Chem chapter 8
Calculating ratio of rate of effusion between two molecules
(rate of effusion A)/(rate of effusion B) = (molar mass B)^1/2 / (molar mass A)^1/2
A sample of ammonia is found to occupy 0.250 L under laboratory conditions of 27 °C and 0.850 atm. Find the volume of this sample at 0 °C and 1.00 atm.
.193 L
A sample of carbon dioxide, CO2, occupies 0.300 L at 10 °C and 750 torr. What volume will the gas have at 30 °C and 750 torr?
.321 L
Convert a pressure of 742 torr to atm
.97631 atm
A typical barometric pressure in Denver, Colorado, is 615 mm Hg. What is this pressure in atmospheres and kilopascals?
0.809 atm; 82.0 kPa
A typical barometric pressure in Kansas City is 740 torr. What is this pressure in atmospheres, in millimeters of mercury, in kilopascals, and in bar?
0.974 atm; 740 mm Hg; 98.7 kPa; 0.987 bar
pascal (Pa)
1 Pa = 1 N/m2, where N is the newton, a unit of force defined as 1 kg m/s2. One pascal is a small pressure; in many cases, it is more convenient to use units of kilopascal (1 kPa = 1000 Pa) or bar (1 bar = 100,000 Pa)
inches of mercury (in. Hg)
1 in. Hg = 3386 Pa
kilopascal (kPa)
1 kPa= 1000 Pa
millimeters of mercury (mmHg)
1 mm Hg ~1 torr
torr
1 torr= 1/760 atm
Show the calculation supporting the claim that atmospheric pressure near sea level corresponds to the pressure exerted by a column of mercury that is about 760 mm high. The density of mercury = 13.6 g/cm3. (8.1)
1.01 x 10^5 Pa
Methane, CH4, is being considered for use as an alternative automotive fuel to replace gasoline. One gallon of gasoline could be replaced by 655 g of CH4. What is the volume of this much methane at 25 °C and 745 torr?
1.02 x 10^3 L
A 5.73-L flask at 25 °C contains 0.0388 mol of N2, 0.147 mol of CO, and 0.0803 mol of H2. What is the total pressure in the flask in atmospheres?
1.137 atm
rate of effusion
1/square root of molar mass; amount of gas transferred over time
Calculate the height of a column of water at 25 °C that corresponds to normal atmospheric pressure. The density of water at this temperature is 1.0 g/cm3. (8.1)
10.3 m
What volume of oxygen at 423.0 K and a pressure of 127.4 kPa is produced by the decomposition of 129.7 g of BaO2 to BaO and O2?
10.57 L O2
Millibar (mbar or mb)
1000 mbar= 1 bar
A 2.50-L volume of hydrogen measured at -196 °C is warmed to 100 °C. Calculate the volume of the gas at the higher temperature, assuming no change in pressure.
12.1 L
A 36.0-L cylinder of a gas used for calibration of blood gas analyzers in medical laboratories contains 350 g CO2, 805 g O2, and 4,880 g N2. At 25 degrees C, what is the pressure in the cylinder in atmospheres?
141 atm
An unknown gas effuses 1.66 times more rapidly than CO2. What is the molar mass of the unknown gas? Can you make a reasonable guess as to its identity?
16 g/mol; CH4
A gas was found to have a density of 0.0847 g/L at 17.0 °C and a pressure of 760 torr. What is its molar mass? What is the gas?
2.02 g/mol; therefore, the gas must be hydrogen (H2, 2.02 g/mol)
Canadian tire pressure gauges are marked in units of kilopascals. What reading on such a gauge corresponds to 32 psi?
2.2 × 10^2 kPa
A sample of oxygen, O2, occupies 32.2 mL at 30 °C and 452 torr. What volume will it occupy at -70 °C and the same pressure?
21.6 mL
A weather balloon contains 8.80 moles of helium at a pressure of 0.992 atm and a temperature of 25 °C at ground level. What is the volume of the balloon under these conditions?
