What Volume Of Helium Would Be In A Balloon The Size Of A Soft Drink Bottle?

Learning Outcomes

• Identify the mathematical relationships between the diverse properties of gases
• Apply the ideal gas law, and related gas laws, to compute the values of various gas backdrop nether specified weather

During the seventeenth and peculiarly eighteenth centuries, driven both by a desire to understand nature and a quest to make balloons in which they could fly (Figure 1), a number of scientists established the relationships between the macroscopic concrete backdrop of gases, that is, pressure, book, temperature, and amount of gas. Although their measurements were not precise by today'due south standards, they were able to determine the mathematical relationships between pairs of these variables (due east.chiliad., pressure level and temperature, pressure level and volume) that agree for an ideal gas—a hypothetical construct that real gases estimate under sure weather condition. Somewhen, these private laws were combined into a unmarried equation—the platonic gas law—that relates gas quantities for gases and is quite accurate for depression pressures and moderate temperatures. Nosotros volition consider the key developments in individual relationships (for pedagogical reasons non quite in historical order), then put them together in the ideal gas police.

Figure 1. In 1783, the beginning (a) hydrogen-filled balloon flight, (b) manned hot air balloon flying, and (c) manned hydrogen-filled airship flight occurred. When the hydrogen-filled balloon depicted in (a) landed, the frightened villagers of Gonesse reportedly destroyed it with pitchforks and knives. The launch of the latter was reportedly viewed by 400,000 people in Paris.

Pressure and Temperature: Amontons'south Police force

Imagine filling a rigid container attached to a pressure level estimate with gas and and then sealing the container so that no gas may escape. If the container is cooled, the gas inside likewise gets colder and its pressure is observed to subtract. Since the container is rigid and tightly sealed, both the volume and number of moles of gas remain constant. If we heat the sphere, the gas inside gets hotter (Figure 2) and the pressure increases.

Figure ii. The effect of temperature on gas pressure: When the hot plate is off, the pressure level of the gas in the sphere is relatively low. As the gas is heated, the pressure of the gas in the sphere increases.

This human relationship between temperature and pressure is observed for any sample of gas confined to a constant volume. An example of experimental pressure-temperature data is shown for a sample of air under these conditions in Figure 3. We discover that temperature and pressure are linearly related, and if the temperature is on the kelvin scale, then P and T are direct proportional (again, when book and moles of gas are held abiding); if the temperature on the kelvin scale increases by a certain cistron, the gas pressure increases by the aforementioned cistron.

Figure iii. For a constant volume and corporeality of air, the pressure and temperature are directly proportional, provided the temperature is in kelvin. (Measurements cannot be made at lower temperatures considering of the condensation of the gas.) When this line is extrapolated to lower pressures, it reaches a pressure of 0 at –273 °C, which is 0 on the kelvin scale and the lowest possible temperature, called absolute zero.

Guillaume Amontons was the starting time to empirically establish the relationship between the pressure level and the temperature of a gas (~1700), and Joseph Louis Gay-Lussac adamant the relationship more precisely (~1800). Because of this, the P–T relationship for gases is known as either Amontons's constabulary or Gay-Lussac'southward law. Under either proper noun, it states that the force per unit area of a given amount of gas is directly proportional to its temperature on the kelvin scale when the volume is held constant. Mathematically, this can be written:

[latex]P\propto T\text{ or }P=\text{constant}\times T\text{ or }P=k\times T[/latex]

where ∝ ways "is proportional to," and k is a proportionality constant that depends on the identity, amount, and volume of the gas.

