2. Gases Exert Pressure on Their Surroundings
GASES
PRESSURE
1. A gas uniformly fills any container, is easily compressed, and mixes completely with any other gas.
2. Gases exert pressure on their surroundings.
3. A barometer is used to measure atmospheric pressure.
Units of Pressure
1. The unit most commonly used is ______.
2.
3.
4. In the SI system:
This is called the ______
THE GAS LAWS OF BOYLE, CHARLES AND AVOGADRO
Boyle’s Law
1. Boyle studied the relationship between the pressure of trapped gas and its volume.
2. His data showed:
This is called ______.
3. There is an ______relationship between pressure and volume.
4. Boyle’s law holds precisely at very low pressures.
5. Measurements reveal that at high pressures PV is not a constant, but varies as the pressure is varied.
6. A gas that strictly obeys Boyle’s law is called an ______.
7. Boyle’s law can also be written as:
***** The pressure outside a jet plane flying at high altitude falls considerably below standard atmospheric pressure. Therefore, the air inside the cabin must be pressurized to protect the passengers. What is the pressure, in atmospheres, in the cabin if the barometer reading is 688 mm Hg?
***** A gas occupying a volume of 725 mL at a pressure of 0.970 atm is allowed to expand at constant temperature until its pressure reaches 0.541 atm. What is its final volume?
Charles’ Law
1. The volume of a gas at constant pressure ______with the temperature of the gas.
2. A plot of the volume of a gas (at constant pressure) versus temperature (0C) gives a straight line.
3. Plotting other gases produces similar results. These lines extrapolate to zero at the same temperature: -273.2 0C.
4. On the Kelvin temperature scale, the point is defined as ______which leads to:
5. Plotting volume versus temperature (K) produces results showing that the volume of a gas is directly proportional to its temperature.
6. Charles’ Law:
***** A fixed quantity of gas at 23.0 0C exhibits a pressure of 735 mm Hg and occupies a volume of
5.22 L. Use Charles’ law to calculate the volume the gas will occupy if the temperature is increased to 1650C while the pressure is held constant.
Avogadro’s Law
1. Avogadro postulated that equal volumes of gases at the same temperature and pressure contain the same number of particles.
2. This is ______
3. For a gas at constant temperature and pressure, the volume is directly proportional to the number of moles of a gas.
***** Consider the following chemical reaction:
2 NO2 (g) → N2O4 (g)
If 25.0 mL of NO2 gas is completely converted to N2O4 gas under the same conditions, what volume will the N2O4 occupy?
Gay-Lussac’s Law
1. Describes how the pressure and temperature of a fixed amount of gas at constant volume are related.
2. The law states the pressure of a fixed amount of gas held at constant volume is directly proportional to the Kelvin temperature.
***** The pressure of the oxygen gas inside a canister is 5.00 atm at 25.00C. The canister is located at a camp high on Mount Everest. If the temperature there falls to -10.00C, what is the new pressure inside the canister?
***** The pressure in an automobile tire is 1.88 atm at 25.00C. what will be the pressure if the temperature increases to 37.00C?
Combined Gas Law
1. In a number of applications involving gases, pressure, temperature, and volume might all change.
2. Boyle’s, Charle’s, and Gay-Lussac’s Laws can be combined into a single law.
3. This is known as the ______.
***** A gas at 110 kPa and 30.00C fills a flexible container with an initial volume of 2.00 L. If the temperature is raised to 80.00C and the pressure increases to 440.0 kPa, what is the new volume?
***** A sample of air in a syringe exerts a pressure of 1.02 atm at 22.00C. The syringe is placed in a boiling water bath at 100.00C. The pressure is increased to 1.23 atm by pushing the plunger in, which reduces the volume to 0.224 mL. What was the initial volume?
THE IDEAL GAS LAW
1. So far we have examined:
Boyle’s law:
Charles’ law:
Avogadro’s law:
Gay-Lussac’s Law
2. These relationships can be combined as follows:
3. When P is expressed in atmospheres and V in liters:
4. The ideal gas law is expressed as:
5. The ideal gas law is an equation of state for a gas where the state of the gas is its condition at a given time.
6. A particular state of a gas is described by its pressure, volume, temperature, and number of moles.
7. The ideal gas law is an empirical equation; it is based on experimental measurements of the properties of gases.
***** A 5.00 L flask contains 0.600g O2 at a temperature of 22.00C. Determine the pressure (in atm) inside the flask.
***** Determine the volume occupied by 2.00g of He at 25.00C and a pressure of 775 mm Hg.
***** A balloon has a volume of 175 cm3 at 19.00C. Determine the temperature at which the volume of the balloon will have increased by 25.0% at constant pressure.
