Gas LawsGas LawsA reviewA review

Important InformationImportant Information

• What is STP?• Standard Temperature and Pressure.• 1 atm pressure and 273 Kelvin• What are standard conditions?• Pressure is still 1 atm, but the

temperature is 25 degrees C or 298 K

• What is STP?• Standard Temperature and Pressure.• 1 atm pressure and 273 Kelvin• What are standard conditions?• Pressure is still 1 atm, but the

temperature is 25 degrees C or 298 K

UnitsUnits

• Units are very important in this chapter.

• One must be consistent or be incorrect.• All temperature must be in Kelvin.• °C + 273 = Kelvin• Pressure may be in one of these

choices:• 1 atm 760 mmHg• 760 torr 101.3 kPa

• Units are very important in this chapter.

• One must be consistent or be incorrect.• All temperature must be in Kelvin.• °C + 273 = Kelvin• Pressure may be in one of these

choices:• 1 atm 760 mmHg• 760 torr 101.3 kPa

Effusion and DiffusionEffusion and Diffusion

EffusionEffusion DiffusionDiffusion• The rate at which a

gas moves from area of high concentration to low concentration

• The rate at which a gas moves from area of high concentration to low concentration

• The passage of a gas through a tiny orifice.

• The passage of a gas through a tiny orifice.

Boyles LawBoyles Law

• http://en.wikipedia.org/wiki/Boyle's_law• Pressure and Volume are inversely

proportional when temperature is constant.

• As Pressure increases, Volume decreases and visa versa.

• P1V1=P2V2

• If a system with a pressure of 5 atm and 45 ml is compressed to 30 ml, what is the new pressure?

• http://en.wikipedia.org/wiki/Boyle's_law• Pressure and Volume are inversely

proportional when temperature is constant.

• As Pressure increases, Volume decreases and visa versa.

• P1V1=P2V2

• If a system with a pressure of 5 atm and 45 ml is compressed to 30 ml, what is the new pressure?

Boyle’s LawBoyle’s Law

• P1 V1= P2 V2

• 5 atm 45 ml = X 30 ml• X=(5atm*45ml)/30ml• X= 7.5 atm

• P1 V1= P2 V2

• 5 atm 45 ml = X 30 ml• X=(5atm*45ml)/30ml• X= 7.5 atm

Charles’ LawCharles’ Law

• http://en.wikipedia.org/wiki/Charles's_law

• Volume and Temperature are directly proportional when pressure is constant.

• As Volume increases, so does Temperature.

• V1 = V2• T1 T2• What happens to a 1 liter balloon at 25

degrees Celsius if the temperature is reduced to 0 degrees Celsius?

• http://en.wikipedia.org/wiki/Charles's_law

• Volume and Temperature are directly proportional when pressure is constant.

• As Volume increases, so does Temperature.

• V1 = V2• T1 T2• What happens to a 1 liter balloon at 25

degrees Celsius if the temperature is reduced to 0 degrees Celsius?

Charles’ LawCharles’ Law

• V1 1 liter = V2 X• T1 25°C T2 0°C• Temperature must be in Kelvin!!!! C+

273=K• V1 1 liter = V2 X• T1 298 K T2 273 K• X= (1 L*273 K)/298K• X=0.916 L new volume

• V1 1 liter = V2 X• T1 25°C T2 0°C• Temperature must be in Kelvin!!!! C+

273=K• V1 1 liter = V2 X• T1 298 K T2 273 K• X= (1 L*273 K)/298K• X=0.916 L new volume

Gay-Lussac’s LawGay-Lussac’s Law

• Pressure and Temperature are directly proportional when the volume remains constant.

• The pressure increases as the temperature in kelvin increases.

• Pressure and Temperature are directly proportional when the volume remains constant.

• The pressure increases as the temperature in kelvin increases.

Gay-Lussac’s LawGay-Lussac’s Law

• What is the new pressure if a ridged container at 1 atm and 25 °C is heated to 75° C?

• P1 1 atm = P2 X• T1 25°C T2 75°C• Temperature must be in Kelvin!!!! C+

273=K• P1 1 liter = P2 X• T1 298 K T2 348 K

• What is the new pressure if a ridged container at 1 atm and 25 °C is heated to 75° C?

• P1 1 atm = P2 X• T1 25°C T2 75°C• Temperature must be in Kelvin!!!! C+

273=K• P1 1 liter = P2 X• T1 298 K T2 348 K

Gay-Lussac’s LawGay-Lussac’s Law

• X= (1 L*348 K)/298K• X= 1.17 L

• X= (1 L*348 K)/298K• X= 1.17 L

Combined Gas LawCombined Gas Law

• Pressure and volume are inversely proportional. Both Pressure and Volume are directly proportional to temperature.

• We can combine Charles’, Boyle’s and Gay-Lussac’s Law to form the Combined gas law.

• Pressure and volume are inversely proportional. Both Pressure and Volume are directly proportional to temperature.

• We can combine Charles’, Boyle’s and Gay-Lussac’s Law to form the Combined gas law.

Combined Gas LawCombined Gas Law

• You have an expandable syringe holding a volume of 20ml at STP.

• What is the new volume at Standard Conditions?

