if it’s heated to 62 °C with a final volume of 1150 m3?

•IV. Sample Problem

•What volume, in mL, does a 0.245 g sample of N2 occupy at 21 °C and 750 torr?

•IV. Sample Problem

•A sample of N2 has a volume of 880 mL and a pressure of 740 torr. What pressure will change the volume to 870 mL at the same temperature?

•IV. Other Uses of Ideal Gas Law

•The ideal gas law can be used to find other physical values of a gas that are not as obvious.

gas density, d = mass/volume

gas molar mass, MW = mass/mole

stoichiometry, via moles and a balanced equation

•IV. Sample Problem

•Find the density of CO2(g) at 0 °C and 380 torr.

•IV. Sample Problem

•An unknown noble gas was allowed to flow into a 300.0 mL glass bulb until the P = 685 torr. Initially, the glass bulb weighed 32.50 g, but now it weighs 33.94 g. If the temperature is 27.0 °C, what’s the identity of the gas?

•IV. Sample Problem

•How many mL of HCl(g) forms at STP when 0.117 kg of NaCl reacts with excess H2SO4?

•V. Partial Pressures

•Each gas in a mixture behaves like it’s the only gas there.

•Dalton’s Law of Partial Pressures states that the total pressure of a mixture of unreacting gases is the sum of all individual pressures.

•Each individual pressure is a partial pressure.

§Ptotal = P1 + P2 + P3 + P4 + …

•V. Partial Pressures

•You already have experience with partial pressures.

•Ptotal = PH2 + PH2O

•V. An O2/N2 Gas Mixture

•Let’s say we have O2 and N2 as a gas mixture. Then Ptotal = PO2 + PN2. Applying the ideal gas law…

•V. An O2/N2 Gas Mixture

•Now we add the individual pressures to find the total pressure.

•Note that the total pressure is related to the total moles.

•V. An O2/N2 Gas Mixture

•What happens if we divide PO2 by Ptotal?

•A new quantity which we call the mole fraction appears.

•V. Mole Fraction

•We define a new unit of concentration, the mole fraction (X).

•Partial pressures are directly related to the mole fraction.

•For the O2/N2 mixture, for N2 specifically, we have…

•V. Sample Problem

•Calculate the partial pressures of 5.50 g He, 15.0 g Ne, and 35.0 g Kr at STP.

•VI. Kinetic-Molecular Theory

•Why do gas laws work well for all gases?

•The Kinetic-Molecular Theory of gases was proposed which consists of 3 postulates.

1)Gas particles are negligibly small, and any sample has a huge # of particles. The volume of each particle is so small that we assume they have mass but no volume.

2)The average kinetic energy of a particle is proportional to the kelvin temperature

3)Gas particles collide in perfectly elastic collisions w/ themselves and container walls and they move in straight lines between collisions, neither attracting nor repelling one another.

•VI. Imagining a Sample of Gas

•We imagine a sample of gas – chaos, molecules bumping into each other constantly.

•After a collision, 2 molecules may stop completely until another collision makes them move again.

•Some molecules moving really fast, others really slow.

•But, there is an average speed.

•VI. Gas Molecular Speeds

•As temp increases, avg. speed increases.

•i.e. avg. KE is related to temp!!

•Any 2 gases at same temp will have same avg. KE!

•VI. Why Do Gas Laws Work So Well?

•Recall that the gas laws apply to any gas – the chemical identity is not important.

•Gas particles only interact when they collide. Since this interaction is so short, chemical properties don’t have time to take effect!!

•VI. Explaining Boyle’s Law

•VI. Explaining Charles’s Law

•VI. Explaining Avogadro’s Law

•VI. Explaining Dalton’s Law

•VII. Deviations from PV=nRT

•Under extreme conditions (high P or low T), gases deviate from ideal gas law predictions.

•Why? What’s so different about these conditions?

•VII. Gas Particle Volume

•Gas molecules do take up space! When very close to one another, entire volume of container is not available for travel, so actual volume of gas is larger.

•VII. Intermolecular Forces

•Gas molecules interact if they are very close to one another…

•VII. van der Waals Equation

•Under extreme conditions, ideal gas law cannot be used.

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