Chapter 14 – Gases1

Chapter 14.1 The Gas Laws Let’s remember the kinetic theory – Gas particles behave differently than those of liquids and solids. Kinetic Theory assumes the following concepts are true for gases:  

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Gas particles do not attract or repel each other o Gas particles are free to move without interference from other particles Gas particles are much smaller than the distances between them o Gas particles themselves have virtually no volume (most of the volume of a gas is empty space) o Gases can be compressed Gas particles are in constant, random motion o Gases mix together because of the random motion o Gas particles move in straight lines until they collide with other particles or the walls of the container No kinetic energy is lost when gas particles collide with each other or the walls of the container o Elastic collisions o If the temperature stays the same, the KE of the system remains constant All gases have the same average kinetic energy at a given temperature o Temperature increases, total energy of the system increases, vice-versa

Real gases don’t obey all the assumptions made by the Kinetic Theory. The behavior of many gases do approximate the behavior assume by the KT.

Assumptions of the kinetic theory are based on 4 factors that work together:    

Number of particles present Temperature Pressure Volume of the sample

Boyle’s Law – named after Robert Boyle (1627-1691)

Volume of a gas held at a constant temperature is inversely proportional to pressure. V1P1 = V2P2 V1 and P1 represent initial conditions; V2 and P2 represent the new conditions. Sample problem: A sample of helium gas in a balloon is compressed from 4.0 L to 2.5 L at a constant temperature. If the pressure of the gas in the 4.0 L volume is 210 kPa, what will the pressure be at 2.5 L?

Chapter 14 – Gases2

Charles’s Law Relating volume and temperature 

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As temperature increases, the volume of a gas increases, when the pressure is held constant o Kinetic-molecular theory – at a higher temperature, gas particles move faster o More collisions, greater force exerted in the collisions For the pressure to remain constant, the volume of the gas must increase (particles now have farther to travel before colliding with the walls of the container) Volume is proportional to temperature at a constant pressure V1/T1 = V2/T2 Relationship between volume and temperature is linear, but not direct (0° does not correspond to 0 volume) o Increasing the temperature from 25° to 50° does not double the volume o If Kelvin scale is used for temperature, then the relationship is direct. o TK = TC + 273 o Temperature must be expressed in Kelvin units when using Charles’s law

Gay-Lussac’s Law Pressure and temperature   

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Pressure results from collisions between gas particles and the container walls An increase in temperature results in more collisions, which increases pressure if volume is not increased. Pressure of a given mass of gas varies directly with the temperature when the volume remains constant o Temperature must be in Kelvin P1/T1 = P2/T2

Sample problem: A gas sample at 40.0°C occupies a volume of 2.32 L. If the temperature is raised to 75.0°C, what will the volume be, assuming the pressure remains constant?

Sample problem: The pressure of a gas in a tank is 3.20 atm at 22.0°C. If the temperature rises to 60.0°C, what will be the gas pressure in the tank?

Chapter 14 – Gases3

Chapter 14.2 The Combined Gas Law and Avogadro’s Principle We’ve looked at problems where either pressure, volume, or temperature was held constant while the other two variables changed. What do you do when all three variables change? Combined Gas Law

Sample Problem: A gas at 110 kPa and 30.0°C fills a flexible container with an initial volume of 2.00 L. If the temperature is raised to 80.0°C and the pressure increased to 440 kPa, what is the new volume?

The combined gas law states the relationship among pressure, volume, and temperature of a fixed amount of gas.

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3 variables still have the same relationship learned in the previous gas laws Pressure is inversely proportional to volume and directly proportional to temperature P1V1 = P2V2 T1 T2 You use known values for the variables under 1 condition to solve for an unknown variable from another set of conditions Only equation you need to remember!

Avogadro’s Principle

Sample Problem

Avogadro’s principle: equal volumes of gases at the same temperature and pressure contain equal numbers of particles.

Calculate the volume that 0.881 mol of gas at standard temperature and pressure (STP) will occupy.

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Mole has 6.02 x 1023 particles Molar volume for a gas is the volume that one mole occupies at 0.0°C and 1 atm pressure o 0.0°C and 1 atm are known as standard temperature and pressure (STP) o 1 mole of any gas will occupy a volume of 22.4 L at STP o Volume of any gas at STP = 22.4 L o Conversion factor: 22.4 L 1 mol

Example: Find the number of particles in a sample of gas that has a volume of 3.72L at STP. 3.72L x 1 mol = 0.166 mol 22.4 L 0.166 mol x 6.02 x 1023 particles = 9.99 X 1022 pt. 1 mol

Chapter 14 – Gases4

Avogadro’s Principle – Using Mass

Work space for problem!