For a confined, constant volume of gas, the ratio [latex]\dfrac{P}{T}[/latex] is therefore constant (i.e., [latex]\dfrac{P}{T}=m[/latex] ). If the gas is initially in "Condition 1" (with [latex]P=P_{1}\text{ and }T = T_{1})[/latex], and then changes to "Condition ii" (with [latex]P=P_{2}\text{ and }T = T_{2})[/latex], we have that [latex]\dfrac{{P}_{ane}}{{T}_{i}}=k[/latex] and [latex]\dfrac{{P}_{2}}{{T}_{2}}=k,[/latex] which reduces to [latex]\dfrac{{P}_{1}}{{T}_{i}}=\dfrac{{P}_{2}}{{T}_{two}}[/latex]. This equation is useful for pressure level-temperature calculations for a confined gas at constant volume. Note that temperatures must be on the kelvin calibration for any gas law calculations (0 on the kelvin scale and the lowest possible temperature is called absolute null). (Also note that there are at least 3 ways we can draw how the pressure of a gas changes as its temperature changes: We can utilize a table of values, a graph, or a mathematical equation.)

Case i: Predicting Change in Pressure with Temperature

A tin of pilus spray is used until it is empty except for the propellant, isobutane gas.

1. On the can is the warning "Store only at temperatures below 120 °F (48.8 °C). Exercise not incinerate." Why?
2. The gas in the tin is initially at 24 °C and 360 kPa, and the can has a volume of 350 mL. If the can is left in a car that reaches fifty °C on a hot day, what is the new pressure in the tin?

Check Your Learning

A sample of nitrogen, N₂, occupies 45.0 mL at 27 °C and 600 torr. What pressure volition it accept if cooled to –73 °C while the volume remains constant?

Volume and Temperature: Charles'south Constabulary

If we make full a balloon with air and seal it, the airship contains a specific corporeality of air at atmospheric pressure level, let's say 1 atm. If we put the airship in a refrigerator, the gas inside gets common cold and the balloon shrinks (although both the corporeality of gas and its pressure level remain constant). If we make the balloon very cold, it will shrink a bully deal, and it expands once again when it warms up.

This video shows how cooling and heating a gas causes its book to subtract or increment, respectively.

You can view the transcript for "Liquid Nitrogen Experiments: The Airship" here (opens in new window).

These examples of the effect of temperature on the volume of a given amount of a confined gas at abiding pressure are true in full general: The book increases as the temperature increases, and decreases as the temperature decreases. Volume-temperature information for a 1-mole sample of marsh gas gas at one atm are listed and graphed in Effigy 4.

Figure 4. The volume and temperature are linearly related for 1 mole of methane gas at a constant pressure level of 1 atm. If the temperature is in kelvin, book and temperature are direct proportional. The line stops at 111 Chiliad because marsh gas liquefies at this temperature; when extrapolated, it intersects the graph'south origin, representing a temperature of absolute zero.

The human relationship between the volume and temperature of a given amount of gas at constant pressure is known as Charles's law in recognition of the French scientist and airship flight pioneer Jacques Alexandre César Charles. Charles'south police force states that the volume of a given corporeality of gas is straight proportional to its temperature on the kelvin scale when the pressure level is held constant.

Mathematically, this can be written as:

[latex]V\propto T\qquad\text{or}\qquad{V}=\text{abiding}\cdot T\qquad\text{or}\qquad{V}=k\cdot T\qquad\text{or}\qquad{V}_{1}\text{/}{T}_{ane}={Five}_{two}\text{/}{T}_{2}[/latex]

with yard being a proportionality constant that depends on the amount and pressure level of the gas.

For a confined, constant pressure gas sample, [latex]\dfrac{Five}{T}[/latex] is constant (i.e., the ratio = k), and as seen with the [latex]5-T[/latex] relationship, this leads to another grade of Charles's law: [latex]\dfrac{{5}_{1}}{{T}_{ane}}=\dfrac{{V}_{2}}{{T}_{ii}}.[/latex]

Example ii: Predicting Modify in Volume with Temperature

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?

Check Your Learning

A sample of oxygen, O_two, occupies 32.2 mL at 30 °C and 452 torr. What book will it occupy at –seventy °C and the same pressure?

Example iii: Measuring Temperature with a Volume Change

Temperature is sometimes measured with a gas thermometer by observing the modify in the book of the gas equally the temperature changes at constant pressure. The hydrogen in a particular hydrogen gas thermometer has a book of 150.0 cm³ when immersed in a mixture of ice and water (0.00 °C). When immersed in boiling liquid ammonia, the volume of the hydrogen, at the same pressure, is 131.vii cmⁱⁱⁱ. Find the temperature of humid ammonia on the kelvin and Celsius scales.

