Pressure and gas laws notes answers.notebook

Pressure and gas laws notes answers.notebook December 12, 2013

Nov 1311:23 PM

Chapter 10: Gases

Pick up all of the papers that you need from the lab table.

Nov 1311:23 PM

Vapors:* gaseous substances that exist as solids or liquids

under ordinary conditions

Nov 1311:31 PM

Pressure:

defined as:

caused by:

units:

Nov 1311:45 PM

Barometer:

Nov 1311:52 PM

Sample Exercise 10.1(a) Convert 0.357 atm to torr(b) Convert 6.6 x 102 torr to atm(c) Convert 147.2 kPa to torr

Nov 1311:54 PM

Practice Exercise: (Page 403)(a) In countries that use the metric system, such as Canada, atmospheric pressure in weather reports is given in units of kPa. Convert a pressure of 745 torr to kPa. (b) An English unit of pressure sometimes used in engineering is pounds per square inch (lb/in2) or psi: 1 atm = 14.7 psi. If a pressure is reported as 91.5 psi, express the measurement in atmospheres.


Nov 1311:57 PM

Manometers* tool used to measure pressure of enclosed gases

Dec 210:15 AM

EXAMPLE 1: A container of gas measures the pressure to be 104.9 kPa. Convert this pressure to psi.

EXAMPLE 2: Atmospheric pressure is reported as 30.1 inches Mercury. Convert this to torr.

EXAMPLE 3: An enclosed container of gas is connected to a manometer. The mercury level is 8 cm lower on the side connected to the gas sample. If atmospheric pressure is 0.984 atm find the pressure of the gas in the container.

Nov 1412:01 AM

Sample Exercise 10.2On a certain day the barometer in a laboratory indicates that the atmospheric pressure is 764.7 torr. A sample of gas is placed in a flask attached to an openend mercury manometer, shown in Figure 10.3. A meter stick is used to measure the height of the mercury above the bottom of the manometer. The level of the mercury in the openend arm of the manometer has a height of 136.4 mm, and the mercury in the arm that is in contact with the gas has a height of 103.8 mm. What is the pressure of the gas (a) in atmospheres (b) in kPa?

Nov 1412:04 AM

Practice Exercise: (page 404)Convert a pressure of 0.975 atm into Pa and kPa

Nov 1412:10 AM

Charles's Law:* TemperatureVolume relationship:

* Expressed mathematically:

* Absolute temperature scale proposed by Lord Kelvin is

based on absolute zero = 273.15oC

Nov 1412:05 AM

Boyle's Law:* PressureVolume relationship

* Expressed mathematically as:


Nov 1412:14 AM

Avogadro's Law* Quantity Volume relationship:

* Avogadro's Law:

* Expressed mathematically:

Nov 1412:19 AM

Sample Exercise 10.3Suppose we have a gas confined to a cylinder as shown in Figure 10.12. Consider the following changes (a) Heat the gas from 298 K to 360 K (b) Move the piston to reduce the volume of gas from 1 L to 0.5 L. (c) Inject additional gas through the gas inlet valve. Indicate how each of these changes will affect the average distance between molecules, the pressure of the gas, and the number of moles of gas present in the cylinder.

Nov 1412:22 AM

Practice Exercise: (page 408)What happens to the density of a gas as (a) the gas is heated in a constantvolume container (b) the gas is compressed at constant temperature (c) additional gas is added to a constantvolume container

Nov 1412:24 AM

The Ideal Gas Equation:• PV = nRT

• An ideal gas is a hypothetical gas whose pressure, volume, and temperature behavior is completely described by the idealgas equation

• R = the ideal gas constant (most often we will use 0.0821 L atm/ mol K)

• 1 mole of any gas at standard temperature and pressure has a volume of 22.4 L

• STP = 0 degrees C and 1 atmosphere pressure

Nov 1412:31 AM

Sample Exercise 10.4Calcium carbonate, CaCO 3 (s), decomposes upon heating to give CaO (s) and CO2 (g). A sample of CaCO3 is decomposed, and the carbon dioxide is collected in a 250mL flask. After the decomposition is complete, the gas has a pressure of 1.3 atm at a temperature of 31 oC. How many moles of CO2 gas were generated?

