chapter 10
partial pressure
(Pn) -The pressure due to any individual component in a gas mixture is its ... -can calculate ... from the ideal gas law by assuming that each gas component acts independently .... Pn = n RT/V -fro a multicomponent gas mixture... Pa =naRT/V; Pb =nbRT/V; Pc =ncRT/V Ptotal =Pa +Pb +Pc +....
gases behave ideally when these 2 things are true
(a) the volume of the gas particles is small compared to the space between them; and (b) the forces between the gas particles are not significant. At STP, these assumptions are valid for most common gases. However, these assumptions break down at higher pressures or lower temperatures.
HW
-As the temperature of a gas sample increases, the distribution of molecular velocities shifts toward a higher velocity and becomes less sharply peaked, because a higher temperature results in higher average velocities, which leads to a broadening of the velocity range. Since the peak for the curve corresponding to temperature T1T1 is sharper and is located at the mark of 1000 m/sm/s and, for the curve corresponding to temperature T2T2, the peak is wider and located beyond the mark of 1000 m/sm/s, temperature T2T2 is higher. -Since as the temp of a gas sample increases, the velocity distribution of the molecules shifts toward a HIGHER velocity and becomes less sharply peaked Temp 2 is greater. -The kinetic energy of a gas depends only on its temperature, so all of these atoms have the same kinetic energy. -ideal gases behave ideally at STP, -At very high pressures, a gas will occupy a larger volume than predicted by the ideal gas law. -At high pressures the volume of gas particles becomes important, and at low temperatures the effect of intermolecular forces becomes significant. this is why the behavior of a real gas deviates from an ideal behavior
HW
-kinetic molecular theory: The collisions of particles with one another is completely elastic. -Although the velocity tails of each atom have different lengths, the average length of the tails on the argon atoms (blue dots) are longer than the average length of the tails on the xenon atoms (red dots). Because the argon atoms are lighter, they must on average move faster than the xenon atoms to have the same kinetic energy. -if all Three identical flasks contain three different gases at standard temperature and pressure. then they All contain same number of molecules. -temperature and pressure at STP. is 0°C and 1.00 atm
HW
-molecules of real gases are attracted to each other. -the pressure of a real gas is due to collisions with the container. -nonideal gas behavior is described by the Van der Waals Equation. -the pressure of a real gas at low temperatures is lower than for ideal gases.
newtons second law
-the force (F) associated with an individual collision is given by F = ma, where m is the mass of the particle and a is its acceleration as it changes its direction of travel due to the collision
kinetic molecular theory
1. small: molecules are very very small and on avg. very far apart 2. random motion: molecules move in constant straight line motion in diff. directions 3. Kintetic energy: KE=KT (K is constant) increase in temp= increase in KE 4. collisions: occur often and are elastic so there is no loss of energy when molecules collide. 5. NOT REALLY TRUE: no interparticle forces! no attractions nor repulsions between molecules
mean free path
A molecule in a volume of gas follows a haphazard path, involving many collisions with other molecules. -the average distance between collisions is the mean free path -at room temperature and atmospheric pressure, a molecule in the air experiences several billion collisions per second. -The average distance that a molecule travels between collisions is its mean free path. -Mean free path increases with decreasing pressure.
intermolecular forces
At low temperatures, the pressure of xenon is less than an ideal gas exerts because interactions among xenon molecules reduce the number of collisions with the walls of the container. -the ideal gas law predicts a pressure that is too large at low temperatures. Van der Waals suggested a small correction factor that accounts for the intermolecular forces between gas particles: Ideal behavior P= nRT/V Corrected for intermolecular forces P=nRT/V- a(n/V)squared rearranged corrected equation P+ a(n/V)squared= nRT/V a is a constant -the correction factor increases as n/V (the number of moles of particles per unit volume) increases because a greater concentration of particles makes it more likely that they will interact with one another.
Gay-Lussac's Law
Gay-Lussac's Law Because n and V are constant and R is always a constant: P = (constant) * T -This relationship between pressure and temperature is known as Gay-Lussac's law. -As the temperature of a fixed amount of gas in a fixed volume increases, the pressure increases. -In an aerosol can, this pressure increase can blow the can apart, which is why aerosol cans should not be heated or incinerated. They might explode.
temperature and molecular velocities
In a gas mixture at a given temperature, lighter particles travel faster (on average) than heavier ones. root mean square velocity... is a kind of avg. velocity the expression for mean square velocity as a function of temperature is the following: Urms= sqrt(3RT/M) when M is avogadros number* mass M is molar mass in kg/mol R=8.314 J/mol*K the lighter molecules move much faster -Lighter particles travel faster on average than heavier ones. -Higher temperature results in higher average velocities. -As the temperature increases, the root mean square velocity increases and the distribution becomes broader.
kinetic energy equation
KE=1/2mv^2 kinetic energy of a particle depends on its mass and velocity according to the equation -The only way for particles of different masses to have the same kinetic energy is for them to have different velocities,
hypoxia
Low oxygen levels produce a physiological condition called ... or oxygen starvation -severe ... occurs when (PO2) drops below 0.1 atm, may result in unconsciousness or even death.
