Standard Temperature and Pressure 1

Download Report

Transcript Standard Temperature and Pressure 1

Standard Temperature and Pressure

• • • •

Standard temperature and pressure is given the symbol STP.

– It is a reference point for some gas calculations.

Standard P



1.00000 atm or 101.3 kPa Standard T



273.15 K or 0.00

o C

– Gas laws must use the Kelvin scale to be correct.

Relationship between Kelvin and centigrade.

K = C + 273

Boyle’s Law: The Volume-Pressure Relationship

• V 

1/P or

• V= k (1/P) or PV = k • P

1 V 1

• P

2 V 2 = k = k 1 2 for one sample of a gas.

for a second sample of a gas.

• k

1 = k 2 for the same sample of a gas at the same T.

• Thus we can write Boyle’s Law

mathematically as P 1 V 1 = P 2 V 2 Robert Boyle (1627-1691). Son of Earl of Cork, Ireland.

Charles’ Law: The Volume-Temperature Relationship; The Absolute Temperature Scale

• Mathematical form of Charles’ law. V 1 T 1 V  T or V = kT or V T  k  k and V 2 T 2  k however th e k' s are equal so V 1 T 1  V 2 in the T 2 most useful form

Jacques Charles (1746-1823). Isolated boron and studied gases. Balloonist.

35 30 25 20 15 10 5 0 0 Charles’ Law: The Volume-Temperature Relationship; The Absolute Temperature Scale 50 Gases liquefy before reaching 0K 100 150 200 250 Temperature (K)

300 350 400 4

The Combined Gas Law Equation

• Boyle’s and Charles’ Laws combined into one

statement is called the combined gas law equation.

– Useful when the V, T, and P of a gas are

changing.

Boyle' s Law Charles' Law P 1 V 1  P 2 V 2 V 1 T 1  V 2 T 2 For a given sample of gas : The combined gas law is : P V T  k P 1 V 1 T 1  P 2 V 2 T 2

Avogadro’s Law and the Standard Molar Volume

• Avogadro’s Law states that at the same

temperature and pressure, equal volumes of two gases contain the same number of molecules (or moles) of gas.

• If we set the temperature and pressure for any gas

to be STP, then one mole of that gas has a volume

called the standard molar volume. • The standard molar volume is 22.4 L at STP. – This is another way to measure moles. – For gases, the volume is proportional to the

number of moles.

Boyle’s Law: The Volume-Pressure Relationship

• At 25

o C a sample of He has a volume of 4.00 x 10 under a pressure of 7.60 x 10 2 2 mL torr. What volume would it occupy under a pressure of 2.00 atm at the same T?

Charles’ Law: The Volume-Temperature Relationship; The Absolute Temperature Scale

• A sample of hydrogen, H

2 , occupies 1.00 x 10 2 mL at 25.0

o C and 1.00 atm. What volume would it occupy at 50.0

o C under the same pressure?

The Combined Gas Law Equation

• A sample of nitrogen gas, N

2 , occupies 7.50 x 10 2 75.0

0 C under a pressure of 8.10 x 10 2 would it occupy at STP?

mL at torr. What volume 9

Avogadro’s Law and the Standard Molar Volume

• One mole of a gas occupies 36.5 L and its density is 1.36 g/L

at a given temperature and pressure. (a) What is its molar mass? (b) What is its density at STP?

Summary of Gas Laws: The Ideal Gas Law

• Boyle’s Law - V  • Charles’ Law – V 

1/P (at constant T & n) T (at constant P & n)

• Avogadro’s Law – V 

n (at constant T & P)

• Combine these three laws into one statement



nT/P

• Convert the proportionality into an equality.

V = nRT/P

• This provides the Ideal Gas Law. PV = nRT • R is a proportionality constant called the universal gas

constant. 0.08206 L atm mol -1 K -1 11

•

Summary of Gas Laws: The Ideal Gas Law

What volume would 50.0 g of ethane, C 2 H 6 , occupy at 1.40 x 10 2 o C under a pressure of 1.82 x 10 3 torr?

Summary of Gas Laws: The Ideal Gas Law

• Calculate the number of moles in, and the mass of, an 8.96 L

sample of methane, CH 4 , measured at standard conditions?

Dalton’s Law of Partial Pressures

• Dalton’s law states that the pressure exerted by a mixture of

gases is the sum of the partial pressures of the individual gases.

P total = P A + P B + P C + .....