Check Your Learning

What is the volume of a sample of ethane at 467 K and 1.ane atm if it occupies 405 mL at 298 Thousand and 1.1 atm?

Volume and Pressure: Boyle'southward Law

If we partially fill an airtight syringe with air, the syringe contains a specific corporeality of air at constant temperature, say 25 °C. If we slowly push in the plunger while keeping temperature constant, the gas in the syringe is compressed into a smaller volume and its pressure increases; if we pull out the plunger, the volume increases and the force per unit area decreases. This example of the result of volume on the pressure level of a given amount of a confined gas is true in general. Decreasing the book of a contained gas volition increase its pressure level, and increasing its book will decrease its pressure. In fact, if the volume increases by a certain factor, the pressure decreases past the same factor, and vice versa. Volume-pressure data for an air sample at room temperature are graphed in Figure v.

Figure v. When a gas occupies a smaller volume, it exerts a college pressure; when it occupies a larger book, information technology exerts a lower pressure (bold the amount of gas and the temperature do non change). Since P and V are inversely proportional, a graph of 1/P vs. V is linear.

Unlike the P–T and V–T relationships, pressure and book are not directly proportional to each other. Instead, P and V exhibit inverse proportionality: Increasing the force per unit area results in a decrease of the volume of the gas. Mathematically this can be written:

[latex]P\blastoff 1\text{/}Five\qquad\text{ or }\qquad{P}=g\cdot 1\text{/}Five\qquad\text{ or }\qquad{P}\cdot V=k\qquad\text{ or }\qquad{P}_{1}{5}_{1}={P}_{ii}{V}_{2}[/latex]

Effigy 6. The relationship between pressure and book is inversely proportional. (a) The graph of P vs. 5 is a parabola, whereas (b) the graph of (1/P) vs. Five is linear.

with k being a constant. Graphically, this relationship is shown by the straight line that results when plotting the inverse of the pressure [latex]\left(\dfrac{i}{P}\right)[/latex] versus the book (V), or the inverse of volume [latex]\left(\dfrac{i}{V}\right)[/latex] versus the pressure level (5). Graphs with curved lines are difficult to read accurately at depression or high values of the variables, and they are more difficult to apply in plumbing fixtures theoretical equations and parameters to experimental data. For those reasons, scientists often try to observe a manner to "linearize" their information. If we plot P versus V, we obtain a hyperbola (come across Effigy 6).

The human relationship betwixt the volume and force per unit area of a given corporeality of gas at constant temperature was offset published past the English natural philosopher Robert Boyle over 300 years agone. It is summarized in the argument now known as Boyle's law: The volume of a given amount of gas held at abiding temperature is inversely proportional to the pressure level under which it is measured.

Example 4: Volume of a Gas Sample

The sample of gas in Effigy v has a volume of fifteen.0 mL at a pressure level of 13.0 psi. Determine the pressure level of the gas at a volume of 7.5 mL, using:

1. the P–5 graph in Effigy 5
2. the [latex]\dfrac{1}{P}[/latex] vs. V graph in Figure v
3. the Boyle's law equation

Comment on the likely accuracy of each method.

Check Your Learning

The sample of gas in Figure five has a book of xxx.0 mL at a pressure of 6.5 psi. Determine the volume of the gas at a pressure of 11.0 mL, using:

1. the P–5 graph in Figure 5
2. the [latex]\dfrac{one}{P}[/latex] vs. V graph in Figure 5
3. the Boyle'due south law equation

Comment on the likely accuracy of each method.