Pressure
Low pressure is unstable weather High pressure is clear weather the fewer the gas particles in a container, the lower the force per unit area and the lower the pressure -pressure decreases with increasing altitude -pressue exerted by gas is an important property. force per unit area -collisons of molecules with the walls of the container cause pressure psi stand for pound per square area common units... atm(atmosphere) torr and mmHg (which are the same) Pascal (Pa) newton per square meter N/m2 at sea level 1 atm=760 torr= 760 mmHg= 101,325 Pa=14.7 psi= 29.92 in Hg bar is 1atm= 1.013 bar
molar volumes of real gasses
Molar Volumes of Real Gases The molar volumes of several gases at STP are close to 22.414 L, indicating that their departures from ideal behavior are small.
daltons law of partial pressures
Ptotal =Pa +Pb +Pc +... Ptotal is the total pressure and Pa, Pb, Pc, ... , are the partial pressures of the components. -mole fraction (xa): xa = na/ ntotal Pa = XaPtotal PN2 = 0.78 * 1.00 atm = 0.78 atm partial pressure of oxygen in air at 1.00 atm is 0.21 atm Ptotal = PN2 + PO2 + PAr Ptotal = 0.78 atm + 0.21 atm + 0.01 atm = 1.00 atm when using this law to solve problems you also want to use the ideal gas law
Stoichiometry
Stoichiometry mass A-> amount A (in moles) -> amount B (in moles) -> mass B so... P,V,T, of gas A-> amount A (in moles) -> amount B (in moles) -> P,V,T of gas B Molar volume and stoichiometry 1mol= 22.4 L (ideal gas at STP)
kinetic molecular theory
The behavior of gases can be explained (and in fact predicted) by a model called ... -The core of this model is that gases are composed of particles in constant motion. -Matter is particulate, and its behavior can be understood in terms of particles.
finite volume
The finite volume of gas particles—that is, their actual size—becomes important at high pressure because the volume of the particles themselves occupies a significant portion of the total gas volume -As a gas is compressed, the gas particles themselves begin to occupy a significant portion of the total gas volume, leading to deviations from ideal behavior. -As the pressure increases, particles occupy a larger portion of volume.
vapor pressure
The partial pressure of water in the mixture, which we call its VP, depends on temperature -Vapor pressure increases with increasing temperature because higher temperatures cause more water molecules to evaporate.
diffusion
The process by which gas molecules spread out in response to a concentration gradient is ..., and even though the particles undergo many collisions, the root mean square velocity still influences the rate of diffusion. -Heavier molecules diffuse more slowly than lighter ones, so the first molecules you smell from a perfume mixture (in a room with no air currents) are the lighter ones.
the ideal gas law
V ∝ 1/P (Boyles law) V=nRT/P= Boyles law because constant n and T V ∝ T (Charles law) V=nRT/P= Charles law because constnat n and p V ∝ n (Avogadros law) V=nRT/P= avogadros law because constant P and T Combining these three expressions, we get: V ∝ nT/P -volume of a gas is directly proportional to the number of moles of gas and to the temperature of the gas but is inversely proportional to the pressure of the gas -R, a proportionality constant called the ideal gas constant: V= RnT/ P rearranging PV = nRT PV = nRT is the ideal has law equation. R is the ideal gas constant R = 0.08206 L*atm/mol*K always use these units • pressure (P) in atm, volume (V) in L, moles (n) in mol, temperature (T) in K
avogadros law
Volume and Amount (in moles) assumes constant temperature and constant pressure and is independent of the nature of the gas. -kinetic molecular theory, when we increase the number of particles in a gas sample, the greater number of particles occupy a greater volume (at constant pressure and temperature). -Avogadro's Law: As amount of gas increases, volume increases. -relationship is linear -Avogadro's law: V ∝ n (constant T and P) -expressed as V1/n1= V2/n2 n=number of moles in the gas
ideal gas law and kinetic molecular theory
We can get the complete ideal gas law postulate 2 of the kinetic molecular theory which states that the average kinetic energy (1/2mv2) is proportional to the temperature in Kelvins (T) -the kinetic molecular theory (a model for how gases behave) predicts behavior that is consistent with our observations and measurements of gases- the theory agrees with the experiments. -PV=nRT
nitrogen narcosis
When PN2 increases beyond about 4 atm, a condition called ... or rapture of the deep results.
