Boyle's Law

8 Key excerpts on "Boyle's Law"

• 

  eBook - ePub

  Chemistry

  Concepts and Problems, A Self-Teaching Guide

  • Richard Post, Chad Snyder, Clifford C. Houk(Authors)
  • 2020(Publication Date)
  • Jossey-Bass

    (Publisher)

  Boyle's Law states that at constant temperature, the volume of a confined dry gas is inversely proportional to the pressure. (Dry indicates no water present.) Mathematically, Boyle's Law is stated as:

  Pressure and volume are inversely proportional. Mathematically this means that if we multiply pressure by some number, we must divide the volume by that same number, or vice versa. For example, assume the constant is equal to the number 4. Assume that the pressure and the volume each are equal to 2:

  If we divide the pressure by 2, we must multiply the volume by 2 in order for the constant to remain unchanged:

  If we multiply the pressure by 10, we must divide the volume by 10 in order for the constant to remain unchanged:

  At constant temperature with a confined specific amount of gas molecules: (a) if the volume is decreased, the pressure is __________ and (b) if the pressure is increased, the volume is _________________.

  Answer: (a) increased; (b) decreased

  The pressure (P) multiplied by the volume (V) is a constant (unchanging) number if the temperature remains constant. Note that Boyle's Law is based on a theoretically ideal gas. Real gases behave in a similar fashion to an ideal gas at moderate temperatures and pressures. Unless otherwise stated, we will assume that all gases behave exactly like an ideal gas. Since all gases are assumed to behave ideally, one gas will behave exactly like any other gas.

  According to the equation for Boyle's Law at constant temperature:

  1. increasing P causes a corresponding ______________ in V.
  2. increasing V causes a corresponding _______________ in P.

  Answer: (a) decrease; (b) decrease

  Boyle's Law can be applied in practical situations involving the pressure and volume of a gas at constant temperature. A gas originally occupies a volume, which can be called

  V1

  , at the pressure of

  P1

  . By Boyle's Law, we know that multiplying P1 times

  V1

  gives a number that is a constant. This same gas undergoes an increase in pressure to

  P2

  and a corresponding decrease in volume to

  V2

  . There is no change in temperature. How does the numerical constant obtained by multiplying

  P1

  by

  V1

  compare with the numerical constant obtained by multiplying P2 by

  V2

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  100 Science Discoveries That Changed the World

  • Colin Salter(Author)
  • 2021(Publication Date)
  • Pavilion

    (Publisher)

  The concept of air pressure was already known, but it was believed that air, and other gases, consisted of small particles surrounded by tiny invisible springs. When a Jesuit challenged Boyle’s publication he responded with the equation that has become known as Boyle’s Law. It states that, for a constant mass of gas at a constant temperature, the pressure is inversely proportional to the volume – in other words, the greater the pressure, the smaller the volume.

  Although others earlier in the century had noticed something similar, it was Boyle’s experimental proof that confirmed it. His Law was the first major one to be expressed as a mathematical equation. It is a cornerstone of classic mechanics in its application to pneumatic machines.

  Boyle also made groundbreaking studies in genetics, concluding that all mankind shared a common ancestry and that physical characteristics were defined by the act of conception. He was unusual among his Anglo-Irish peers in believing that the Irish language was worth keeping and in the 1680s he funded the production of a complete edition of the Bible in Gaelic.

  Not everything about Boyle was modern, however. Although he held enlightened views about human equality, he was a devout Christian and believed that the source of all mankind was Adam and Eve, whom he declared to be Caucasian. And despite his firm belief in evidence-based science instead of mere hypotheses, he was a committed alchemist who still believed that base metals could be transmuted into precious ones.

  An illustration of the apparatus Boyle used for experiments with air, taken from his publication A Continuation of New Experiments Physico-Mechanical, Touching the Spring and Weight of the Air, and its Effects (1669). This was a continuation of an earlier work of 1660, and was followed by a second part in 1682.

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  AP® Chemistry All Access Book + Online + Mobile

  • Kevin Reel, Derrick C. Wood, Scott A. Best(Authors)
  • 2014(Publication Date)
  • Research & Education Association

    (Publisher)

  Gases exhibit properties that are easily measured and manipulated by chemists: temperature, pressure, volume, and amounts (moles). Before early scientists had definitive proof about the chemical makeup of gases they were able to discover fundamental relationships or gas laws. There are five basic gas laws: Boyle’s law, Charles’ law, Gay-Lussac’s law, combined gas law, and the ideal gas law.

  Boyle’s Law

  Boyle’s law states that pressure and volume are inversely related when the temperature and number of moles are kept constant. EXAMPLE: A 4.0-L elastic weather balloon travels from sea level, at 1.0 atm pressure, to a higher altitude, where the pressure is 0.20 atm. What is the new volume of the balloon? SOLUTION:

  Charles’ Law

  Charles’ law states that volume is directly related to the absolute temperature (Kelvin) when the pressure and moles are kept constant.