Chemistry in Action: Breathing and Boyle'due south Law

What exercise you lot do about xx times per minute for your whole life, without break, and frequently without even being aware of it? The reply, of course, is respiration, or animate. How does information technology work? It turns out that the gas laws apply hither. Your lungs take in gas that your body needs (oxygen) and go rid of waste product gas (carbon dioxide). Lungs are made of spongy, stretchy tissue that expands and contracts while you breathe. When you inhale, your diaphragm and intercostal muscles (the muscles between your ribs) contract, expanding your chest cavity and making your lung book larger. The increase in volume leads to a decrease in pressure (Boyle'due south police force). This causes air to catamenia into the lungs (from high pressure level to depression force per unit area). When you exhale, the process reverses: Your diaphragm and rib muscles relax, your chest cavity contracts, and your lung volume decreases, causing the pressure to increase (Boyle'south law again), and air flows out of the lungs (from high pressure level to low pressure). You so breathe in and out again, and again, repeating this Boyle's law bicycle for the residue of your life (Figure seven).

Figure 7. Breathing occurs because expanding and contracting lung volume creates pocket-sized pressure differences between your lungs and your environment, causing air to be fatigued into and forced out of your lungs.

Moles of Gas and Book: Avogadro's Law

The Italian scientist Amedeo Avogadro avant-garde a hypothesis in 1811 to account for the beliefs of gases, stating that equal volumes of all gases, measured under the aforementioned weather condition of temperature and pressure level, contain the aforementioned number of molecules. Over fourth dimension, this relationship was supported by many experimental observations equally expressed by Avogadro's law: For a confined gas, the volume (V) and number of moles (n) are directly proportional if the pressure and temperature both remain constant.

In equation form, this is written as:

[latex]5\propto{n}\qquad\text{or}\qquad{Five}=1000\times{n}\qquad\text{or}\qquad\dfrac{{Five}_{1}}{{n}_{1}}=\dfrac{{5}_{2}}{{due north}_{two}}[/latex]

Mathematical relationships tin also be determined for the other variable pairs, such as [latex]P[/latex] versus [latex]northward[/latex], and [latex]northward[/latex] versus [latex]T[/latex].

Visit this interactive PhET simulation link to investigate the relationships between pressure level, volume, temperature. and amount of gas. Use the simulation to examine the consequence of changing one parameter on another while belongings the other parameters abiding (every bit described in the preceding sections on the various gas laws).

The Ideal Gas Law

To this point, four dissever laws have been discussed that relate force per unit area, volume, temperature, and the number of moles of the gas:

• Boyle's police force: [latex]PV =[/latex] constant at constant [latex]T[/latex] and [latex]n[/latex]
• Amontons'south police force: [latex]\dfrac{P}{T}[/latex] = constant at constant V and n
• Charles'southward police force: [latex]\dfrac{Five}{T}[/latex] = constant at constant P and n
• Avogadro's police: [latex]\dfrac{V}{n}[/latex] = constant at constant P and T

Combining these four laws yields the ideal gas law, a relation between the pressure, book, temperature, and number of moles of a gas:

[latex]PV=nRT[/latex]

where P is the pressure of a gas, V is its volume, n is the number of moles of the gas, T is its temperature on the kelvin scale, and R is a constant called the ideal gas constant or the universal gas constant. The units used to limited force per unit area, book, and temperature will make up one's mind the proper form of the gas abiding as required by dimensional analysis, the about unremarkably encountered values being 0.08206 L atm mol^–ane K^–1 and 8.314 kPa L mol^–one K^–i.

Gases whose properties of P, V, and T are accurately described by the platonic gas law (or the other gas laws) are said to showroom ideal behavior or to approximate the traits of an ideal gas. An ideal gas is a hypothetical construct that may be used along with kinetic molecular theory to effectively explain the gas laws as volition be described in a later module of this chapter. Although all the calculations presented in this module presume ideal beliefs, this assumption is only reasonable for gases under conditions of relatively low pressure and high temperature. In the concluding module of this chapter, a modified gas law will be introduced that accounts for the non-ideal behavior observed for many gases at relatively high pressures and low temperatures.

The ideal gas equation contains five terms, the gas abiding R and the variable properties P, Five, north, and T. Specifying any 4 of these terms will permit use of the ideal gas constabulary to calculate the fifth term equally demonstrated in the following instance exercises.

