CHEMISTRY 100 Problem Set Chapter 5

The physical behavior of most gases is nearly independent of chemical composition. The physical behavior of a gas is predominantly determined by VOLUME, AMOUNT (moles), TEMPERATURE, and PRESSURE. These four physical properties are related and dependent upon one another.

VOLUME
A gas expands uniformly to fill any container in which it is placed. This means that the volume of a gas is the volume of its container. Volumes of gases can be expressed in liters or cubic decimeters.

1 L = 1 dm3 = 1 x 103 cm3 = 1 x 10-3 m3

AMOUNT
Most commonly, the amount of matter in a gaseous sample is expressed in terms of the number of moles (n). In some cases, the mass is given instead. These two quantities are related through the molar mass, MW.

n = mass/MW

TEMPERATURE
The temperature of a gas is ordinarily measured using a thermometer marked in degrees Celsius. However, in any calculation involving the physical behavior of gases, temperatures must be expressed using the Kelvin scale (K). The formula for converting between oC and K is:

K = oC + 273.15

PRESSURE
Pressure is defined as force per unit area. The SI unit for pressure is the pascal (Pa) the pressure exerted by a force of one newton on an area of one square meter (kg/ms2). Atmospheric pressure is about 105 Pa or 100 kilopascals (kPa).

Some common units for pressure are:

atmospheres (atm), defined by the relation: 1 atm = 1.01325 x 105 Pa.

millimeters of mercury (mmHg), the pressure exerted by a column of mercury one millimeter high. A column of mercury 760 mm high exerts a pressure of one atmosphere. The unit mmHg is often called the Torr.

1 standard atmosphere = 1 atm = 760 mmHg = 760 Torr

Units of Pressure
1 atm = 760 mmHg = 29.921 in Hg
         = 760 Torr
         = 14.696 lb/in2 = 14.696 psi
         = 101,325 N/m2
         = 101,325 Pa = 1.01325 x 105 Pa
         = 101.325 kPa
         = 1.01325 bar
         = 1013.25 mb

STANDARD TEMPERATURE and PRESSURE (STP)
The conditions of 0oC (273.15 K), and 1 atm (760 Torr, 760 mmHg) are referred to as standard temperature and pressure (STP).

PROBLEM 1
Convert 0.9870 atm to:     a) Pa     b) mmHg

BOYLE'S LAW     Pressure and Volume are INDIRECTLY proportional.

    PV = k' {at constant temperature}

P1V1 = P2V2

PROBLEM 2
A sample of chlorine gas occupies a volume of 946 mL at a pressure of 726 mmHg. Calculate the pressure of the gas if the volume is reduced to 154 mL. Assume that the temperature remains constant.

PROBLEM 3
An inflated balloon has a volume of 0.55 L at sea level (1.0 atm) and is allowed to rise to a height of 6.5 km, where the pressure is about 0.40 atm. Assuming that the temperature remains constant, what is the final volume of the balloon?

CHARLES' LAW Volume and Temperature are DIRECTLY proportional.

V/T = k" {at constant pressure}

V1/T1 = V2/T2

PROBLEM 4
Argon is an inert gas used in light bulbs. In one experiment, 452 mL of the gas is heated from 22oC to 187oC at constant pressure. What is its final volume?

PROBLEM 5
A sample of carbon monoxide, a poisonous gas, occupies 3.20 L at 125oC. Calculate the temperature in Celsius at which the gas will occupy 1.54 L if the pressure remains constant.

COMBINED GAS LAW

P1V1 / T1 = P2V2 / T2

PROBLEM 6
A sample of gas at 780 Torr and 4oC has a volume of 0.35 L. If the volume and temperature are changed to 0.31 L and 50oC, calculate the pressure.

PROBLEM 7
A small bubble rises from the bottom of a lake, where the temperature and the pressure are 8oC and 6.4 atm, to the water's surface, where the temperature is 25oC and pressure is 1.0 atm. Calculate the final volume (in mL) of the bubble if its initial volume was 2.1 mL.

AVOGADRO'S LAW equal volumes of any two gases at the same temperature and pressure contain the same number of molecules.

1 mol gas = 22.4 L (at STP)

THE IDEAL GAS LAW

PV = nRT

    R is the universal gas constant which has a value of:
            0.0821 L.atm/mol.K  if the pressure is in atm.
            62.4 L.Torr/mol.K  if the pressure in Torr or mmHg

PROBLEM 8
Sulfur hexafluoride (SF6) is a colorless, odorless, very unreactive gas. Calculate the pressure (in atm) exerted by 1.82 moles of gas in a steel vessel of volume 5.43 L at 69.5oC.

PROBLEM 9
Calculate the volume of 6.46 grams of helium at 27.0oC at a pressure of 2.37 atm?

PROBLEM 10
A 2.00 L flask at 25oC and 730 Torr contains CH4 gas. How many moles of gas are in the flask?

