Application of Gas Laws

Line can be extrapolated to find V of a gas at _ K

0

(R = gas constant=______ L atm/mol.K)

0.08206

One half mole of o2 occupies what volume under standard conditions? = ___ L

11.2

Atmospheric pressure at sea level in the partial pressure are as follows. O2 = ___ mmHg @ 21%. N2 = ___ mmHg @ 79%. Total of ___ mmHg

160 mmHg @ 21%. N2 = 600 mmHg @ 79%. Total of 760 mmHg

3 moles of hydrogen reacting with 1 mole of nitrogen will form 2 moles of ammonia. But because V is proportional to n, then it is safe to say that 3 volumes of hydrogen reacting with 1 volume of nitrogen will form _ volumes of ammonia. Note that these coefficients exists as small whole number ratios.

2

One mole of gas at Standard temp (0 deg. C) and standard pressure (1 atm) occupies a volume of ___ L

22.4 L

Standard Temperature and Pressure (STP) Standard Temperature = ___ K or _ oC. Standard Pressure = _ atm. 1.0 L O2 and 1.0 L N2 at STP contain the same number of molecules

273 K or 0.0 oC, 1 atm.

The volumes of different gases are generally compared at standard temperature and pressure. For gases, the standard temperature is ___ Kelvins or _ degree Celsius, and the standard pressure is _ atmosphere.

273 Kelvins or 0.0 degree Celsius, 1.0 atmosphere

Two moles of gaseous nitrous occupy what volume under standard conditions? = ___ L

44.8

Sample Problem: what are the partial pressures of N20 and O2 if they are delivered to the patient in a 70/30 N20/O2 mixture =

532/228

1 mole of gas = _______ x 1023 gas molecules = Avogadro's number

6.023

The amount of the gas in a system can be expressed in grams, in number of molecules, or in moles, which is the SI unit. One mole of any gas contains exactly _______ gas molecules.

6.023 x 10 ^23

At STP, a mole of any gas contains _______ gas molecules and occupies a volume of ___ Liters.

6.023 x 10 ^23, 22.4 Liters

Charles and Gay-Lussac were the main contributors to our understanding of the pressure-temperature law. However, ________ was the one who devised a gas thermometer for measuring the change in temperature that accompanies a proportional change in pressure.

Amontons

At the same pressure and temperature, equal volumes of different gases contain the same number of molecules.

Avogadro's Hypothesis

At a fixed temperature and pressure, the volume of a gas is directly proportional to the number of molecules in the gas. Defines which gas law?

Avogadro's Law

________ or _________ states that at the same pressure and temperature, equal volumes of different gases contain the same number of molecules or, in the case of a monoatomic gas, the same number of atoms.

Avogadro's hypothesis or Avogadro's principle

_______ relates the volume of the gas to the moles of gas present

Avogadro's law

6.023 x 10 ^23 is known as _______

Avogadro's number

______ law can Mathematically be written as P1V1 = P2V2.

Boyle's

_______ conclusion states that under the volume and pressure are inversely proportional to each other. If this relationship holds, then the product of the pressure and the volume will always be constant for a fixed amount of gas at a fixed temperature.

Boyle's

The volume of a fixed sample of gas at a constant temperature varies inversely with the applied pressure. Defines which gas law?

Boyle's Law

Pressurized cylinder-opened and slowly emptied so that the temp does not change, the volume of gas released from the cylinder can be explained by _______.

Boyle's law

To further illustrate _______, consider the two cylinders shown on this slide. Cylinder A contains a fixed volume of gas at a given pressure. As depicted in cylinder B, forcing the piston inward decreases the volume of the gas, while increasing the number of collisions and the overall pressure of the gas.

Boyle's law

We learned from _______ that the pressure of a gas is inversely proportional to its volume at constant temperature. As the volume of the container decreases, the number of collisions between the container and the gas particles increase, leading to a higher pressure.

Boyle's law

_______ relates the volume of a gas to its pressure

Boyle's law

Squeezing and Ambu Bag- raise pressure and decreases volume is an example of which gas law?

Boyle's law example of ambu bag under pressure

Cylinder of oxygen (a small volume of gas, under high pressure) will release into the atmosphere at about 625L, which is large volume under low pressure. This is an example of which gas law?

Boyle's law example of cylinder under pressure

Simple breathing (inspiration) when breathing spontaneously, intrapulmonary pressure falls and volume increases. (Expiration) Intrapulmonary pressure increases, and volume decreases. This is an example of which gas law?

Boyle's law example of inspiration/expiration

The volume of the gas in the left cylinder is 0.5 Liter at 200 Kelvins. Increasing the temperature of the gas to, say, 400 K, increases the kinetic energy of molecules and causes them to strike the piston with more force. This in turn causes the piston to expand until volume doubles and the pressure returns to its original value. This is an example of which gas law?