217 L
Standard mole volume
22.4 L
A spray can is used until it is empty except for the propellant gas, which has a pressure of 1344 torr at 23 °C. If the can is thrown into a fire (T = 475 °C), what will be the pressure in the hot can?
3.40 x 10^3 torr
Calculate the pressure in bar of 2520 moles of hydrogen gas stored at 27 °C in the 180-L storage tank of a modern hydrogen-powered car.
350 bar
A cylinder of O2(g) used in breathing by emphysema patients has a volume of 3.00 L at a pressure of 10.0 atm. If the temperature of the cylinder is 28.0 °C, what mass of oxygen is in the cylinder?
38.8 g
Calculate the density of Freon 12, CF2Cl2, at 30.0 °C and 0.954 atm.
4.64 g/L
A sample of nitrogen, N2, occupies 45.0 mL at 27 °C and 600 torr. What pressure will it have if cooled to -73 °C while the volume remains constant?
400 torr
Calculate the root-mean-square velocity for an oxygen molecule at -23 °C
441 m/s
A 20.0-L cylinder containing 11.34 kg of butane, C4H10, was opened to the atmosphere. Calculate the mass of the gas remaining in the cylinder if it were opened and the gas escaped until the pressure in the cylinder was equal to the atmospheric pressure, 0.983 atm, and a temperature of 27 °C.
46.4 g
Calculate the ratio of the rate of effusion of hydrogen to the rate of effusion of oxygen.
4:1 Hydrogen effuses four times as rapidly as oxygen.
Calculate the root-mean-square velocity for a nitrogen molecule at 30 °C.
519 m/s
At a particular pressure and temperature, nitrogen gas effuses at the rate of 79 mL/s. Using the same apparatus at the same temperature and pressure, at what rate will sulfur dioxide effuse?
52 mL/s
A cylinder of medical oxygen has a volume of 35.4 L, and contains O2 at a pressure of 151 atm and a temperature of 25 °C. What volume of O2 does this correspond to at normal body conditions, that is, 1 atm and 37 °C?
5561 L
When filled with air, a typical scuba tank with a volume of 13.2 L has a pressure of 153 atm (Figure). If the water temperature is 27 °C, how many liters of air will such a tank provide to a diver's lungs at a depth of approximately 70 feet in the ocean where the pressure is 3.13 atm?
667 L
How many grams of gas are present in 0.100 L of CO2 at 307 torr and 26 °C
7.24 x 10^-2 g
What is the molar mass of a gas if 0.281 g of the gas occupies a volume of 125 mL at a temperature 126 °C and a pressure of 777 torr?
72 g/mol
Convert a pressure of 29.2 in. Hg to torr
742 torr
How many moles of gaseous boron trifluoride, BF3, are contained in a 4.3410-L bulb at 788.0 K if the pressure is 1.220 atm? How many grams of BF3?
8.190 x 10^-2 mol, 5.553 g
The density of a certain gaseous fluoride of phosphorus is 3.93 g/L at STP. Calculate the molar mass of this fluoride and determine its molecular formula
88.1 g/mol; PF3
Convert a pressure of .97631 atm to kPa
98.9 kPa
Convert a pressure of 98.9 kPa to mbar
989 mbar
manometer
A device used to measure the pressure of a sample of gas in a container. A closed-end manometer is a U-shaped tube with one closed arm, one arm that connects to the gas to be measured, and a nonvolatile liquid (usually mercury) in between.
effusion
A process by which gas particles pass through a tiny opening
Standard Temperature and Pressure (STP)
A temperature of 273 K and a pressure of 1.00 atm
Cyclopropane, a gas once used with oxygen as a general anesthetic, is composed of 85.7% carbon and 14.3% hydrogen by mass. Find the empirical formula. If 1.56 g of cyclopropane occupies a volume of 1.00 L at 0.984 atm and 50 °C, what is the molecular formula for cyclopropane?
