Solution - PowerPoint Presentation

Slide1

Solutiona. temperatureb. pressurec. volumeStudy Check 8.1As more helium gas is added to a balloon, the number of grams of helium increases.What property of a gas is described?AnswerThe mass, in grams, gives the amount of gas.

Identify the property of a gas that is described by each of the following:a. increase the kinetic energy of gas particlesb. the force of the gas particles hitting the walls of the containerc. the space that is occupied by a gas

Sample Problem

8.1 Properties of GasesSlide2

SolutionThe equality 1 atm = 760 mmHg can be written as two conversion factors:

The oxygen in a tank in the hospital respiratory unit has a pressure of 4820 mmHg. Calculate the pressure, in atmospheres, of the oxygen gas (see Table 8.2).

Sample Problem

8.2

Units of PressureSlide3

Using the conversion factor that cancels mmHg and gives atm, we can set up the problem asStudy Check 8.2A tank of nitrous oxide (N2O) used as an anesthetic has a pressure of 48 psi. What is that pressure in atmospheres

(see Table 8.2)?Answer3.3 atmSample Problem 8.2 Units of Pressure

ContinuedSlide4

SolutionStep 1 Organize the data in a table of initial and final conditions. To match the units for the initial and final pressures, we can convert either atm to mmHg or mmHg to atm.

When Whitney had her asthma attack, oxygen was delivered through a face mask. The gauge on a 12-L tank of compressed oxygen reads 3800 mmHg. How many liters would this same gas occupy at a pressure of 0.75 atm when temperature and amount of gas do not change?

Sample Problem

8.3 Calculating Volume When Pressure ChangesSlide5

We place the gas data using units of mmHg for pressure and liters for volume in a table. (We could have both pressures in units of atm as well.) The properties that do not change, which are temperature and amount of gas, are shown below the table. We know that pressure decreases, and can predict that the volume increases. Factors that remain constant: T and n

Step 2 Rearrange the gas law equation to solve for the unknown quantity. For a PV relationship, we use Boyle’s law and solve for V2 by dividing both sides by P2. According to Boyle’s law, a decrease in the pressure will cause an increase in the volume when T and n remain constant.

Continued

Sample Problem

8.3 Calculating Volume When Pressure ChangesSlide6

Step 3 Substitute values into the gas law equation and calculate. When we substitute in the values with pressures in units of mmHg or atm, the ratio of pressures (pressure factor) is greater than 1, which increases the volume as predicted in Step 1.

Study Check 8.3In an underground natural gas reserve, a bubble of methane gas, CH4, has a volume of 45.0 mL at 1.60 atm. What volume, in milliliters, will the gas bubble occupy when it reaches the surface where the atmospheric pressure is 744 mmHg, if there is no change in the temperature or amount of gas?Answer73.5 mL

Continued

Sample Problem

8.3

Calculating Volume When Pressure ChangesSlide7

SolutionStep 1 Organize the data in a table of initial and final conditions. The properties that change, which are the temperature and volume, are listed in the following table. The properties that do not change, which are pressure and amount of gas, are shown below the table. When the temperature is given in degrees Celsius, it must be changed to kelvins. Because we know the initial and final temperatures of the gas, we know

that the temperature increases. Thus, we can predict that the volume increases. T1 = 15 °C + 273 = 288 K T2 = 42 °C + 273 = 315 K Factors that remain constant: P and nStep 2 Rearrange the gas law equation to solve for the unknown quantity. In this problem, we want to know the final volume (V2) when the temperature increases. Using Charles’s law, we solve for V2

by multiplying both sides by T2.

Helium gas is used to inflate the abdomen during laparoscopic surgery. A sample of helium gas has a volume of 5.40 L and a temperature of 15

°

C. What is the final volume, in liters, of the gas if the temperature has been increased to 42 °C at constant pressure and amount of gas?

Sample Problem

8.4

Calculating Volume When Temperature ChangesSlide8

Step 3 Substitute values into the gas law equation and calculate. From the table, we see that the temperature has increased. Because temperature is directly related to volume, the volume must increase. When we substitute in the values, we see that the ratio of the temperatures 1temperature factor2 is greater than 1,

which increases the volume as predicted in Step 1.Study Check 8.4A mountain climber with a body temperature of 37 °C inhales 486 mL of air at a temperature of –8 °C. What volume, in milliliters, will the air occupy in the lungs, if the pressure and amount of gas do not change?Answer569 mL

Continued

Sample Problem

8.4

Calculating Volume When Temperature ChangesSlide9

SolutionStep 1 Organize the data in a table of initial and final conditions. We list the properties that change, which are the pressure and temperature, in a table. The properties that do not change, which are volume and amount of gas, are shown below the table. The temperatures given in degrees Celsius must be changed to kelvins. Because we know the initial and final temperatures of the gas, we know that the temperature increases.