Nov 1412:34 AM

Practice Exercise: (page 410)Tennis balls are usually filled with air or N2 gas to a pressure above atmospheric pressure to increase their "bounce." If a particular tennis ball has a volume of 144 cm 3 and contains 0.33 g of N2 gas, what is the pressure inside the ball at 24 oC?


Nov 1412:37 AM

Sample Exercise 10.5The gas pressure in an aerosol can is 1.5 atm at 25 oC. Assuming that the gas inside obeys the ideal gas equation, what would the pressure be if the can were heated to 450oC?

Nov 1412:38 AM

Practice Exercise: (page 412)A large natural gas storage tank is arranged so that the pressure is maintained at 2.20 atm. On a cold day in December when the temperature is 15 oC (4oF), the volume of gas in the tank is 28,500 ft3. What is the volume of the same quantity of gas on a warm July day when the temperature is 31oC (88oF)?

Nov 1412:41 AM

Sample Exercise 10.6An inflated balloon has a volume of 6.0 L at sea level (1.00 atm) and is allowed to ascent in altitude until the pressure is 0.45 atm. During the ascent the temperature of the gas falls from 22oC to 21oC. Calculate the volume of the balloon at this final altitude.

Nov 1412:43 AM

Practice Exercise: (page 413)A 0.50mol sample of oxygen gas is confined at 0oC in a cylinder with a moveable piston, such as that shown in Figure 10.12. The gas has an initial pressure of 1.0 atm. The gas is then compressed by the piston so that its final volume is half the initial volume. The final pressure of the gas is 2.2 atm. What is the final temperature of the gas in degrees Celsius?

Nov 1412:46 AM

Sample Exercise 10.7What is the density of carbon tetrachloride vapor at 714 torr and 125oC?

Nov 1412:47 AM

Practice Exercise: (page 414)The mean molar mass of the atmosphere at the surface of Titan, Saturn's largest moon, is 28.6 g/mol. The surface temperature is 95 K, and the pressure is 1.6 atm. Assuming ideal behavior, calculate the density of Titan's atmosphere.


Nov 1412:49 AM

Sample Exercise 10.8A series of measurements are made in order to determine the molar mass of an unknown gas. First, a large flask is evacuated and found to weigh 134.567 g. It is then filled with the gas to a pressure of 735 torr at 31 oC and reweighted; its mass is now 137.456 g. Finally, the flask is filled with water at 31 oC and found to weigh 1067.9 g. (The density of water at this temperature is 0.997 g/mL). Assuming that the ideal gas equation applies, calculate the molar mass of the unknown gas.

Nov 1412:53 AM

Practice Exercise: (page 415)Calculate the average molar mass of dry air if it has a density of 1.17 g/L at 21oC and 740.0 torr.

A

Nov 1412:54 AM

Sample Exercise 10.9The safety air bags in automobiles are inflated by nitrogen gas generated by the rapid decomposition of sodium azide, NaN 3:

2 NaN3 (s) => 2Na(s) + 3N2(g)If an air bag has a volume of 36 L and is to be filled with nitrogen gas at a pressure of 1.15 atm at a temperature of 26.0oC, hwo many grams of NaN3 must be decomposed?

Nov 1412:59 AM

Practice Exercise: (page 416)The first step in the industrial process for making nitric acid, ammonia reacts with oxygen the presence of a suitable catalyst to form nitric oxide and water vapor:

4NH3(g) + 5O2(g) => 4NO(g) + 6H2O(g)

How many liters of NH 3(g) at 8500C and 5.00 atm are required to react with 1.00 mol O 2(g) in this reaction?

Nov 141:03 AM Nov 179:09 PM

Kinetic Molecular Theory:* Helps to explain why gases behave the way they do* Summarized by the following statements:

1) Gases consist of large numbers of molecules that are in constant, random motion.