Empirical formula is CH2. Molecular formula is C3H6
Acetylene, a fuel used welding torches, is comprised of 92.3% C and 7.7% H by mass. Find the empirical formula. If 1.10 g of acetylene occupies of volume of 1.00 L at 1.15 atm and 59.5 °C, what is the molecular formula for acetylene?
Empirical formula, CH; Molecular formula, C2H2
Amonton's Law describing gas behavior
If the temperature is increased, the average speed and kinetic energy of the gas molecules increase. If the volume is held constant, the increased speed of the gas molecules results in more frequent and more forceful collisions with the walls of the container, therefore increasing the pressure
Why should you roll or belly-crawl rather than walk across a thinly-frozen pond?
Lying down distributes your weight over a larger surface area, exerting less pressure on the ice compared to standing up. If you exert less pressure, you are less likely to break through thin ice.
Molar mass of a gas
M=mRT/PV, m=mass of substance
compressibility factor (Z)
One way in which the accuracy of PV = nRT can be judged is by comparing the actual volume of 1 mole of gas (its molar volume, Vm) to the molar volume of an ideal gas at the same temperature and pressure.
combined gas law
P1V1/T1=P2V2/T2 when moles of ideal gas are kept constant
Boyle's Law
P1V1=P2V2. The volume of a given amount of gas held at constant temperature is inversely proportional to the pressure under which it is measured
pressure formula
P=F/A
Ideal Gas Law
PV=nRT
SI units of pressure
Pascal, kilopascal, psi, or atmospheres (atm)
Why are sharp knives more effective than dull knives (Hint: think about the definition of pressure)?
The cutting edge of a knife that has been sharpened has a smaller surface area than a dull knife. Since pressure is force per unit area, a sharp knife will exert a higher pressure with the same amount of force and cut through material more effectively.
If the volume of a fixed amount of a gas is tripled at constant temperature, what happens to the pressure?
The pressure decreases by a factor of 3.
hydrostatic pressure
The pressure exerted by a fluid due to gravity, P=hpg. where h is the height of the fluid, ρ is the density of the fluid, and g is acceleration due to gravity.
rate of effusion and average speed of its molecules
The rate of effusion of a gas depends directly on the (average) speed of its molecules(Urms). (effusion rate A/effusion rate B)= (Urms A/Urms B)
Charle's Law
V1/T1=V2/T2. the volume of a given amount of gas is directly proportional to its temperature on the kelvin scale when the pressure is held constant
Avogadro's Law
V1/n1=V2/n2. For a confined gas, the volume (V) and number of moles (n) are directly proportional if the pressure and temperature both remain constant
Explain how the volume of the bubbles exhausted by a scuba diver change as they rise to the surface, assuming that they remain intact.
As the bubbles rise, the pressure decreases, so their volume increases as suggested by Boyle's law.
Avogadro Law describing gas behavior
At constant pressure and temperature, the frequency and force of molecule-wall collisions are constant. Under such conditions, increasing the number of gaseous molecules will require a proportional increase in the container volume in order to yield a decrease in the number of collisions per unit area to compensate for the increased frequency of collisions
Daltons Law describing gas behavior
Because of the large distances between them, the molecules of one gas in a mixture bombard the container walls with the same frequency whether other gases are present or not, and the total pressure of a gas mixture equals the sum of the (partial) pressures of the individual gases.
How would the use of a volatile liquid affect the measurement of a gas using open-ended manometers vs. closed-end manometers?
With a closed-end manometer, no change would be observed, since the vaporized liquid would contribute equal, opposing pressures in both arms of the manometer tube. However, with an open-ended manometer, a higher pressure reading of the gas would be obtained than expected, since Pgas = Patm + Pvol liquid.
Can the speed of a given molecule in a gas double at constant temperature? Explain your answer.