Thus, we can predict that the pressure increases. T1 = 25 °C + 273 = 298 K T2 = 402 °C + 273 = 675 K Factors that remain constant: V and n

Home oxygen tanks, which provide an oxygen-rich environment, can be dangerous

if they are heated, because they can explode. Suppose an oxygen tank has a pressure of 120 atm at a room temperature of 25 °

C. If a fire in the room causes the temperature of the gas inside the oxygen tank to reach 402 °C, what will be its pressure in atmospheres? The oxygen tank may rupture if the pressure inside exceeds 180 atm. Would you expectit to rupture?

Sample Problem

8.5

Calculating Pressure When Temperature ChangesSlide10

Step 2 Rearrange the gas law equation to solve for the unknown quantity. Using Gay-Lussac’s law, we can solve for P2 by multiplying both sides by T2.Step 3

Substitute values into the gas law equation and calculate. When we substitute in the values, we see that the ratio of the temperatures (temperature factor), is greater than 1, which increases pressure as predicted in Step 1. Because the calculated pressure of 270 atm of the gas exceeds the limit of 180 atm, we would expect the oxygen tank to rupture.

Continued

Sample Problem

8.5

Calculating Pressure When Temperature ChangesSlide11

Study Check 8.5In a storage area of a hospital where the temperature has reached 55 °C, the pressure of oxygen gas in a 15.0-L steel cylinder is 965 Torr. To what temperature, in degrees Celsius, would the gas have to be cooled to reduce the pressure to 850. Torr when the volume and amount of the gas do not change?Answer16 °C

Continued

Sample Problem

8.5

Calculating Pressure When Temperature ChangesSlide12

SolutionStep 1 Organize the data in a table of initial and final conditions. We list the properties that change, which are the pressure, volume, and temperature, in a table. The property that remains constant, which is the amount of gas, is shown below the table. The temperatures in degrees Celsius must be changed to kelvins. T1 = 11

°C + 273 = 284 K T2 = 18 °C + 273 = 291 K Factors that remain constant: n

A 25.0-mL bubble is released from a diver’s air tank at a pressure of 4.00

atm and a temperature of 11 °C. What is the volume, in milliliters, of the bubble when it reaches the ocean surface, where the pressure is 1.00 atm and the temperature is 18 °C? (Assume the amount of gas in the bubble does not change

.)

Sample Problem

8.6

Using the Combined Gas LawSlide13

Step 2 Rearrange the gas law equation to solve for the unknown quantity.Step 3 Substitute values into the gas law equation and calculate. From the data table, we determine that both the pressure decrease and the

temperature increase will increase the volume. However, when the unknown value is decreased by one change but increased by the second change, it is difficult to predict the overall change for the unknown.

Continued

Sample Problem

8.6

Using the Combined Gas LawSlide14

Study Check 8.6A weather balloon is filled with 15.0 L of helium at a temperature of 25 °C and a pressure of 685 mmHg. What is the pressure, in millimeters of mercury, of the helium in the balloon in the upper atmosphere when the temperature is –35 °C and the final volume becomes 34.0 L, if the amount of He does not change?Answer241 mmHg

Continued

Sample Problem

8.6

Using the Combined Gas LawSlide15

SolutionStep 1 Organize the data in a table of initial and final conditions. We list those properties that change, which are volume and amount (moles) of gas, in a table. The properties that do not change, which are pressure and temperature, are shown below the table. Because there is an increase in the number of moles of gas, we can predict that the volume increases.

Factors that remain constant: P and TStep 2 Rearrange the gas law equation to solve for the unknown quantity. Using Avogadro’s law, we can solve for V2 by multiplying both sides by n2.

A weather balloon with a volume of 44 L is filled with 2.0 moles of helium. What is

the final volume, in liters, if 3.0 moles of helium gas are added, to give a total of 5.0 moles of helium gas, if the pressure and temperature do not change?

Sample Problem

8.7

Calculating Volume for a Change in MolesSlide16

Step 3 Substitute values into the gas law equation and calculate. When we substitute in the values, we see that the ratio of the moles (mole factor) is greater than 1, which increases the volume as predicted in Step 1.

Study Check 8.7A sample containing 8.00 g of oxygen gas has a volume of 5.00 L. What is the final volume, in liters, after 4.00 g of oxygen gas is added to the 8.00 g of oxygen in the balloon, if the temperature and pressure do not change?Answer7.50 L

Continued

Sample Problem

8.7

Calculating Volume for a Change in MolesSlide17

SolutionStep 1 State the given and needed quantities.Step 2 Write a plan to calculate the needed quantity. The grams of O

2 are converted to moles using molar mass. Then a molar volume conversion factor is used to convert the number of moles to volume (L).Step 3 Write the equalities and conversion factors including 22.4 L/mole at STP.

What is the volume, in liters, of 64.0 g of O

2 gas at STP?