  DID YOU

  KNOW?

  Cake mixes include high-altitude baking instructions to account for the lower pressures experienced at high altitudes. Otherwise, the cake would rise too much in the oven, which would inhibit the structural integrity of the cake when it cools—and it would become flat as a pancake!

  TEST TIP Make sure for all gas law calculations that the temperature is in Kelvin. This is a common and costly mistake.

  EXAMPLE: A gas occupies 2.0 L at 27°C. What is the volume of the gas at –73°C, assuming that the pressure is held constant? SOLUTION:

  Gay-Lussac’s Law

  Gay-Lussac’s law states that pressure is directly related to the absolute temperature (Kelvin) when the volume and moles are kept constant. EXAMPLE: A gas in a rigid container exerts 6.0 atm at 300. K. What is the pressure that the gas exerts at 500. K? SOLUTION:

  Combined Gas Law

  The combined gas law unifies all the variables in Boyle’s, Charles’, and Gay-Lussac’s laws into one equation. This equation is used when comparing two different conditions of a gas. The equation is:

  In this equation, V is the volume, P is the pressure, and T is the absolute temperature of the gas for two different conditions represented by the two sets of subscripts. In solving these types of gas law problems, it is helpful to initially list the variables and then substitute into the combined gas law equation.

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  Fundamentals of Air Sampling

  • Gregory D. Wight(Author)
  • 2018(Publication Date)
  • CRC Press

    (Publisher)

  From the Ideal Gas Law, two special cases also of great importance to air sampling work can be derived. Boyle’s Law Named after Robert Boyle, Boyle’s Law states that when the temperature of an ideal gas is held constant, the volume of a given mass varies inversely as the absolute pressure. V 2 V 1 = P 1 P 2 (2.10) Charles’ Law Named after Jacques Charles, Charles’ Law states that when the pressure of an ideal gas is held constant, the volume varies directly as the absolute temperature. V 2 V 1 = T 2 T 1 (2.11) (Temperatures must be in absolute: Kelvin or Rankine.) For example, if 5 L of an ideal gas at 1 atm and 20 °C are heated at constant pressure until T = 40 °C, the gas will expand to a volume V 2 : V 2 = 5 × (40 + 273) (20 + 273) = 5.34 liters Both Boyle’s and Charles’ Laws are often employed together in air sampling to find the equivalent volume of an ideal gas at a temperature and. pressure different from actual. V 2 = V 1 × (P 1 P 2) × (T 2 T 1) (2.12) Standard Temperature and Pressure To be able to compare gas sampling data collected by various organizations or under differing conditions, all gas volumes must be corrected to a set of predetermined or standard conditions. As noted earlier, for atmospheric or ambient sampling, the EPA has set these conditions as: 25 ∘ C = (298 K) and 1 atmosphere (= 760 mm Hg) For emission monitoring, EPA specifies Standard Temperature as 20 °C or 293 K. For example, if 3 L of ambient air are sampled at 35 °C and a pressure of 742 mm Hg, the sampled volume can be corrected to standard conditions by application of Boyle’s and Charles’ Laws (Equation 2.12). V std = V sampled × (P samp / P std) × (T std / T samp) = 3 L × (742 / 760) × [ 298 / (35 + 273) ] = 2.83 std liters 2.5  GAS DENSITY Another adaptation of the Ideal Gas Equation of State is for the calculation of gas density (density =

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  General Chemistry for Engineers

  • Jeffrey Gaffney, Nancy Marley(Authors)
  • 2017(Publication Date)
  • Elsevier

    (Publisher)

  If a 1.5 L gas sample at a pressure of 3.0 atm is reduced to a pressure of 0.5 atm, what is the final volume of the gas sample if the temperature remains the same? According to Boyle’s law:

  P 1

  = 3.0 atm ,

  P 2

  = 0.5 atm ,

  V 1

  = 1.5 L

  So

  P 1

  V 1

  =

  P 2

  V 2

  V 2

  =

  P 1

  V 1

  /

  P 2

  =

  3.0 atm

  1.5 L

  0.5 atm

  = 9.0 L

  Example 6.2: Determining the Pressure of a Gas From a Change in Volume at Constant Temperature and Mass A gas sample occupies 10.5 L at 0.8 atm. What is the pressure of the gas sample if the volume is increased to 5.0 L at the same temperature? According to Boyle’s law:

  P 1

  = 0.8 atm ,

  V 1

  = 10.5 L ,

  V 2

  = 5.0 L

  So

  P 1

  V 1

  =

  P 2

  V 2

  P 2

  =

  P 1

  V 1

  /

  V 2

  =

  0.8 atm

  10.5 L

  5.0 atm

  = 1.7 L

  6.3 Charles’ Law

  Charles’ law deals with the relationship between the temperature and volume of a gas when the pressure and mass remain constant. Temperature is viewed as an objective measure of how hot or cold something is. However, like pressure, it can be related to the motion of the molecules in the gas sample. The faster the molecules move, the higher the temperature. The measure of the relative speed of the molecular movement in the gas sample is known as the average kinetic energy of the gas, which depends only on the temperature of the gas. So, the average kinetic energy of the gas molecules increases as the temperature increases and the gas molecules move faster. If the gas pressure remains constant, this increased motion causes an increase in the volume, or the amount of space occupied by the gas. This view of temperature and pressure as related to the motion of the gas molecules is known as the kinetic-molecular theory of gases.

