Chapter 13Chapter 13

The Gas LawsThe Gas Laws

Robert Boyle studied how Robert Boyle studied how gas volume varied with gas volume varied with changes in pressure. changes in pressure.

Boyles Law - The volume of a fixed Boyles Law - The volume of a fixed mass of gas varies inversely with the mass of gas varies inversely with the pressure at constant temperature.pressure at constant temperature.

P1V1 = P2V2

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How is this related to Boyles’ Law ?How is this related to Boyles’ Law ?

Jacques Charles studied the Jacques Charles studied the variation of gas volume with variation of gas volume with

changes in temperature. changes in temperature.

Charles found that the volume of a gas Charles found that the volume of a gas changes by 1/ 273 of the original volume changes by 1/ 273 of the original volume for each Celsius degree, at constant for each Celsius degree, at constant pressure.pressure.

Using this information he was able to Using this information he was able to predict the value of absolute zero, the predict the value of absolute zero, the point where all motion stops. -273point where all motion stops. -27300CC

Charles’s Law- The volume of a fixed Charles’s Law- The volume of a fixed mass of gas at constant pressure varies mass of gas at constant pressure varies directly with the Kelvin temperature.directly with the Kelvin temperature.

Charles Law MathCharles Law Math

VV11 = = VV2 2 or V or V11TT22 = V = V22TT11

TT11 T T22

Lord Kelvin ak Sir William Lord Kelvin ak Sir William ThompsonThompson

Kelvin didn’t like negative numbers, so he Kelvin didn’t like negative numbers, so he created a system that started at the created a system that started at the coldest possible temperature.coldest possible temperature.

- 273- 273°C became 0° K°C became 0° K

To convert celsius to kelvin,To convert celsius to kelvin, Add 273Add 273 To covert kelvin to celsius To covert kelvin to celsius Subtract 273 Subtract 273

All temperatures in all gas law problems must be in degrees Kelvin

Joseph Gay-Lussac studied the Joseph Gay-Lussac studied the variation of gas pressure with variation of gas pressure with

changes in temperature.changes in temperature.

Gay-Lussac Law – The pressure of Gay-Lussac Law – The pressure of a fixed mass of gas at constant a fixed mass of gas at constant volume varies directly with the volume varies directly with the

Kelvin temperature.Kelvin temperature.

P1 = P2 or P1T2 = P2T1

T1 T2

Unknown math guy Combined the Unknown math guy Combined the above three equations in to the above three equations in to the

Combined Gas LawCombined Gas Law

PP11VV11 = = PP22VV22 or P or P11VV11TT22 = P = P22VV22TT1 1

TT11 T T22

Daltons law of Partial pressure – Daltons law of Partial pressure – The total pressure of a mixture of The total pressure of a mixture of gases is equal to the sum of the gases is equal to the sum of the

partial pressures of the component partial pressures of the component gases. gases.

Math PMath PTT = P = P11 + P + P2 2 + P + P33 + …….. + ……..

Avogadro’s Law - Equal volumes of Avogadro’s Law - Equal volumes of gases at the same temperature and gases at the same temperature and pressure contain equal numbers of pressure contain equal numbers of

molecules. molecules. Thus Molar Volume - The volume Thus Molar Volume - The volume

occupied by one mole of a gas at STP is occupied by one mole of a gas at STP is known as the standard molar volume of a known as the standard molar volume of a gas, it is 22.4 liters. 1 Mole of a gas = gas, it is 22.4 liters. 1 Mole of a gas = 22.4 liters @ STP.22.4 liters @ STP.

Ideal Gas law - The ideal gas law Ideal Gas law - The ideal gas law is the mathematical relationship of is the mathematical relationship of pressure, volume, temperature and pressure, volume, temperature and

the number of moles of a gas. the number of moles of a gas. ( Combined gas law and ( Combined gas law and

Avogadro’s law , combined ) Avogadro’s law , combined )

Math PV = nRT Math PV = nRT P is pressure in ATM, V is volume in P is pressure in ATM, V is volume in

Liters, T is temperature in degrees K Liters, T is temperature in degrees K And r is a gas constant, which And r is a gas constant, which

varies according to the units of pressure varies according to the units of pressure used. used.

When P is ATM r = .0821When P is ATM r = .0821 mmHg r = 62.4mmHg r = 62.4 Kpa r = 8.31 Kpa r = 8.31 For any other pressure convert the For any other pressure convert the

pressure to one of the three above.pressure to one of the three above.

Molar mass and density with the Ideal gas law

PV = nRT substitute n = m PV = mRT M M

mass / molar mass = moles

To find molar mass rearrange to M = mRT

PV

Density Density substitute substitute mm = D = D

V V

M = M = mRT mRT PV PV

M = M = DRTDRT

P P

Rearrange this to solve for density

D = MP RT

Grams X Grams X 1 mole1 mole X X moles looking for (from equation)moles looking for (from equation) X X FW of looking forFW of looking for

Given FW of given moles given (from equation) 1 mole of looking for Given FW of given moles given (from equation) 1 mole of looking for

Remember –mass/mass problemsRemember –mass/mass problems

Now we can use 1 mole = 22.4 liters @STP to find moles given, or convert moles to volume at STP.

If the given information about the gas is not at STP , we can use

PV = nRT to do the same thing.

Instead of calling them just mass / mass problems we can call them

Gas / mass and mass / gas problems

Also have to divide the water level difference by 13.6 to convert it to mm Hg