Charles' law example piston

The volume (V) of a gas at constant pressure (P) is directly proportional to the absolute temperature (T) defines which gas law?

Charles's Law

_______ states Volume is directly proportional to absolute temp. (K) at constant pressure; when temp increases... volume of gas increases

Charles's Law

Inflatable cuff of LMA expands when placed into auto-clave for sterilization is an example of which gas law?

Charles's Law example involving LMA cuff

According to ______, the volume of a gas is directly proportional to the absolute temperature at constant pressure.

Charles's law

_______ relates the volume of the gas to its temperature

Charles's law

As a mathematical equation, _______ is often written as either V T or V1/T1 = V2/T2.

Charles's law math equation

Ideal Gas Law was First described by _______

Clapeyron

Using the gas laws described thus far, ________ was able to derive a single gas law to show how the pressure, volume, temperature and moles of a gas are related to each other.

Clapeyron

The volume occupied by a fixed amount of gas is proportional to the absolute temperature divided by the pressure.

Combined Gas Laws

The total pressure (Ptotal) of a gaseous mixture is the sum of the partial pressures of the component gases. Defines which gas law?

Dalton's Law of Partial Pressures

_______ can be defined as the escape of gas molecules through a small hole

Effusion

Gas collisions are ______.

Elastic

The more particles there are in a gas sample, the more V will be needed, at constant P and T, to avoid increasing their collisions with the container. Thus, V increases as amount increases. which law?

Explaining Avogadro's Law (V n)

Gas pressure results from collisions between gas particles and the container. A decrease in V leads to more collisions and increased P. which law?

Explaining Boyle's Law (P 1/V)

Temperature is a measure of the average kinetic energy of a gas. The higher the T , the faster the gas particles move, and the more room they require. Thus, V increases with increasing T. which law?

Explaining Charles's Law (V T)

The total P of a fixed V of gas depends only on T and the total number of moles of gas. The pressure exerted by a specific kind of particle depends on the mole fraction of that kind of particle. which law?

Explaining Dalton's law (Ptot = P1 + P2 + ...)

(1) Molar mass of the gas, 2. Size of the hole, (2) Number of Molecules (3) Average Molecular Speed

Factors affecting Effusion

______ Can also be calculated using the ideal gas law

Gas Density

_______ (d) equals mass per unit volume (d = m/V)

Gas Density

d = _𝑷 𝒙 𝑴𝒐𝒍𝒂𝒓 𝑴𝒂𝒔𝒔_𝑹 𝑻_

Gas Density

_______ is Expressed in grams, number of molecules, or number of moles

Gas Quantity

This relationship between the quantity of gas and its volume was first tested by _______ and subsequently explained by Avogadro.

Gay-Lussac

The pressure (P) of a fixed volume (V) of gas varies proportionately with its absolute temperature (T). defines which gas law?

Gay-Lussac's Law

_______ explains the decrease in pressure, as temp in a constant volume cylinder decrease, the pressure of the gas in the cylinder decreases

Gay-Lussac's Law

The volumes of reactant gases at constant pressure and temperature are in ratios of small whole numbers. Discusses which gas law?

Gay-Lussac's Law of Combining Volumes

_________ which relates temperature and pressure

Gay-Lussac's law

The movement of gas particles through a small hole is which gas law?

Graham's Law of Effusion

PV = nRT, where R is the gas constant, and P, V, T and n are as previously defined. Although ideal gases don't exist, as long as the pressure on the gas isn't too ____ and the temperature isn't too ___, real gases approximate ideal behavior. This assumption allows us to use the ideal gas law for applications involving real gases.

High, low

_____ strictly obeys all the simple gas laws and has a molar volume of 22.4 L at STP

Ideal Gas

_____ how V of a gas is affected by changes in P, T, and n.

Ideal Gas Law

_________ Combines Boyle's law, Charles's law, and Avogadro's law into a single statement

Ideal Gas Law

PV = nRT

Ideal Gas Law equation

As a result of his work with balloons________ was one of the first scientists to show that the volume of a fixed amount of gas at constant pressure is proportional to its absolute temperature.

Jacques Charles

According to ________, the total pressure exerted by a mixture of gases is equal to the sum of the partial pressures exerted by the individual gases.