Example 5: Using the Ideal Gas Law

Methyl hydride, CH_iv, is being considered for apply equally an culling automotive fuel to replace gasoline. One gallon of gasoline could exist replaced past 655 g of CH_four. What is the book of this much methyl hydride at 25 °C and 745 torr?

Bank check Your Learning

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.

If the number of moles of an ideal gas are kept constant under two different sets of weather condition, a useful mathematical relationship called the combined gas law is obtained: [latex]\dfrac{{P}_{1}{V}_{1}}{{T}_{1}}=\dfrac{{P}_{2}{V}_{2}}{{T}_{two}}[/latex] using units of atm, L, and K. Both sets of conditions are equal to the product of n × R (where northward = the number of moles of the gas and R is the ideal gas law constant).

Example 6: Using the Combined Gas Law

Figure viii. Scuba divers use compressed air to breathe while underwater. (credit: modification of work by Mark Goodchild)

When filled with air, a typical scuba tank with a book of thirteen.ii L has a pressure of 153 atm (Figure eight). If the h2o temperature is 27 °C, how many liters of air will such a tank provide to a diver's lungs at a depth of approximately lxx feet in the sea where the pressure level is 3.13 atm?

Check Your Learning

A sample of ammonia is found to occupy 0.250 L nether laboratory weather of 27 °C and 0.850 atm. Find the volume of this sample at 0 °C and 1.00 atm.

The Interdependence between Ocean Depth and Pressure in Scuba Diving

Figure 9. Scuba divers, whether at the Groovy Barrier Reef or in the Caribbean area, must be aware of buoyancy, pressure level equalization, and the amount of time they spend underwater, to avoid the risks associated with pressurized gases in the torso. (credit: Kyle Taylor)

Whether scuba diving at the Great Barrier Reef in Australia (shown in Figure nine) or in the Caribbean, defined must understand how pressure affects a number of issues related to their comfort and safety.

Pressure level increases with body of water depth, and the force per unit area changes nearly apace as divers accomplish the surface. The pressure a diver experiences is the sum of all pressures above the diver (from the water and the air). Nigh pressure level measurements are given in units of atmospheres, expressed equally "atmospheres accented" or ATA in the diving community: Every 33 feet of salt water represents 1 ATA of pressure in addition to one ATA of force per unit area from the atmosphere at body of water level.

Every bit a diver descends, the increase in pressure causes the body'southward air pockets in the ears and lungs to shrink; on the ascent, the subtract in pressure causes these air pockets to aggrandize, potentially rupturing eardrums or bursting the lungs. Divers must therefore undergo equalization by calculation air to torso airspaces on the descent by animate normally and calculation air to the mask past breathing out of the nose or adding air to the ears and sinuses by equalization techniques; the corollary is also true on ascent, divers must release air from the body to maintain equalization.

Buoyancy, or the ability to control whether a diver sinks or floats, is controlled past the buoyancy compensator (BCD). If a diver is ascending, the air in his BCD expands because of lower force per unit area according to Boyle's law (decreasing the pressure of gases increases the book). The expanding air increases the buoyancy of the diver, and she or he begins to ascend. The diver must vent air from the BCD or hazard an uncontrolled rise that could rupture the lungs. In descending, the increased pressure causes the air in the BCD to compress and the diver sinks much more quickly; the diver must add air to the BCD or run a risk an uncontrolled descent, facing much higher pressures most the ocean flooring.

The force per unit area also impacts how long a diver tin can stay underwater before ascending. The deeper a diver dives, the more compressed the air that is breathed considering of increased pressure: If a diver dives 33 anxiety, the pressure level is 2 ATA and the air would be compressed to one-half of its original volume. The diver uses up available air twice as fast equally at the surface.

Standard Weather condition of Temperature and Pressure

We have seen that the volume of a given quantity of gas and the number of molecules (moles) in a given book of gas vary with changes in pressure and temperature. Chemists sometimes make comparisons against a standard temperature and force per unit area (STP) for reporting properties of gases: 273.15 K and ane atm (101.325 kPa). At STP, an platonic gas has a volume of near 22.4 L—this is referred to every bit the standard molar volume (Figure x).