oxygen toxicity
When PO2 increases beyond 1.4 atm, the increased oxygen concentration in body tis- sues causes a condition called ... that results in muscle twitching, tunnel vision, and convulsions.
kinetic molecular theory
a gas is a collection of particles (either molecules or atoms, depending on the gas) in constant motion -1. The size of a particle is negligibly small. the gas particles themselves occupy no volume, even though they have mass. justified because, under normal pressures, the space between atoms or molecules in a gas is very large compared to the size of the atoms or molecule themselves. -2. The average kinetic energy of a particle is proportional to the temperature in kelvins. motion of atoms or molecules in a gas is due to thermal energy, which distributes itself among the particles in the gas. the higher the temperature, the faster the overall motion, and the greater the average kinetic energy. kinetic energy- not velocity- is proportional to temp. -3. The collision of one particle with another (or with the walls of its container) is completely elastic. when two particles collide, they may exchange energy, but there is no overall loss of energy. When two billiard balls collide, the collision is elastic—the total kinetic energy of the colliding bodies is the same before and after the collision. in inelastic collision the KE dissipates in form of heat during collision.
manometer
a way to measure pressure in the laboratory A ... measures the pressure exerted by a sample of gas Height difference (h) indicates pressure of gas relative to atmospheric pressure. is a U shaped tube containing a dense liquid, usually mercury one end of the tube is open to atmospheric pressure and the other is attached to a flask containing a gas sample. -If the pressure of the sample is greater than atmospheric pressure, the mercury level on the left side of the tube is h higher than the level on the right -If the pressure of the sample is less than atmospheric pressure, the mercury level on the left side is lower than the level on the right. -cant use this alone you also need a barometer
intermolecular forces
are attractions between the atoms or molecules that compose any substance. -do not matter much at low pressure, They also do not matter much at high temperatures, -At lower temperatures, however, the collisions occur with less kinetic energy, and weak attractions can affect the collisions. -Think of bollard balls with a sticky substance, when moving fast they are unaffected but when moving slow they can stick. The effect of these weak attractions between particles is a decrease in the number of collisions with the surfaces of the container, and a corresponding decrease in the pressure compared to that of an ideal gas -
our lungs breathe oxygen at what pressure?
at a partial pressure of PO2 = 0.21 atm. -The partial pressure of oxygen in air at sea level is 0.21 atm. Partial pressures of oxygen below 0.1 atm and above 1.4 atm are dangerous to humans. -When a diver breathes compressed air, the abnormally high partial pressure of oxygen in the lungs leads to an elevated concentration of oxygen in body tissues.
the effect of particle volume
at pressures, 1 mol of argon occupies a larger volume than 1 mol of an ideal gas because of the volume of the argon atoms themselves. (This example was chosen to minimize the effects of intermolecular forces, which are very small in argon at 500 K, thereby isolating the effect of particle volume.) -NONideal behavior: the effect of particle volume -At high pressure, volume is higher than predicted.
simple gas laws
describe the relationships between pairs of these properties. For example, one simple gas law describes how volume varies with pressure at constant temperature and amount of gas; another law describes how volume varies with temperature at constant pressure and amount of gas.
real gas
for an ideal gas PV/RT=n so one mol of ideal gas is equal to q for real gases however, PV/RT deviates from 1 but the deviations are uniform. For 1 mol of an ideal gas, PV,RT is equal to 1.The combined effects of the volume of gas particles and the interactions among them cause each real gas to deviate from ideal behavior in a slightly different way. These curves were calculated at a temperature of 500 K.
Pressure
is the force exerted per unit area by gas particles as they strike the surfaces around them -collisions create .... -... is lower at higher elevations -The result of the constant collisions between the atoms or molecules in a gas and the surfaces around them is ... ? =Force/ Area
mmhg
millimeter of mercury originates from how pressure is measured with a barometer mercury is very dense often referred as TORR, Torricelli invented the barometer
van der waals
modified the ideal gas equation to fit the behavior of real gases. From the graph for argon in, we can see that the ideal gas law predicts a volume that is too small. Van der Waals suggested a small correction factor that accounts for the volume of the gas particles themselves: Ideal behavior V=nRT/P Corrected for volume of gas particles V= nRT/P+ nb Rearranged corrected equation (V-nb)= nRT/P The correction adds the quantity nb to the volume, where n is the number of moles and b is a constant that depends on the gas
molar mass of gas
molar mass= mass(m)/ moles (n)
molar volume
molar volume at standard temperature and pressure -volume occupied by one mole of a substance is its molar volume -For gases, we often specify the molar volume under conditions known as standard temperature (T = 0 °C or 273 K) and pressure (P = 1.00 atm), abbreviated as STP. -the molar volume of an ideal gas at STP is 22.4 L. One mole of any gas occupies approximately 22.4 L at standard temperature (273 K) and pressure (1.0 atm).