2) The combined volume of all the molecules is negligible relative to the total volume in which the gas is contained.

3) Attractive and repulsive forces between gas molecules are negligible.

4) Energy can be transferred between molecules during collisions, but the average kinetic energy of the molecules does not change with time, as long as temperature is constant. In other words, collisions are perfectly elastic.

5) The average kinetic energy of the molecules is proportional to the absolute temperature. At any given temperature the molecules of all gases have the same average kintic energy.


Nov 184:30 AM

KineticMolecular Theory:* Explains both temperature & pressure at the molecular level* Absolute temperature of a gas is a measure of the average kinetic energy of its molecules* Molecular motion increases with increasing temperature* Not all molecules in a sample move with the same speed* root mean square speed (rms speed), u, the speed of a molecule possessing average kinetic energy* The rms speed is not the same as the average (mean) speed...but the difference between the two is small* The average kinetic energy of the gas molecules in a sample is directly related to u2

Nov 184:38 AM

Kinetic Theory & The Gas Laws:1) Effect of volume increase at constant temperature:

*no change in speed of molecules*larger volume will cause less collisions of molecules with

walls of container...which caused pressure to decrease*this verifies Boyle's Law

2) Effect of a temperature increase at constant volume* increases average kinetic energy of molecules* volume doesn't change so there will be an increase in the # of collisions with the walls of the container... increases pressure

Nov 184:46 AM

Molecular Effusion & Diffusion* The gas particles with a given absolute temperature have a particular average kinetic energy* lighter and heavier particles at the same temperature will have the same average kinetic energy* For this to be the case, the lighter particles must move faster (have higher u) than the heavier particles* The following equation can then be derived from the kinetic molecular theory

Nov 184:53 AM

Effusion:* the escape of gas molecules through a tiny hole in an evacuated space

Diffusion: * the spread of one substance throughout space or throughout another substance

Nov 184:56 AM

Graham's Law of Effusion:* Effusion rate of a gas is inversely proportional to the square

root of its molecular mass* At the same temperature and pressure, a lighter gas will

effuse at a higher rate than a heavier gas

Nov 185:01 AM

Diffusion and Mean Free Path:* Diffusion is also faster for lighter molecules* Diffusion of gases is much slower than molecular speeds because of molecular collisions* Because of collisions the direction of a gas molecule is constantly changing (as is the speed)* Mean free path...is the average distance traveled by a molecule between collisions* Mean free path decreases with increasing pressure


Nov 185:08 AM

Real Gases: Deviations from Ideal Behavior* All real gases fail to follow the idealgas equation to some

degree* Real gases do not behave ideally at high pressure* At lower pressures (usually below 10 atm) the deviation

from ideal behavior is small* In general deviations from ideal behavior increase as

temperature decreases* Deviations of real gases from ideal behavior can be linked to

the assumptions of the ideal gas...it is assumed that ideal gases have no attraction for one another and do not take up space...Real molecules do have volume and attract one another

Nov 185:19 AM

The van der Waals Equation:* Useful for predicting behavior of real gases at high pressures* Corrects the ideal gas equation for volume occupied by the

gas molecules and the attractive forces between the molecules

Nov 185:28 AM

Gas Mixtures and Partial Pressures:* The pressure exerted by a particular component of a mixture of gases is the partial pressure

Nov 185:32 AM

Sample Exercise 10.10A gaseous mixture made from 6.00 g O 2 and 9.00 g CH4 is placed in 15.0 L vessel at 0oC. What is the partial pressure of each gas and what is the total pressure in the vessel?

Nov 185:34 AM

Practice Exercise (page 418)What is the total pressure exerted by a mixture of 2.00 g H2 and 8.00 g of N2 at 273 K in a 10.0 L vessel?