Figure 10. Since the number of moles in a given book of gas varies with pressure level and temperature changes, chemists use standard temperature and force per unit area (273.15 K and one atm or 101.325 kPa) to report properties of gases.

Fundamental Concepts and Summary

The beliefs of gases tin be described by several laws based on experimental observations of their properties. The pressure of a given amount of gas is direct proportional to its absolute temperature, provided that the volume does not change (Amontons's constabulary). The volume of a given gas sample is directly proportional to its absolute temperature at constant pressure level (Charles'due south law). The volume of a given amount of gas is inversely proportional to its pressure when temperature is held abiding (Boyle's law). Under the same atmospheric condition of temperature and force per unit area, equal volumes of all gases contain the same number of molecules (Avogadro's law).

The equations describing these laws are special cases of the ideal gas police, [latex]PV=nRT[/latex], where P is the pressure of the gas, V is its volume, n is the number of moles of the gas, T is its kelvin temperature, and R is the ideal (universal) gas constant.

Primal Equations

• [latex]PV=nRT[/latex]

Try It

1. Sometimes leaving a bike in the sun on a hot day will cause a blowout. Why?
2. Explicate how the volume of the bubbles exhausted by a scuba diver (Figure 8) alter as they rise to the surface, assuming that they remain intact.
3. One fashion to land Boyle's law is "All other things being equal, the pressure of a gas is inversely proportional to its volume."
   1. What is the meaning of the term "inversely proportional?"
   2. What are the "other things" that must be equal?
4. An alternating way to state Avogadro's law is "All other things being equal, the number of molecules in a gas is directly proportional to the volume of the gas."
   1. What is the pregnant of the term "straight proportional?"
   2. What are the "other things" that must be equal?
5. How would the graph in Figure 4 change if the number of moles of gas in the sample used to determine the curve were doubled?
6. How would the graph in Effigy five alter if the number of moles of gas in the sample used to decide the bend were doubled?
7. In add-on to the information plant in Figure v, what other information do we demand to find the mass of the sample of air used to determine the graph?
8. Determine the volume of one mol of CH₄ gas at 150 K and one atm, using Figure iv.
9. Decide the pressure of the gas in the syringe shown in Figure five when its volume is 12.5 mL, using:
   1. the appropriate graph
   2. Boyle's law
10. A spray tin 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 burn (T = 475 °C), what volition exist the pressure in the hot can?
11. What is the temperature of an 11.2-Fifty sample of carbon monoxide, CO, at 744 torr if it occupies 13.3 50 at 55 °C and 744 torr?
12. 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 force per unit area.
13. A airship inflated with three breaths of air has a volume of ane.seven L. At the aforementioned temperature and pressure, what is the volume of the balloon if v more same-sized breaths are added to the balloon?
14. A weather balloon contains 8.eighty 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 airship under these atmospheric condition?
15. The volume of an automobile air bag was 66.viii Fifty when inflated at 25 °C with 77.8 g of nitrogen gas. What was the pressure in the pocketbook in kPa?
16. How many moles of gaseous boron trifluoride, BF₃, are independent in a 4.3410-50 bulb at 788.0 K if the force per unit area is ane.220 atm? How many grams of BF₃?
17. Iodine, I_ii, is a solid at room temperature but sublimes (converts from a solid into a gas) when warmed. What is the temperature in a 73.3-mL bulb that contains 0.292 one thousand of I₂ vapor at a force per unit area of 0.462 atm?
18. How many grams of gas are nowadays in each of the following cases?
    1. 0.100 L of CO₂ at 307 torr and 26 °C
    2. viii.75 L of C₂H₄, at 378.3 kPa and 483 Chiliad
    3. 221 mL of Ar at 0.23 torr and –54 °C
19. A loftier altitude balloon is filled with 1.41 × x^iv L of hydrogen at a temperature of 21 °C and a pressure of 745 torr. What is the volume of the balloon at a elevation of 20 km, where the temperature is –48 °C and the pressure is 63.one torr?
20. A cylinder of medical oxygen has a book of 35.4 L, and contains O_two at a force per unit area of 151 atm and a temperature of 25 °C. What volume of O₂ does this represent to at normal trunk conditions, that is, ane atm and 37 °C?
21. A large scuba tank (Figure eight) with a book of 18 Fifty is rated for a pressure of 220 bar. The tank is filled at 20 °C and contains enough air to supply 1860 L of air to a diver at a pressure of two.37 atm (a depth of 45 feet). Was the tank filled to chapters at 20 °C?
22. A xx.0-Fifty cylinder containing eleven.34 kg of butane, C₄H₁₀, was opened to the temper. Summate 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 level, 0.983 atm, and a temperature of 27 °C.
23. While resting, the average lxx-kg man male person consumes 14 L of pure O₂ per hour at 25 °C and 100 kPa. How many moles of O_ii are consumed by a 70 kg man while resting for 1.0 h?
24. For a given amount of gas showing ideal behavior, describe labeled graphs of:
    1. the variation of P with 5
    2. the variation of 5 with T
    3. the variation of P with T
    4. the variation of [latex]\dfrac{1}{P}[/latex] with V
25. A liter of methane gas, CH₄, at STP contains more atoms of hydrogen than does a liter of pure hydrogen gas, H₂, at STP. Using Avogadro'southward police force every bit a starting point, explicate why.
26. The result of chlorofluorocarbons (such every bit CCl_twoF₂) on the depletion of the ozone layer is well known. The use of substitutes, such as CH_threeCH₂F(grand), for the chlorofluorocarbons, has largely corrected the problem. Calculate the volume occupied by 10.0 g of each of these compounds at STP:
    1. CCl₂F_ii(g)
    2. CH₃CH₂F(g)
27. As 1 g of the radioactive element radium decays over 1 yr, it produces 1.xvi × x^xviii blastoff particles (helium nuclei). Each alpha particle becomes an atom of helium gas. What is the pressure in pascal of the helium gas produced if it occupies a volume of 125 mL at a temperature of 25 °C?
28. A balloon that is 100.21 L at 21 °C and 0.981 atm is released and only barely clears the top of Mount Crumpet in British Columbia. If the final volume of the balloon is 144.53 Fifty at a temperature of 5.24 °C, what is the pressure experienced by the balloon equally it clears Mount Crumpet?
29. If the temperature of a stock-still corporeality of a gas is doubled at abiding volume, what happens to the force per unit area?
30. If the volume of a fixed amount of a gas is tripled at constant temperature, what happens to the pressure?