GAS STOICHIOMETRY
1. One mole of an ideal gas at 00C (273.2 K) and at 1.00 atm will occupy ______. This is the ______of an ideal gas.
2. The conditions of 00C and 1.00 atm are called standard temperature and pressure, or ______.
***** A student adds 4.00g of dry ice to a balloon. What will be the volume of the balloon at STP after all the dry ice sublimes?
***** The method used by Joseph Priestley to obtain oxygen made use of the thermal decomposition of mercuric oxide:
∆
2 HgO (s) → 2 Hg (l) + O2 (g)
What volume of oxygen gas, measured at 30.00C and 725 torr can be produced from the complete decomposition of 4.10g of HgO?
***** Air bags are activated when a severe impact causes a steel ball to compress a spring and electrically ignite a detonator cap. This causes sodium azide to decompose explosively according to the following reaction:
2 NaN3 (s) → 2 Na (s) + 3 N2 (g)
What mass of NaN3 must be reacted in order to inflate an air bag to 70.0 L at STP?
***** Urea (H2NCONH2) is used extensively as a nitrogen source in fertilizers. It is produced commercially from the reaction of ammonia and carbon dioxide:
2 NH3 (g) + CO2 (g) → H2NCONH2 (s) + H2O (g)
Ammonia gas at 2230C and 90.0 atm flows into a reactor at a rate of 500.0 L/min. Carbon dioxide at 2230C and 45.0 atm flows into the reactor at a rate of 600.0 L/min. What mass of urea is produced per minute by this reaction assuming 100% yield?
Molar Mass of a Gas
1. One important use o the ideal gas law is to calculate the molar mass of a gas from its measured density.
2. This relationship develops as:
***** A compound has the empirical formula CHCl. A 256 mL flask at 373K and 750.0 torr contains 0.800g of the gaseous compound. Determine the molecular formula.
***** Calculate the density of ammonia gas at 27.00C and 635 torr.
DALTON’S LAW OF PARTIAL PRESSURES
1. For a mixture of gases in a container, the total pressure exerted is the sum of the pressures that each gas would exert if it were alone.
2. Dalton’s law of partial pressures:
3. It can also be expressed as:
4. For a mixture of ideal gases, it is the total number of moles of particles that is important, not the identity or composition of the involved gas particles.
5. The pressure exerted by an ideal gas is not affected by the identity, or composition, of the gas particles. This reveals two things about ideal gases:
a. the volume of the individual gas particles must not be important
b. the forces among the particles must not be important
***** A mixture of 1.00g H2 and 1.00g He is placed in a 1.00 L container at 27.00C. Calculate the partial pressure of each gas and the total pressure of the mixture.
6. ______is the ratio of the number of moles of a given component in a mixture to the total number of moles in the mixture.
7. The mole fraction of each component in a mixture of ideal gases is directly related to its partial pressure:
8. This can be rearranged to:
***** At 0.000C a 1.00 L flask contains 5.00 x 10-2 mol N2, 1.50 x 102 mg O2, and 5.00 x 1021 molecules of NH3. Determine the partial pressure of each gas and the total pressure in the flask.
9. A mixture of gases results whenever a gas is collected by displacement of water.
10. Pressure is exerted by the water molecules in the vapor, so that the partial pressure is called the ______.
***** Helium is collected over water at 25.00C and 1.00 atm total pressure. What total volume of gas must be collected to obtain 0.586g of helium? (at 25.00C the vapor pressure of water is 23.8 torr)
THE KINETIC MOLECULAR THEORY OF GASES
1. Based on observations from different types of experiments, we know that at pressures of less than 1.00 atm most gases closely approach the behavior described by the ideal gas law.
2. The ______attempts to explain the properties of an ideal gas.
3. This model is based on speculation about the behavior of individual gas particles (atoms or molecules).
4. The postulates of KMT are:
a. The particles are so small compared with the distances between them that the volume of the individual particles can be assumed to be negligible (zero).
b. The particles are in constant motion. The collisions of the particles with the walls of the container are the cause of the pressure exerted by the gas.
c. The particles are assumed to exert no forces on each other; they are assumed neither to attract nor repel each other.
d. The average kinetic energy of a collection of gas particles is assumed to be directly proportional to the Kelvin temperature of a gas.
