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Chapter 9—Ideal Gas Law. Today we move into Chapter 5, quite possibly the easiest chapter (in terms of problems) this term. Can you remember one simple equation? If so, then Chapter 9 will be ridiculously simple PV = nRT Five types of problems come from that equation

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Chapter 9—Ideal Gas Law

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Chapter 9 ideal gas law l.jpg

Chapter 9—Ideal Gas Law

  • Today we move into Chapter 5, quite possibly the easiest chapter (in terms of problems) this term.

  • Can you remember one simple equation? If so, then Chapter 9 will be ridiculously simple

    • PV = nRT

  • Five types of problems come from that equation

    • Plug and chugpartial pressure

    • Densitymolecular mass

    • Change in one variable


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Gases … What Are They Like?

  • Gases are composed of widely separated particles in constant, random motion.

  • Gases flow readily and occupy the entire volume of their container.

  • Vapor – a gas that is a liquid at room temperature and pressure (water vapor and methanol vapor, but gaseous oxygen and gaseous hydrogen).

  • Many low molar mass molecular compounds are either gases or easily vaporizable liquids.


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An Introduction toKinetic-Molecular Theory

  • Provides a model for gases at the microscopic level.

  • Molecules are in rapid, random motion.

  • Movement of gases through three-dimensional space is called translational motion.

  • Pressure: collision of gas molecules with wall of container.

  • Temperature: related to average speed of gas molecules.


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Gas Pressure

  • Pressure is the force per unit area.

  • In SI, force is expressed in newtons (N) and area in square meters (m2).

  • The unit of pressure in SI is the pascal (Pa) with the units N/m2.

  • Kilopascals (kPa) are often used instead since the pascal is such a small unit.

  • The atmosphere and mmHg(Torr) are the most common scientific units for pressure.

  • Converting from one unit to another simply requires the appropriate conversion factor(s).


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Barometers

  • Used to measure atmospheric pressure.

  • One atmosphere (atm):pressure exerted by a column of mercury exactly 760 mm high.

  • One millimeter of mercury is called a Torr.

    1 atm= 760 mmHg

    = 760 Torr

    = 101.325 kPa


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Leading up to the Ideal Gas Law

  • There were three critical experiments that combined to yield the IGL…

    • Boyle’s Law—relating pressure and volume

    • Charles Law—relates volume and temperature

    • Avogadro’s Law—relates volume to an amount (MOLAR)

  • When these three relationships were combined, it yielded the IGL


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Boyle’s Law:Pressure-Volume Relationship

  • For a fixed amount of a gas at constant temperature, the volume of the gas varies inversely with its pressure.

    • i.e. Increase the pressure, lower the volume (compression)

    • Decrease the pressure, the volume INCREASES

  • For a fixed amount of a gas at constant temperature, the product of pressure and volume is a constant.

PV = constant or PinitialVinitial = PfinalVfinal


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Charles’s Law:Temperature-Volume Relationship

  • The volume of a fixed amount of a gas at constant pressure is directly proportional to its Kelvin (absolute) temperature.

  • Absolute zero is the temperature obtained by extrapolation to zero volume.

  • Absolute zero on the Kelvin scale = –273.15 °C


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Avogadro’s Law:Mole-Volume Relationship

  • At a fixed temperature and pressure, the volume of a gas is directly proportional to the amount of gas in moles (n) or to the number of molecules of gas.

    Van V = cn V/n = c

  • Standard temperature and pressure (STP) is equal to 0 °C and 1 atm.

  • The molar volumeof a gas is the volume occupied by one mole of the gas.

  • At STP, molar volume of an ideal gas is 22.4 liters.


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Problem solving with IGE

  • Said before that there are five problem types you’ll see solving problems

    • Plug/chug

    • Density

    • Molecular mass

    • Change in variable

    • Partial pressure

  • First kind is stupidly simple…if given four variables (remember you know R)…find fifth.


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Homer Simpson Simple

What is the pressure exerted by 0.508 mol O2 in a 15.0-L container at 303 K?

P = nRT/V (0.508 mol)(0.08206 L atm/mol K)(303) / 15 L

don’t screw up data entry into the calculator…

What is the volume occupied by 16.0 g ethane gas (C2H6) at 720 Torr and 18 °C?

ooooo!!! A wrinkle—conversions!

g—mol, Torr—atm and C—K, plug/chug and done


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OK, so moving along

  • If it stands that

  • then change one variable

    • Gives condition (2)

  • STILL = R (the constant)

  • Yields the following…

PV

—— = constant

nT

We can cancel any term (P, V, n, T) that is the same on both sides.

P1V1 P2V2

—— = ——

n1T1 n2T2


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Change of variable problems

  • Important to note that not ALL variables change.

    • some terms drop from that eq.

    • Moles mostly

  • Simplifies the equation

    • Often means we can use the units given…don’t ALWAYS have to convert.

    • Though you do when dealing w/ T changes.

P1V1 P2V2

—— = ——

n1T1 n2T2


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The flasks pictured in the cartoon below contain O2(g), the one on the left at STP and the one on the right at 100 °C. What is the pressure at 100 °C?

SAME # moles, SAME volume…

What pressure would be exerted if the vessel were transferred to an oil bath at 200 °C?


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Calcs part 3—Molecular Mass

M = molar mass and m = mass in grams

m (grams) m

M =————— so n = —

n (moles) M

PV

n =——

RT

The ideal gas equation rearranges to:

mPV

— =——

MRT

Setting the equations equal to one another:

Alternative to equation: (A) find n using the ideal gas equation; (B) Divide m (grams) by n (moles) to get grams/mol.

mRT

M =———

PV

… and solving for M:


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If 0.550 g of a gas occupies 0.200 L at 0.968 atm and 289 K, what is the molecular mass of the gas?

Calculate the molecular mass of a liquid that, when vaporized at 100 °C and 755 Torr, yields 185 mL of vapor that has a mass of 0.523 g.


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Calculations Part 4—Gas Densities

Density of a gas is directly proportional to its molar mass and pressure, and is inversely proportional to Kelvin temperature.

  • Gases are much less dense than liquids and solids, so gas densities are usually reported in g/L.

Alternative: find volume of one mole (n = 1) or other fixed quantity of gas. Divide mass of that quantity by volume to find g/L.

mRT m MP

M =——— rearranges to — = ——

PV V RT

m MP

and density = — so d = ——

V RT


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Calculate the density of methane gas, CH4, in grams per liter at 25 °C and 0.978 atm.

Under what pressure must O2(g) be maintained at 25 °C to have a density of 1.50 g/L?


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