Glossary

absolute zilch:temperature at which the volume of a gas would be zero co-ordinate to Charles's law.

Amontons's police:(besides, Gay-Lussac's police force) pressure of a given number of moles of gas is direct proportional to its kelvin temperature when the volume is held constant

Avogadro's law:volume of a gas at constant temperature and pressure is proportional to the number of gas molecules

Boyle'due south law:book of a given number of moles of gas held at constant temperature is inversely proportional to the pressure under which it is measured

Charles'south law:book of a given number of moles of gas is directly proportional to its kelvin temperature when the pressure is held constant

ideal gas:hypothetical gas whose physical properties are perfectly described past the gas laws

platonic gas abiding (R):abiding derived from the ideal gas equation R = 0.08226 L atm mol^–1 One thousand^–1 or 8.314 Fifty kPa mol^–1 K^–ane

ideal gas law:relation between the force per unit area, volume, corporeality, and temperature of a gas under weather condition derived by combination of the uncomplicated gas laws

standard conditions of temperature and pressure (STP):273.fifteen K (0 °C) and 1 atm (101.325 kPa)

standard molar volume:volume of 1 mole of gas at STP, approximately 22.4 50 for gases behaving ideally

What Volume Of Helium Would Be In A Balloon The Size Of A Soft Drink Bottle?,

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