1.3 Reacting Masses and VolumesReacting Gases

Kristin PageIB SL Chemistry

Understandings

• Avogadro’s law enables the mole ratio of reacting gases to be determined from volumes of the gases.

• The molar volume of an ideal gas is a constant at specified temperature and pressure.

• The molar concentration of a solution is determined by the amount of solute and the volume of solution.

• A standard solution is one of known concentration.

Application & Skills• Calculation of reacting volumes of gases using Avogadro’s law.• Solution of problems and analysis of graphs involving the relationship between

temperature, pressure and volume for a fixed mass of an ideal gas.• Solution of problems relating to the ideal gas equation.• Explanation of the deviation of real gases from ideal behavior at low

temperature and high pressure.• Obtaining and using experimental values to calculate the molar mass of a gas

from the ideal gas equation.• Solution of problems involving molar concentration, amount of solute and

volume of solution.• Use of the experimental method of titration to calculate the concentration of a

solution by reference to a standard solution.

Kinetic Theory of Gases• Gas particles have high energy are separated by a lot

of space • Gas particles are move rapidly in straight lines but

random directions• Gas particles collide with each other and with the

container but do not lose energy• There is no attractive force between gas particles• These hold true for IDEAL GASES

Ideal Gases• Model of the behavior of real gases• Under “normal” conditions known as standard temperature and

pressure (STP)• STP: P = 100 kPa and T = 273°K• Useful conversions: 100 kPa = 1atm and 273°K = 0°C

• Gas particles have high energy are separated by a lot of space • Gas particles are move rapidly in straight lines but random directions• Gas particles collide with each other and with the container but do

not lose energy• There is no attractive force between gas particles

Absolute Zero• When dealing with gases we need to use STP. This means that units

of temperature must be in Kelvin (°K)• 273°K = 0°C• The Kelvin scale starts at absolute zero (0°K)• It is not actually possible to reach absolute zero since this would be

the point at which particles stopped all motion*• * Actually technically not true anymore but for our purposes we will

stick with this. If you are curious go to http://www.nature.com/news/quantum-gas-goes-below-absolute-zero-1.12146

Avogadro’s Law• Relationship between amount of gas

(n) and the volume (m3)• At constant temperature & pressure

(m3 )

00

• This means that volumes can be used directly instead of moles in equations involving gases.

• Ex: H2(g) + Cl2(g) 2HCl(g)

Avogadro’s Law Problems• Consider the following reaction for the synthesis of

methanol: CO(g) + 2H2(g)CH3OH(g) (Assume same T & P)

• What volume of H2 reacts exactly with 2.50dm3 of CO?

• Mole ratio CO: H2 = 1:2

• = 5.00 dm3 of H2 reacts

• What volume of CH3OH is produced?

• Mole ratio CO: CH3OH = 1:1

Avogadro’s Law Problems• If 100 cm3 of oxygen reacts with 30cm3 of methane in the following

reaction, how much oxygen will be left over at the end of the reaction? CH4(g) + 2O2(g)CO2(g)+H2O(g) (Assume same T & P)

• Mole ratio CH4: O2 = 1:2

Molar Volume• According to Avogadro’s law, the volume of 1 mole of and ideal gas at

STP is constant, this is known as the Molar Volume

• Molar volume = 22.7 dm3 mol-1

• Note: 1 dm3 = 1L =1000cm3

• Calculate the number of moles in 250.cm3 of O2 at STP

• Calculate the volume of 0.135 mol CO2 at STP

Boyle’s Law• Relationship between pressure and

volume• At constant temperature, the volume of

a fixed mass of an ideal gas is inversely proportional to its pressure

• Gases in smaller volume will have more collisions with the container and so higher pressure

• This can also be written where and

http://www.uccs.edu/vgcl/gas-laws/experiment-1-boyles-law.html

Boyle’s Law Example

• , , kPa, ,

To make an air horn, 1.50 dm3 of air at 101 kPa are compressed into a can with a volume of 0.462 dm3. Assuming a constant temperature, what is the pressure on the compressed air?

Charles’s Law• Relationship between volume and

temperature• At constant pressure the volume

of a fixed mass of ideal gas is directly proportional to its temperature (K)

• or • As temperature increase particles

move more rapidly (higher kinetic energy) and collide with surface more causing an increase in volume

• Temp. must be in Kelvin!http://www.uccs.edu/vgcl/gas-laws/experiment-2-charles-law.html

Charles’s Law Example

• Temp. must be in Kelvin!

On hot days, you may have noticed that potato chip bags seem to “inflate”, even though they have not been opened. If I have a 250mL bag at a temperature of 19°C, and I leave it in my car which has a temperature of 45°C, what will the new volume of the bag be?

Gay-Lussac’s Law (1778-1850)

• 1800’s studied gases using hot air balloons• When volume is constant, pressure of the gas

is directly proportional to temperature• or • Pressure in Nm-2 (Pa)• Temp in K

http://www.uccs.edu/vgcl/gas-laws/experiment-3-gay-lussacs-law.html

Combined Gas Law• All 3 gas laws can be combined into one

equation known as the combined gas law

• For a fixed amount of gas

• This equation can technically be used for ANY gas law problem since the constant variable will cancel out.

• Note: all units must be the same on both sides of the equation and temperature must be in Kelvin!

Combined Gas Law Example

• so

If the volume of an ideal gas collected at 0°C and 100 kPa is 50.0cm3, what would be the volume at 60°C and 108 kPa?

Ideal Gas Equation• Now we can add the gas equations with Avogadro’s

Law to get the ideal gas equation

• R = gas constant = 8.31 J K-1mol-1 (Data Book p.2)• Must use the following units:• p (Pa)• V (m3)• T (K)• Conversion Factors• 1 Pa = 1 J m-3

• 1 dm3 = 1 x 10-3 m3 (Data book)

Ideal Gas Equation Practice

• R = 8.31 J K-1mol-1

An ideal gas occupies 590 cm3 at 120°C and 202 kPa. What amount of gas (in moles) is present?

Ideal Gas Equation PracticeA gas has a density of 1.24 g dm-3 at 0°C and 1.00 x 105 Pa. Calculate its molar mass.