John Dalton

_________ published data to support Charles' law.

Joseph Gay-Lussac

The formula to convert K to C°

K= °C + 273

n is the number of moles or molecules of gas. V is the volume of the gas _𝑉1_𝑛1_ = _𝑉2_𝑛2_

Mathematical Statement of Avogadro's Law

Ptotal = P1 + P2 + á á á Pn. P1 and P2 = Partial pressures of gas 1 and gas 2, etc

Mathematical Statement of Dalton's Law

P _1_𝑉_ PV= constant, k P1V1= k and P2V2 = k P1V1 = P2V2

Mathematical statement of Boyle's Law

V T à _𝑉1_𝑇1_ = k à _𝑉2_𝑇2_= k à _𝑉1_𝑇1_= _𝑉2_𝑇2_ =

Mathematical statement of CharlesÕs Law

P T _𝑃1/𝑇1_ = _𝑃2/𝑇2_

Mathematical statement of Gay-Lussac's Law

Factors affecting Effusion (1) _____ of the gas, 2. Size of the ____, (2) ______ of Molecules (3) Average Molecular _____

Molar mass, hole, Number, Speed

Even when the temperature of the gas is held constant, increasing the _______ of gas in a container will lead to more collisions and higher pressure. To avoid this, the volume of the gas must increase concurrently with the moles of gas, as dictated by _______.

Moles, Avogadro's law

Properties Used to Characterize a Gas

Pressure (P) Temperature (T) Volume (V) Number of moles (n)

Gay-Lussac's Law (or ______ Law or _______ Law)

Pressure Law or Amontons' Law

if _______ is too high, and _______ too low, the forces of attraction between the gas particles may increase and the molecules can potentially transition from a gas to a liquid or solid.

Pressure, temperature

Using a J tube with a known volume of air in the sealed end, and a column of mercury in open end, ________ was able to show that, at constant temperature, as the column of Hg (and hence the pressure) increases, the volume of air in the closed end of the tube decreases.

Robert Boyle

Root-Mean-Square Speed (urms) of Gas Molecules u = ________, R= _______ J/(mol K)

Root mean speed, 8.314

Two moles of any gas will contain ______ this number of molecules.

Twice

Deviations of Real gases (2)A second assumption is that there are no attractive forces between particles. At high pressures, the particles are much closer together and the ________ cannot be ignored. Since molecules draw together somewhat, the volume is decreased for a given pressure (or the pressure is decreased for a given volume).

attractive forces

How a gas _______ is largely dependent of its pressure, temperature, volume, and the number of molecules making up the gas.

behaves

Boyle's Law, Charles's law, and Gay-Lussac's Law can be combined into one general law that relates pressure, volume, and temperature. It is known as the ________, and states that the volume occupied by a fixed amount of gas is proportional to the absolute temperature divided by the pressure.

combined gas law

Experiments have shown that any gas that meets the characteristics described earlier and is not near its ________, should conform in physical behavior to one of several gas laws.

condensation point

Gas molecules are in ______, ______ motion

constant, random motion

According to Boyle's Law, If the pressure that is applied to a gas is, say, P1 and the resulting volume is V1, increasing the pressure to P2 will _______ its volume to V2, but the pressure-volume product before and after these changes will remain the same.

decrease

If we decrease the number of gas molecules, the volume of the gas will also ______

decrease

full cylinder of gas is moved from the loading dock where the temp is 46 deg. C (summer) then to the OR of 20 deg. C, the pressure in the cylinder will ________

decrease

Pressure is _______ proportional to absolute temp (K); if volume is constant, when the temp of a gas in a container at a constant volume increase, pressure will also increase

directly

This is the premise of Avogadro's law which states that the volume of a gas, at a fixed temperature and pressure, is _______ proportional to the number of gas molecules

directly

There are no attractive or repulsive forces between the gas particles, so all collisions are _____

elastic

The rate of effusion is mainly affected by the molar mass of the molecules, with lighter molecules effusing ______

faster

Deviations of Real gases (1) For an ideal gas, the volume of the gas particles is negligible compared to the total gas volume at STP. At ________ where the volume of the molecules may be a significant proportion of the total volume, the volume of the gas particles is not negligible.

high pressures

For such an ________, the particles are very far apart, their forces of attraction or repulsion are less significant, and their size is negligible compared to the empty space between them.

ideal gas

If the pressure, temperature and molar mass of the gas are known, the density can be obtained using the formula shown here. If not, the density can be determined using the _______

ideal gas law

As a general rule, if we know the moles of gas in a system will the increase, the volume of the gas will also ______

increase

When a full cylinder of gas is moved from a loading dock with a temp of 0 degree C (winter) to the operating room with temp of 20 degree C; inside of that cylinder, the pressure will _______.

increase

Increasing the size of the hole, the number of molecules in the gas, and the speed of the molecules can _______ the rate of _______

increase the rate of effusion

The rate of effusion of a gas is ______ proportional to the square root of the molar mass (M) of the gas at constant temperature and pressure.

inversely

As a nitrous cylinder empties, the pressure in the tank decreases even if nitrous liquid is still present. The laws that explain this is the _________- why the temp of a cylinder of compressed gas decreases as the gas is released.