Sample Problem

8.8

Using Molar Volume to Find Volume at STPSlide18

Step 4 Set up the problem with factors to cancel units.Study Check 8.8How many grams of N2(g) are in 5.6 L of N2(g

) at STP?Answer7.0 g of N2Continued

Sample Problem

8.8

Using Molar Volume to Find Volume at STPSlide19

SolutionStep 1 State the given and needed quantities. When three of the four quantities (P, V, n, and T) are known, we use the ideal gas law equation to solve for the unknown quantity. It is helpful to organize the data in a table. The temperature is converted from degrees Celsius to kelvins so that the units of

V, n, and T match the unit of the gas constant R.

Dinitrogen

oxide, N2O, which is used in dentistry, is an anesthetic also called laughing gas. What is the pressure, in atmospheres, of 0.350 mole of N2O at 22 °C in a 5.00-L container?

Sample Problem

8.9

Using the Ideal Gas LawSlide20

Step 2 Rearrange the ideal gas law equation to solve for the needed quantity. By dividing both sides of the ideal gas law equation by V, we solve for pressure, P.Step 3 Substitute the gas data into the equation and calculate the

needed quantity.Study Check 8.9Chlorine gas, Cl2, is used to purify water. How many moles of chlorine gas are in a 7.00-L tank if the gas has a pressure of 865 mmHg and a temperature of 24 °C?Answer0.327 mole of Cl2

Continued

Sample Problem

8.9

Using the Ideal Gas LawSlide21

SolutionStep 1 State the given and needed quantities. When three of the quantities (P, V, and T) are known, we use the ideal gas law equation to solve for the unknown quantity, moles (n). Because the pressure is given in mmHg, we will use

R in mmHg. The volume given in milliliters (mL) is converted to a volume in liters (L). The temperature is converted from degrees Celsius to kelvins.

Butane, C

4H10, is used as a fuel for camping stoves. If you have 108 mL of butane gas at 715 mmHg and 25 °C , what is the mass, in grams, of butane?

Sample Problem

8.10

Calculating Mass Using the Ideal Gas LawSlide22

Step 2 Rearrange the ideal gas law equation to solve for the needed quantity. By dividing both sides of the ideal gas law equation by RT, we solve for moles, n.Step 3 Substitute the gas data into the equation and calculate the needed quantity

. Now we can convert the moles of butane to grams using its molar mass of 58.12 g/mole:Continued

Sample Problem

8.10

Calculating Mass Using the Ideal Gas LawSlide23

Study Check 8.10What is the volume, in liters, of 1.20 g of carbon monoxide at 8 °C if it has a pressure of 724 mmHg?Answer1.04 L

Continued

Sample Problem

8.10

Calculating Mass Using the Ideal Gas LawSlide24

SolutionStep 1 State the given and needed quantities.

Step 2 Write a plan to convert the given quantity to the needed moles.Calcium carbonate, CaCO3, in antacids reacts with HCl in the stomach to reduce acid reflux.

How many liters of CO2 are produced at 752 mmHg and 24 °

C from a 25.0-g sample of calcium carbonate?

Sample Problem

8.11

Gases in Chemical ReactionsSlide25

Step 3 Write the equalities and conversion factors for molar mass and mole–mole factors.Step 4 Set up the problem to calculate moles of needed quantity.

Step 5 Convert the moles of needed quantity to mass or volume using the molar mass or the ideal gas law equation.Continued

Sample Problem

8.11

Gases in Chemical ReactionsSlide26

Study Check 8.11If 12.8 g of aluminum reacts with HCl, how many liters of H2 would be formed at 715

mmHg and 19 °C?Answer18.1 L of H2Continued

Sample Problem

8.11

Gases in Chemical ReactionsSlide27

SolutionStep 1 Write the equation for the sum of the partial pressures.Step 2 Rearrange the equation to solve for the unknown pressure. To solve for the partial pressure of helium (

PHe), we rearrange the equation to give the following:Convert units to match.A heliox breathing mixture of oxygen and helium is prepared for a patient with

COPD (chronic obstructive pulmonary disease). The gas mixture has a total pressure of 7.00 atm. If the partial pressure of the oxygen in the tank is 1140 mmHg, what is

the partial pressure, in atmospheres, of the helium in the breathing mixture?

Sample Problem

8.12

Partial Pressure of a Gas in a MixtureSlide28

Step 3 Substitute known pressures into the equation and calculate the unknown partial pressure.Study Check 8.12An anesthetic consists of a mixture of cyclopropane gas, C3H6, and oxygen gas, O2. If the mixture has a total pressure of 1.09 atm, and the partial pressure of the

cyclopropane is 73 mmHg, what is the partial pressure, in millimeters of mercury, of the oxygen in the anesthetic?Answer755 mmHgContinued

Sample Problem

8.12

Partial Pressure of a Gas in a Mixture