the combined gas law
putting Boyles and Charles law together assuming that number of moles is constant, but P,V, and T can change P1/V1=P2/V2 ---- ------ T1. T2
grahams law of effusion
rateA/rateB=sqrt(MB/MA) M=molar mass rateA and rateB are the effusion rates of gases A and B and MA and MB are their molar masses. explains, in part, why helium balloons only float for a day or so. Because helium has such a low molar mass, it escapes from the balloon quite quickly. A balloon filled with air, by contrast, remains inflated longer because the gas particles within it have a higher average molar mass.
density of a gas
the density of a gas is: density = molar mass/ molar volume, using 22.4 L as the molar volume. the density of a gas is directly proportional to its molar mass. The greater the molar mass of a gas, the more dense the gas. a gas with a molar mass lower than that of air tends to rise in the air. d = PM/ RT molar mass (M) -density increases with increasing molar mass -density decreases with increasing temperature. -convert to atm, keep temp in Kelvins
kinetic molecular theory
the particles in a gas mixture have negligible size and they do not interact. -each of the components in an ideal gas mixture acts independently of the others. -According to kinetic molecular theory, the only property that distinguishes one type of particle from another is its mass -particles of different masses have the same average kinetic energy at a given temperature. -the average kinetic energy is proportional to the temperature in Kelvins
effusion
the process by which a gas escapes from a container into a vacuum through a small hole -Effusion is the escape of a gas from a container into a vacuum through a small hole. -heavier molecules effuse more slowly than lighter ones -the rate of effusion is also related to root mean square velocity- heavier molecules effuse more slowly than lighter ones -the rate of effusion-the amount of gas that effuses in a given time- is inversely proportional to the square root of the molar ass of the gas rate ∝ 1/sqrt(M=molar mass)
van der waals
this describes a non ideal gas behavior [P + a(n/V)2] * [V - nb] = nRT this equation has the correction for intermolecular forces and correction for particle volume. and we can use it to calculate the properties of a gas under nonideal conditions.
when calculating mole fraction and partial pressure...
use xa=na/ntotal (mole fraction definition) PtotalV=ntotalRT (ideal gas law) Pa=XaPtotal
Boyles law
volume and pressure relates the volume of a sample of gas to its pressure at constant temperature -As volume decreases, pressure increases. -used a J tube to measure the volume of a sample of gas at different pressures. Added mercury compresses gas and increases pressure. -Boyle's Law: As pressure increases, volume decreases. at constant temperature and amount of gas. Boyle's law: V ∝ 1/P (constant T and n) V is a constant number then V = (constant) * 1/P or V = constant/P PV = constant P1V1 = constant = P2V2 kinetic molecular theory, if we decrease the volume of a gas, we force the gas particles to occupy a smaller space. -inverse relationship
Charles law
volume and temperature relates the volume of a gas to its temperature at constant pressure. -kinetic molecular theory, when we increase the temperature of a gas, the average kinetic energy, and therefore the average speed, of the particles increases. AKA the volume of gas increases with increasing temperature -faster moving particles collectively occupy more space, resulting in a greater volume -As temperature increases, volume increases. -Charles's Law. As temperature increases, volume increases. The volume of a fixed amount of gas at a constant pressure increases linearly with increasing temperature in kelvins. -linearly related (straight line) -0 K as absolute zero—colder temperatures do not exist. Charles's law: V ∝ T (constant P and n) assume content pressure and constant amount of gas. -when air is heated its volume increases resulting in a lower density. this is why A hot-air balloon floats because the hot air within the balloon is less dense than the surrounding cold air. the gas fills a hot air ballon is warmed with a burner, increasing its volume and lowering its density and coasting it to float in colder denser surrounding air. -SinceV ∝ T, then V = constant * T, V/T= constant so we can say V1/T1= constant= V2/T2 TEMPERATURE ALWAYS IN KELVINS 273.15 K
collecting gas over water
when we collect the gaseous product of a chemical reaction over water, the product molecules (in this case H2) are mixed with water molecules. The pressure of those water molecules is equal to the vapor pressure of water at that temperature. The partial pressure of the product is the total pressure minus the partial pressure of water.