Yes. At any given instant, there are a range of values of molecular speeds in a sample of gas. Any single molecule can speed up or slow down as it collides with other molecules. The average velocity of all the molecules is constant at constant temperature.
atmosphere (atm)
a unit of pressure based on the average pressure of air at sea level; 1 atm = 101,325 Pa
pounds per square inch (psi)
air pressure at sea level is ~14.7 psi. 1 atm= 14.6959 psi
rate of diffusion
amount of gas diffusing through a given area over a given time. time required for diffusion is inversely proportional to the rate of diffusion
barometer
an instrument used to measure atmospheric pressure. It's a glass tube that is closed at one end, filled with a nonvolatile liquid such as mercury, and then inverted and immersed in a container of that liquid. The atmosphere exerts pressure on the liquid outside the tube, the column of liquid exerts pressure inside the tube, and the pressure at the liquid surface is the same inside and outside the tube. The height of the liquid in the tube is therefore proportional to the pressure exerted by the atmosphere.
mean free path
average distance a molecule travels between collisions
Kinetic Molecular Theory
based on the idea that particles of matter are always in motion
diffusion and effusion rate similarities
both depend on the molar mass of the gas. Their rates aren't equal but ratios of their rates are the same
gas pressure definition
caused by the force exerted by gas molecules colliding with the surfaces of objects
Avogadro Law V/n is constant at
constant P and T
Charles Law V/T is constant at
constant P and n
Boyle's law PV is constant at
constant T and n
Amontons Law or Gay Lussacs P/T is constant at
constant V and n
Derivation of a Density Formula from the Ideal Gas Law Use PV = nRT to derive a formula for the density of gas in g/L
g/L = (P x Molar mass)/(RT)
Boyle Law describing gas behavior
if gas volume decreases, container wall area decreases and molecule-wall collision frequency increases, both will increase pressure
Charles Law describing gas behavior
if temperature of gas increases, a constant pressure is only maintained if the volume increases. This results in greater average distances traveled by molecules so surface area increases
If volume decreases and wall area decreases it yields:
increased pressure (Boyles)
If temperature increase and volume is constant it yields:
increased pressure (amontons law)
If container pressure is constant and more gas molecules are added it yields:
increased volume (Avogadros)
Maxwell-Botzmann Distribution
molecular speed distribution. y axis is number of molecules and x axis is velocity
vapor pressure of water
pressure exerted by water vapor in equilibrium with liquid water in a closed container at a specific temperature
pressure, force, and area
pressure is directly proportional to force and inversely proportional to area. pressure can be increased either by increasing the amount of force or by decreasing the area over which it is applied; pressure can be decreased by decreasing the force or increasing the area.
Graham's law of effusion
states that the rate of effusion for a gas is inversely proportional to the square root of its molar mass
Dalton's Law of Partial Pressures
states that the total pressure of a mixture of gases is equal to the sum of the pressures of all the gases in the mixture. Partial pressure of a gas can be determined from ideal gas ea=quation as P= nRT/V
pressure definition
the amount of force exerted per unit area of a surface.
Ideal gas constant
the constant R= .08306 (L atm)/(mol K) or 8.314 kg m^2/ s^2 K
Gay-Lussac's (Amonton's) Law
the pressure of a given amount of gas is directly proportional to its temperature on the kelvin scale when the volume is held constant.
diffusion
the process by which molecules move from an area of higher concentration to an area of lower concentration
root mean square velocity
u(rms)=(3RT/M)^1/2. square root of the average of the squares of the velocities with n = the number of particles
bar (bar or b)
unit of pressure; 1 bar = 100,000 Pa
Most mixtures of hydrogen gas with oxygen gas are explosive. However, a mixture that contains less than 3.0 % O2 is not. If enough O2 is added to a cylinder of H2 at 33.2 atm to bring the total pressure to 34.5 atm, is the mixture explosive?
yes