PROBLEM 11
A 2.00 gram sample of solid CO2 (dry ice) is allowed to sublime in a balloon. If the final pressure in the balloon is 0.565 atm and the volume is 2.00 L, what is the temperature in oC?

GAS DENSITY

d = P(MW)/RT

PROBLEM 12
Calculate the density of N2, O2, CO2, and CH4 at STP?

PROBLEM 13
A 205 mL sample of a gas at 100 oC and 755 Torr is found to have a mass of 1.22 grams. What is the molecular weight of the gas?

GASES IN REACTION STOICHIOMETRY

Law of Combining Gases When gases measured at the same temperature and pressure are allowed to react, the volumes of gaseous reactants and products are in small whole-number ratios.

PROBLEM 14
How many liters of hydrogen chloride can be prepared at STP from the reaction of 6 liters of chlorine gas with excess hydrogen?

PROBLEM 15
If 100.0 grams of H2O(l) are decomposed to H2(g) and O2(g), what is the total volume of the gases at STP?

PROBLEM 16
How many liters of hydrogen gas can form at STP when 8.92 g of Fe react completely with excess HCl?

2 Fe(s) + 6 HCl(aq) ----> 2 FeCl3(aq) + 3 H2(g)

DALTON'S LAW OF PARTIAL PRESSURES

PTotal = PA + PB + PC + ...

PROBLEM 17
If 100.0 mL of O2 are collected over water at 22.0oC and atmospheric pressure of 754 Torr, what is the pressure of the "DRY" O2? The vapor pressure of H2O at 22.0oC is 19.8 Torr.

PROBLEM 18
If 200 mL of N2 at 25oC and a pressure of 250 Torr are mixed with 350 mL of O2 at 25oC and a pressure of 300 Torr, so that the resulting volume is 300 mL, what would be the final pressure of the mixture?

MOLE FRACTION

CA = nA / nTotal  = PA / PTotal

PROBLEM 19
Calculate the mole fraction of each gas in a mixture of 0.210 mol carbon dioxide, 0.750 mol oxygen, and 0.450 mol of nitrogen.  (Ccarbon dioxide  =  0.210/1.41 = 0.149; Coxygen  =  0.750/1.41 = 0.532; Cnitrogen  =  0.450/1.41 = 0.319)

PROBLEM 20
A mixture of gases is composed of 0.563 mol of hydrogen and 0.841 mol of chlorine in a 789 mL container at 84.2oC. What is the partial pressure of each gas in the container and what is the total pressure of the mixture?

PROBLEM 21
A gaseous mixture contains 2.00 moles of O2 and 0.500 moles of H2 and has a total pressure of 3.00 atm. What is the partial pressure of O2?

GRAHAM'S LAW OF EFFUSION

r1/r2 = (MW2/MW1)1/2

[NOTE:    (MW2/MW1)1/2 = the square root of the quotient from the molecular weight of gas 2 divided by the molecular weight of gas 1.]

PROBLEM 22
Order the following gases in increasing rate of effusion.     Xe,  UF6,  Cl2,  C2H6

PROBLEM 23
A balloon is filled with H2(g) and O2(g). If the O2(g) effuses out of the balloon at a rate of 65 ml/hr, calculate the rate of the H2(g) effusion.

PROBLEM 24
Four identical flasks at STP contain 1 mole each of the following gases:  He, Cl2, CH4, NH3
Which gas has the:
    a) highest density?
    b) highest average velocity?
    c) fewest atoms? (He)



ANSWERS
PROBLEM 1    a) 1.000 x105 Pa     b) 750.1 mmHg
PROBLEM 2      4.46 x 103 mmHg
PROBLEM 3    1.4  L
PROBLEM 4    705 mL
PROBLEM 5    -81oC
PROBLEM 6    1027 Torr
PROBLEM 7    14 mL
PROBLEM 8    9.42 atm
PROBLEM 9    16.8 L
PROBLEM 10    7.85 x 10-2 mol
PROBLEM 11    29.85 oC
PROBLEM 12    N2 = 1.25 g/L;   O2 = 1.47 g/L;   CO2 = 1.96 g/L;   CH4 = 0.715 g/L
PROBLEM 13    183 g/mol
PROBLEM 14    12 L
PROBLEM 15    186.6 L
PROBLEM 16    5.37 L
PROBLEM 17    734 Torr
PROBLEM 18    517 Torr
PROBLEM 19    Ccarbon dioxide  =  0.210/1.41 = 0.149;  Coxygen  =  0.750/1.41 = 0.532;  Cnitrogen  =  0.450/1.41 = 0.319
PROBLEM 20    H2 = 1.59 x 104 mmHg,  Cl2 = 2.38 x 104 mmHg;  PT = 3.97x104mmHg
PROBLEM 21    2.4 atm
PROBLEM 22    UF6  <  Xe  <  Cl2  <  C2H6
PROBLEM 23    2.59 x 102ml/hr
PROBLEM 24     a)  Cl2    b)  He    c) He