  The study of the effect of temperature upon the properties of gases took much longer to accomplish than the study of the effect of pressure. This was primarily because there was no quantitative temperature scale available until 1724–42, when the Fahrenheit and Celsius scales were developed. Both of these temperature scales were empirically based. That is, they were based on the direct measurement of the physical properties of materials. The Fahrenheit scale was originally based on the measurement of three fixed temperatures using the mercury thermometer invented by Daniel Fahrenheit shown in Fig. 6.6

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  Underwater Forensic Investigation

  • Ronald F. Becker, Stuart H. Nordby, Jon J.(Authors)
  • 2013(Publication Date)
  • CRC Press

    (Publisher)

  density. Increase the pressure of a fixed volume of gas and the density increases. Of the four laws we will study, Boyle’s is the most important for underwater operations.

  CHARLES’S LAW

  At a constant volume, the pressure of gas varies directly with absolute temperature. Mathematically,

  P 1

  P 2

  =

  T 1

  T 2

  Given a constant volume of gas, the higher the temperature is, the higher the gas pressure and vice versa.

  P1 and P2 are the beginning and final pressures, respectively, and T1 and T2 are the beginning and final temperatures, respectively. The law is useful to keep in mind when filling air tanks when there is a large difference between air and water temperatures. Charles’s law predicts that a steel scuba tank holding 80 cubic feet of air at a pressure of 3,000 psi, filled when the air temperature was 90°F, and taken into water that is 75°F will have an in-water tank pressure lower than 3,000 psi.

  DALTON’S LAW The total pressure exerted by a mixture of gases is equal to the sum of the pressures that would be exerted by each of the gases if it alone were present and occupied the total volume. Mathematically,

  P TOTAL

  =

  P 1

  +

  P 2

  …

  P OTHER

  The pressure of any gas mixture is equal to the sum of pressures exerted by the individual gases. In air, those individual gases would be oxygen, nitrogen, and the minor gases.

  PTOTAL is the total pressure of a gas mixture, and P1 and P2 are the partial pressures of component gases (oxygen and nitrogen). The term POTHER is used to signify partial pressures of all other gases in the mixture.

  Partial pressure is the pressure exerted by an individual gas, whether that gas is part of a mixture (such as air) or dissolved in a liquid (such as blood) or in any body tissue. Partial pressure of a gas P

  G

  is determined by the fraction of the gas in the mixture F

  G

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  Understanding General Chemistry

  • Atef Korchef(Author)
  • 2022(Publication Date)
  • CRC Press

    (Publisher)
• d) low pressure and/or high temperature
• 4. The equation PV = nRT represents
  1. a) the ideal gas law
  2. b) the general gas law for real gases.
  3. c) Boyle’s law
  4. d) Dalton’s law of partial pressures
• 5. Which of the following equations represents the general gas law for real gases?
  1. a) PV = nRT
  2. b) Ptotal  = P1  + P2 +P3 …..
  3. c) Pi  = Xi  × Ptotal
  4. d)
     P + a

     n 2

     V 2

     ×

     V − n b

     = n R T
• 6. Boyle’s law, which relates the pressure and volume at constant amount of a substance and constant temperature, states that the volume of an ideal gas is
  1. a) directly proportional to its pressure
  2. b) inversely proportional to its pressure
  3. c) inversely proportional to the amount of the substance
  4. d) proportional to the gas constant R
• 7. According to Charles’ law, when the volume of an ideal gas increases at constant pressure and gas amount, the temperature
  1. a) increases
  2. b) decreases
  3. c) remains constant
  4. d) both increases and decreases depending on the volume
• 8. When a balloon is filled with oxygen gas at constant pressure and temperature, its volume increases with the increase in the amount of oxygen. This corresponds to
  1. a) Boyle’s law
  2. b) Charles’ law
  3. c) Avogadro’s law
  4. d) Dalton’s law
• 9. Guy-Lussac’s law states that
  1. a) the volume is inversely proportional to the pressure at constant temperature and gas amount
  2. b) the volume is proportional to the temperature at constant pressure and gas amount
  3. c) the volume is proportional to the gas amount at constant pressure and temperature
  4. d) the pressure is proportional to the temperature at constant volume and gas amount
• 10. The equation
  V 1

  T 1

  =

  V 2

  T 2
  is obtained from
  1. a) Boyle’s law
  2. b) Charles’s law
  3. c) Avogadro’s law
  4. d) Guy-Lussac’s law
• 11. Which equation is obtained from Boyle’s law?
  1. a)
     V 1

     n 1

     =

     V 2