• P1=1 atm * V1 =20mL P2=1 atm * V2 =X

• T1 = 273 K = T2 = 298 K

• X= 21.8 ml

• You have an expandable syringe holding a volume of 20ml at STP.

• What is the new volume at Standard Conditions?

• P1=1 atm * V1 =20mL P2=1 atm * V2 =X

• T1 = 273 K = T2 = 298 K

• X= 21.8 ml

Ideal Gas LawIdeal Gas Law

• The main difference with the ideal gas law is that now we take the number of moles of gas into consideration.

• All previous gas laws had a constant amount of gas.

• In the ideal gas law, the number of moles of a gas is also a variable.

• To do this the equation requires a conversion factor called, R.

• The main difference with the ideal gas law is that now we take the number of moles of gas into consideration.

• All previous gas laws had a constant amount of gas.

• In the ideal gas law, the number of moles of a gas is also a variable.

• To do this the equation requires a conversion factor called, R.

Ideal Gas LawIdeal Gas Law

• PV=nRT• Pressure times Volume equals the

number of moles times the gas constant times the Temperature in Kelvin.

• There are many versions of the Gas constant, R. We will use only two.

• R= 0.0821 (L*atm)/(mol*Kelvin)• R= 8.31 (L*kPa)/(mol*Kelvin)

• PV=nRT• Pressure times Volume equals the

number of moles times the gas constant times the Temperature in Kelvin.

• There are many versions of the Gas constant, R. We will use only two.

• R= 0.0821 (L*atm)/(mol*Kelvin)• R= 8.31 (L*kPa)/(mol*Kelvin)

Units and the Ideal Gas Law

Units and the Ideal Gas Law

• The units of your problem must match the units in your gas constant, R.

• If they do not you need to convert those units that do not match.

• Example:• I have 20 grams of neon gas at 760

mmHg and 0° C. What is the volume of this gas?

• The units of your problem must match the units in your gas constant, R.

• If they do not you need to convert those units that do not match.

• Example:• I have 20 grams of neon gas at 760

mmHg and 0° C. What is the volume of this gas?

AnswerAnswer

• Which R? • I chose R=0.08206

(L*atm)/(mole*Kelvin)• First we need moles of gas not grams• 20 g/(20g/mol)=1 mole of Neon• Pressure from mmHg to atm• 760 mmHg*(1 atm/760 mmHg)= 1 atm• Temperture from Celsius to Kelvin• 0° C +273=273 Kelvin

• Which R? • I chose R=0.08206

(L*atm)/(mole*Kelvin)• First we need moles of gas not grams• 20 g/(20g/mol)=1 mole of Neon• Pressure from mmHg to atm• 760 mmHg*(1 atm/760 mmHg)= 1 atm• Temperture from Celsius to Kelvin• 0° C +273=273 Kelvin

Answer continuedAnswer continued

• PV=nRT• 1atm(V)= [1

mol*0.0821(L*atm)/(mol*K)]273K• V=[1mol*0.0821 (L*atm/mol*K)*273K]/1atm• Cancel your units and do the math:• V=0.0821 L/273• V= 22.4 L• In fact, all gases at STP occupy 22.4 L/mol

• PV=nRT• 1atm(V)= [1

mol*0.0821(L*atm)/(mol*K)]273K• V=[1mol*0.0821 (L*atm/mol*K)*273K]/1atm• Cancel your units and do the math:• V=0.0821 L/273• V= 22.4 L• In fact, all gases at STP occupy 22.4 L/mol

How to determine which to use

How to determine which to use

• Ideal or Combined?• Does the problem mention a change in

either Temperature, Pressure or Volume?

• Combined Gas Law!• Does the problem give or ask for the

number of grams of a gas or the number of moles of a gas?

• Ideal Gas law!

• Ideal or Combined?• Does the problem mention a change in

either Temperature, Pressure or Volume?

• Combined Gas Law!• Does the problem give or ask for the

number of grams of a gas or the number of moles of a gas?

• Ideal Gas law!

Dalton’s Law of Partial Pressures

Dalton’s Law of Partial Pressures

• In a mixture of gases, each gas has its own partial pressure. The total pressure in the container is the sum of the partial pressures.

• PT=P1+P2+P3…Pn• It is important that all the pressures are

in the same units before adding them together!

• In a mixture of gases, each gas has its own partial pressure. The total pressure in the container is the sum of the partial pressures.

• PT=P1+P2+P3…Pn• It is important that all the pressures are

in the same units before adding them together!

Graham’s Law of EffusionGraham’s Law of Effusion

• Larger molecules will migrate slower than a smaller molecule under a constant temperature.

• This is in direct violation of the KMT.

• REAL GASES have significant size

• Larger molecules will migrate slower than a smaller molecule under a constant temperature.

• This is in direct violation of the KMT.

• REAL GASES have significant size

Graham’s LawGraham’s Law

• Which of these gases will effuse faster, He, Ne, Xe?

• When all gases are at the same temperature, they have the same kinetic energy. Therefore the smallest gas, Helium, will effuse faster.

• Which of these gases will effuse faster, He, Ne, Xe?

• When all gases are at the same temperature, they have the same kinetic energy. Therefore the smallest gas, Helium, will effuse faster.