Calculate the volume that 2.0 kg of methane gas (CH4) will occupy at STP. Given: Temperature and pressure and mass of the sample. 1 mole of gas occupies 22.4 L at STP. The number of moles can be calculated by dividing the mass of the sample by its molar mass. Chapter 14.3 The Ideal Gas Law The work of Avogadro, Boyle, Charles, and GayLussac can be combined into one equation that describes the relationship among pressure, volume, temperature, and moles of a gas.

Real versus ideal gases

The Ideal Gas Law

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Particle description of the ideal gas 1. Minimal attractive and/or repulsive forces 2. Occupy negligible volume 3. Follows gas laws under all conditions of temperature and pressure Ideal Gas Constant (R) In the ideal gas equation (coming soon!), there is a constant (R) that is based on pressure. The value of R depends on the unit that pressure is given in. R =   

0.0821, when pressure is measured in atm o Most common unit 8.314, when pressure is measured in kPa 62.4, when pressure is measured in mmHg

You must know these values! The Ideal Gas Law is a combination of all previous gas laws.  

Shows the relationship between pressure, volume, temperature, and moles PV = nRT o P = pressure o n = moles (number) o T= temperature (K) o V = volume (L) o R = gas constant

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No gas is truly ideal, but most behave like the ideal gas at many temperatures and pressure levels Real gases deviate from the ideal gas law at high temperatures and/low pressures Polar gases tend to not behave as ideal gases Larger molecules tend to not behave as ideal gases

Ideal Gas Law – using Moles Calculate the number of moles of gas contained in a 3.0-L vessel at 300 K with a pressure of 1.50 atm.

Chapter 14 – Gases5 Molar mass and the ideal gas law

Ideal Gas Law – Using Molar Mass

To find the molar mass of a gas sample, you must know the mass, temperature, pressure, and volume.

What is the molar mass of a pure gas that has a density of 1.40 g/L at STP?

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Moles of a gas (n) = mass(m)/molar mass (M) Replace n in PV=nRT with m/M o PV = mRT M o M = mRT PV If you know mass, you can determine the density (mass/volume) o Density (D) can then take the place of m/V. o M = DRT P

Chapter 14.4 Gas Stoichiometry Time to remember stoichiometry!    

Coefficients in chemical equations represent moles of substances in the reaction. Mole ratios of reactants and products Avogadro’s principle tells us that equal volumes of gases at the same temperature and pressure have equal numbers of particles. With gases, coefficients in a balanced equation represent moles AND relative volumes. 2 C4H10 + 13 O2 8 CO2 + 10 H2O o 2 L C4H10 o 13 L O2 o 8 L CO2 o 10 L H2O

Volume –Volume Problems 1. Start with a balanced equation and the amount of 1 gas 2. Compare the mole ratio from the equation to the known volume to find the unknown. CH4 + 2O2  CO2 + 2H2O  

Coefficients represent volume ratios for gases 2 L of oxygen is required to react completely with 1 L of methane, and will produce 1 L of CO2 and 2 L of H2O vapor.

What volume of methane is needed to produce 26 L of water vapor?   

Volume ratio of methane and water vapor is 1:2, so half as much methane is needed (13L) to produce 26 L of water vapor. What volume of oxygen is needed to produce 6.0 L of CO2? Note: temperature and pressure conditions aren’t mentioned. After mixing, each gas will be at the same temperature and pressure.

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Sample problem What volume of oxygen gas is needed for the complete combustion of 4.00 L of propane gas (C3H8)? Assume constant pressure and temperature.

Volume-Mass Problems 1. Start with a balanced equation 2. At least one mass or volume for another substance is required. 3. You must know the conditions under which the gas volumes were measured (temperature, pressure) 4. Chemical equation gives you moles and volume, not the mass a. Use the ideal gas law to calculate what else you need b. Masses must be converted to moles or volumes before being used in a ratio. c. Temperature must always be in Kelvin Sample Problem Ammonia is synthesized from hydrogen and nitrogen gases. N2 + 3H2  2NH3 If 5.00 L of nitrogen reacts completely by this reaction at a constant pressure and temperature of 3.00 atm and 298 K, how many grams of ammonia are produced?