•Vapor Pressure is the pressure exerted by a substance’s vapor over the substance’s liquid at equilibrium.

John Dalton 1766-1844

Dalton’s Law of Partial Pressures

• If 1.00 x 10

2 mL of hydrogen, measured at 25.0 o C and 3.00 atm pressure, and 1.00 x 10 2 and 2.00 atm pressure, were forced into one of the containers at 25.0 gases?

o mL of oxygen, measured at 25.0 C, what would be the pressure of the mixture of o C 15

Dalton’s Law of Partial Pressures

• A sample of hydrogen was collected by displacement of water

at 25.0 o C. The atmospheric pressure was 748 torr. What pressure would the dry hydrogen exert in the same container?

Mass-Volume Relationships in Reactions Involving Gases

•In this section we are looking at reaction stoichiometry, like in Chapter 3, just including gases in the calculations. 2 KClO 3 (s)  2   2 KCl (s) + 3 O 2 ( g)

2 mol KClO 3 yields 2 mol KCl and 3 mol O 2 2(122.6g) yields 2 (74.6g) and 3 (32.0g) Those 3 moles of O 2 can also be thought of as: 3(22.4L) or 67.2 L at STP 17

Mass-Volume Relationships in Reactions Involving Gases

• What volume of oxygen measured at STP, can be produced by

the thermal decomposition of 120.0 g of KClO 3 ?

Real Gases: Deviations from Ideality

• • •

The reasons for the deviations from ideality are: The molecules are very close to one another, thus their volume is important.

Real gases behave ideally at ordinary temperatures and pressures.

At low temperatures and high pressures real gases do not behave ideally. The molecular interactions also become important.

19 J. van der Waals, 1837-1923, Professor of Physics, Amsterdam. Nobel Prize 1910.

Real Gases: Deviations from Ideality

• van der Waals’ equation accounts for the behavior of real gases at low temperatures and high pressures.  P + 2 n a V 2   V  nb   nRT •

The van der Waals constants a and b take into account two things: a.

a accounts for intermolecular attraction

For nonpolar gases the attractive forces are London Forces b.

For polar gases the attractive forces are dipole-dipole attractions or hydrogen bonds.

2. b accounts for volume of gas molecules

At large volumes a and b are relatively small and van der Waal’s equation reduces to ideal gas law at high temperatures and low pressures.

Real Gases: Deviations from Ideality

• Calculate the pressure exerted by 84.0 g of ammonia, NH

3 , in a 5.00 L container at 200. o C using the ideal gas law.

21 PV = nRT P = nRT/V n = 84.0g * 1mol/17 g T = 200 + 273 P = (4.94mol)(0.08206 L atm mol -1 K -1 )(473 K) (5 L) P = 38.3 atm

Real Gases: Deviations from Ideality

• Calculate the pressure exerted by 84.0 g of ammonia, NH

3 , in a 5.00 L container at 200. o C using the van der Waal’s equation. The van der Waal's constants for ammonia are: a = 4.17 atm L 2 mol -2 b = 3.71x10

-2 L mol -1 22

 P + 2 n a V 2   V  nb   nRT P  nRT V nb 2 n V 2 a

n = 84.0g * 1mol/17 g T = 200 + 273 P = (4.94mol)(0.08206 L atm mol -1 K -1 )(473K) (4.94 mol) 2 *4.17 atm L 2 5 L – (4.94 mol*3.71

E -2 L mol -1 ) (5 L) 2 P = 39.81 atm – 4.07 atm = 35.74

P = 38.3 atm 7% error mol -2

Standard Temperature and Pressure 1

Transcript Standard Temperature and Pressure 1

Standard Temperature and Pressure

K = C + 273

Boyle’s Law: The Volume-Pressure Relationship

The Combined Gas Law Equation

Avogadro’s Law and the Standard Molar Volume

Boyle’s Law: The Volume-Pressure Relationship

The Combined Gas Law Equation

Avogadro’s Law and the Standard Molar Volume

Summary of Gas Laws: The Ideal Gas Law

Summary of Gas Laws: The Ideal Gas Law

Summary of Gas Laws: The Ideal Gas Law

Dalton’s Law of Partial Pressures

Dalton’s Law of Partial Pressures

Dalton’s Law of Partial Pressures

Mass-Volume Relationships in Reactions Involving Gases

Real Gases: Deviations from Ideality

Real Gases: Deviations from Ideality

Real Gases: Deviations from Ideality

Real Gases: Deviations from Ideality

Directory