Nov 185:35 AM

Sample Exercise 10.11A study of the effects of certain gases on plant growth requires a synthetic atmosphere composed of 1.5 mol percent CO 2, 18.0 mol percent O2, and 80.5 mol percent Ar. (a) Calculate the partial pressure of O2 in the mixture if the total pressure of the atmosphere is to be 745 torr. (b) If this atmosphere is to be held in a 120L space at 295 K, how many moles of O2 are needed?


Nov 185:38 AM

Practice Exercise (page 419)From data gathered by Voyager I, scientists have estimated the composition of the atmosphere of Titan, Saturn's largest moon. The total pressure on the surface of Titan is 1220 torr. The atmosphere consists of 82 mol percent N 2, 12 mol percent Ar, and 6.0 mol percent CH 4. Calculate the partial pressure of each of these gases in Titan's atmosphere.

Nov 185:40 AM

Sample Exercise 10.12A sample of KClO3 is partially decomposed, producing O 2 gas that is collected over water as in Figure 10.16. The volume of gas collected is 0.250 L at 26oC and 765 torr total pressure. (a) How many molecules of O 2 are collected? (b) Hwo many grams of KClO3 were decomposed?

Nov 185:43 AM

Practice Exercise (page 420)Ammonium nitrite, NH 4NO2, decomposed upon heating to form N2 gas:NH4NO2(s) > N2(g) + 2H2O(l)When a sample of ammonium nitrite is decomposed in a test tube, as in Figure 10.16, 511 mL of N2 gas is collected over water at 26oC and 745 torr total pressure. How many grams of ammonium nitrite were decomposed?

Nov 186:10 AM

Sample Exercise 10.13A sample of O2 gas at STP is compressed into a smaller volume at constant temperature. What effect does this change have on (a) the average kinetic energy of O2 molecules (b) the average speed of O2 molecules (c) the total number of collisions of O 2 molecules with the walls of the container in a unit time (d) the number of collisions of O 2 molecules with a unit area of container wall per unit time?

Nov 186:13 AM

Practice Exercise (page 423)How is the rms speed of N 2 molecules in a gas sample changed by (a) an increase in temperature (b) an increase in volume (c) mixing with a sample of argon at the same temperature?

Nov 186:14 AM

Sample Exercise 10.14Calculate the rms speed, u, of an N 2 molecule at 25oC.


Nov 186:15 AM

Practice Exercise (page 424)What is the rms speed of an He atom at 25 oC?

Nov 186:16 AM

Sample Exercise 10.15An unknown gas composed of homonuclear diatomic molecules effuses at a rate that is only 0.355 times that of O2 at the same temperature. Calculate the molar mass of the unknown, and identify it.

Nov 187:01 AM

Practice Exercise (page 426)Calculate the ratio of the effusion rates of N 2 and O2, rN2/rO2.

Nov 187:03 AM

Sample Exercise 10.16If 1.000 mol of an ideal gas were confined to 22.41 L at 0.0oC, it would exert a pressure of 1.000 atm. Use the van der Waals equation and the constants in table 10.3 to estimate the pressure exerted by 1.000 mol of Cl2(g) in 22.4 L at 0.0oC.

Nov 187:04 AM

Practice Exercise (page 430)Consider a sample of 1.00 mol of CO 2(g) confined to a volme of 3.000 L at 0.0oC. Calculate the pressure of the gas using (a) the idealgas equation and (b) the van der Waals equation.

Nov 187:06 AM

Sample Integrative Exercise (page 430)Cyanogen, a highly toxic gas, is composed of 4.2% C and 53.8% N by mass. At 25oC and 751 torr, 1.05 g of cyanogen occupies 0.500 L. (a) What is the molecular formula of cyanogen? (b) Predict its molecular structure. (c) Predict the polarity of the compound.


Nov 187:08 AM

End of Chapter Exercises:• 10.57• 10.59• 10.67• 10.73• 10.79• 10.85• 10.90• 10.99

End of Chapter Questions:• 10.9• 10.11• 10.21• 10.23• 10.25• 10.27• 10.29• 10.37• 10.41• 10.45• 10.47• 10.53

Nov 297:52 PM

Documents

Pressure and gas laws notes answers.notebook