5. Of course, the molecules in a real gas have finite volumes and do exert forces on each other. Thus, ______do not conform to these assumptions.
Pressure and Volume (Boyle’s Law)
1.
2. Based on KMT, a decrease in volume means that the gas particles will hit the wall more often, thus increasing pressure.
Pressure and Temperature
1.
2. KMT accounts for this behavior because when the temperature of a gas increases, the speed of its particles increases. The particles hit the wall with greater force and greater frequency.
Volume and Temperature (Charles’s Law)
1.
2. When the gas is heated to a higher temperature, the speeds of its molecules increase and thus they hit the walls more often and with more force. The only way to keep the pressure constant in this situation is to increase the volume of the container.
Volume and Number of Moles (Avogadro’s Law)
1.
2. An increase in the number of particles at the same temperature would cause the pressure to increase if the volume were held constant. The only way to return the pressure to its original value is to increase the volume.
3. The volume of a gas (at constant P and T) depends only on the ______of gas particles present.
Mixture of Gases (Dalton’s Law)
1. Total pressure exerted by a gas mixture is the sum of the pressures of all the individual gases.
2. KMT assumes that all gas particles are independent of one another and that the volumes of the individual particles are unimportant.
The Meaning of Temperature
1. The exact relationship between T and KE can be obtained:
2. It summarizes the meaning of the Kelvin temperature of a gas: The Kelvin temperature is an index of the random motions of the particles of a gas, with higher temperatures meaning greater motion.
Root Mean Square Velocity
1. The average velocity of the gas particles is a special kind of average.
2. The symbol ______means the average of the squares of the particle velocities.
3. The square root of the average of the squares of the particle velocities is called the ______and is symbolized:
4. If we insert gas law information:
5. In order to obtain the units of meters per second, R must be expressed in different units.
6. Using Joules, R becomes ______
***** Calculate the root mean square velocity of the N2 molecules in a sample of N2 gas at 273K and 546K.
7. In a real gas there are large numbers of collisions between particles. This causes delays as a gas permeates a room. The path traveled by the gas atoms (molecules) is very erratic.
8. The average distance a particle travels between collisions in a particular gas sample is called the ______. It is typically a very small distance.
9. Temperature will affect the velocity distribution of gases. As temperature increases, the distribution curve moves toward higher velocity values and the range of velocities becomes larger.
10. Because kinetic energy increases with temperature, it makes sense that the peak of the curve should move to higher values as the temperature of the gas is increased.
EFFUSION AND DIFFUSION
1. ______is the term used to describe the mixing of gases. The rate of diffusion is the rate of the mixing of gases.
2. ______is the term used to describe the passage of a gas through a tiny orifice into an evacuated chamber. The rate of effusion measures the speed at which the gas is transferred into the chamber.
Effusion
1. The relative rates of effusion of two gases at the same temperature and pressure are given by the inverse ratio of the square roots of the masses of the gas particles.
2. This is called ______:
***** The rate of effusion of a particular gas was measured and found to be 24.0 mL/min. Under the same conditions, the rate of effusion of pure methane (CH4) gas is 47.8 mL/min. What is the molar mass of the unknown gas?
***** It took 4.50 minutes for 1.00 L helium to effuse through a porous barrier. How long will it take 1.00 L of Cl2 gas to effuse under identical conditions?
3. KMT correctly predicts the relative effusion rates of gases summarized by Graham’s Law. The faster the gas particles are moving, the more likely they are to pass through the effusion orifice.
Diffusion
1. One might expect that the distances traveled by the two gases are related to the relative velocities of the gas molecules:
2. This turns out to be not true. Diffusion is quite slow and hard to predict due to all the collisions between the gas molecules and the air.
REAL GASES
1. Ideal gas behavior can be best thought of as the behavior approached by ______under certain conditions.
2. A real gas typically exhibits behavior that is closest to ideal behavior at ______and ______.
3. An equation for real gases was developed by van der Waal:
4. Rearranged, it becomes the ______:
The values of a and b are obtained from best fit data for the observed pressure under all conditions.
***** Using the van der Waal’s equation, calculate the pressure exerted by 0.5000 mol of N2 in a 10.000 L container at 25.00C.