joule-Thompson effect

Increasing the temperature of the gas, increases its _________, its speed, and the number of collisions with the container. If the pressure of the gas is to remain constant while the temperature is increasing, the volume of the gas must increase in order to reduce the number of collisions and prevent the pressure from increasing.

kinetic energy

The atoms and molecules in a gas are always in a state of constant random motion. Under ideal conditions of low pressure and high temperature, these particles collide with each other and with the walls of the container, but without losing their ________.

kinetic energy

Deviations of Real gases results in the volume of a real gas is somewhat ______ than the ideal value

larger

If volume and temp are plotted, the line will pass through the origin where both the temperature and volume are zero. This temperature at which the volume of the gas changes to zero is called absolute zero. However, the gas will ______ before reaching absolute zero.

liquefy

The atoms and molecules in a gas are always in a state of constant random motion. Under ideal conditions of low _______ and high _______, these particles collide with each other and with the walls of the container, but without losing their kinetic energy.

low pressure and high temperature

Recall that the density (d) of a substance is obtained by dividing its ____ by its _______ (d = m/V).

mass by its volume

The _________ of each gas (χi) is equal to the moles of that component divided by the total number of moles

mole fraction

To find the ________ for a given gas, simply divide the moles of that component by the total moles.

mole fraction

Gases consist of small particles whose volume is ______ compared to the volume of the gas

negligible

Each gas in a mixture is governed by the ideal gas law. More importantly, each gas in a mixture exerts its own pressure (i.e., _______) on the container.

partial pressure

The _______ of each component (Pi) is equal to the mole fraction of that component (χ) times the total pressure (Ptotal)

partial pressure

if both the total pressure and the partial pressure are known, the mole fraction can be derived by dividing the ________ of the component by the total pressure of the gas.

partial pressure

The total pressure in a mixture of gases is equal to the sum of the pressures of the individual gases. The partial pressure if a gas is calculated by multiplying the ______ gas (*fractional concentration) times the ________.

percent gas, atmospheric pressure

Measurement of FRC- _________ is the device used to measure FRC

plethysmography

Since volume and temperature are _____________, doubling the absolute temperature, will double the volume, and a plot of the volume versus the absolute temperature of the gas gives a straight line similar to what is shown here.

proportional

Gay-Lussac's Law, the pressure law, or Amontons's Law also states that the pressure of a fixed volume of gas varies ________ with the absolute temperature. It can be expressed mathematically as either P T or P1/T1 = P2/T2.

proportionately

GAS Particles Are in constant __________. Undergo _________ with the container and with each other. Are very far apart. Experience negligible forces of ________. Have _______ compared to the empty space between. Expand and compress readily. Occupy more space and has lower density than _______ from which they are formed

random motion, elastic collisions, attraction/repulsion, negligible size, liquids

Gay-Lussac's law:

relates to Temperature and Pressure

Boyle's law:

relates to Volume and Pressure

Charles's law:

relates to Volume and Temperature

Avogadro's law:

relates to Volume and mole (n) of gas

Space between gas particles allows the particles in a gas to compress or expand more noticeably than for an equivalent amount of ______ or ______. This is underscored by the roughly 800-fold increase in volume when a liquid change to a gas.

solid or liquid

Average Kinetic Energy (KE) of Gas Molecules is Related to the _____ (v) and ________ (T) of the gas

speed, temperature

A plot of V versus T gives a ______ line

straight

The molecules in the sample show a range of kinetic energies, but the average KE depends only on the ________

temperature

Root-Mean-Square Speed Depends on ______ & _______, not the type of gas. Heavier molecules and lower temperatures lead to slower average speeds

temperature & molar mass

Graham's Law of effusion which states that the rate of effusion of a gas is inversely proportional to the square root of the molar mass of the gas, at constant _______ and _______

temperature and pressure

The partial pressure of each component in a gaseous mixture is dependent on ________ of that component.

the mole fraction

one liter of oxygen gas and one liter of nitrogen gas, at the same temperature and pressure, contain ________ of molecules. This is true of the molecules in all gases, regardless to their size and their mass.

the same number

Once the mole fraction of a given component is determined, the partial pressure of that component can then be determined by multiplying its mole fraction by the _______ of the mixture.

total pressure

In some ways, Avogadro's law is the direct outcome of Avogadro's principle. If equal volumes of any two gases at the same pressure and temperature contain the same number of molecules, then two volumes of one gas should contain ______ the number of molecules as one volume of a second gas.

twice

Ideal gas law can also be referred to as the ______ gas law

universal

Two modifications can be made to the ideal gas law to deal with these deviations from ideal behavior. The resulting "corrected" gas law uses two correction terms, a and b, and is called the ________

van der Waals equation

Since the volume of a gas at constant pressure and temperature is proportional to the moles of gas, then the ______-______ relationship in a chemical reaction should work the same way as the mole-mole relationship in a chemical equation.

volume-volume