you can predict how pressure, volume, temperature, and number of gas particles are related to each...
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The Gas Laws• You can predict how pressure, volume,
temperature, and number of gas particles are related to each other based on the molecular model of a gas.
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The Gas Laws• The Kinetic Molecular Theory• 1.) Gas particles are in constant motion and move in
a straight line until they hit another gas particle or the side of the container.
• 2.) There are not attractive or repulsive forces between the gas particles.
• 3.) The volume of the actual gas particle is assumed to be zero, since it is insignificant to the volume of the whole sample of gas.
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The Gas Laws• The Kinetic Molecular Theory (cont.)• 4.) The temperature is an indirect measure the
average kinetic energy of all the gas particles in the sample.
Kinetic Energy = ½ (mass) x (velocity)2
• 5.) There is no exchange of energy when 2 gas particles collide, the collision is totally elastic.
(Just like when two billiard balls collide.)
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The Gas Laws• Pressure
• Pressure = Force Applied / Area (P = F / A)
• When the gas molecules collide with the inside wall of the container, it exerts a force over an area. Therefore there is always an internal pressure on a gas.
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The Gas Laws• Measuring Pressure• Pressure can be measured using a device
called a manometer.
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The Gas Laws• Measuring Pressure• Atmospheric Pressure can be measured using
a device called a barometer.
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The Gas Laws• Units for Measuring Pressure• Pascal (Pa) – Metric System unit for pressure• Atmosphere (atm)• Pounds per square inch (psi)• Torricelli (torr)• Millimeter of Mercury (mm Hg)
1 atm = 101,300 Pa = 101.3 kPa = 14.7 psi = 760 torr = 760 mm Hg
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The Gas Laws• Pressure Conversions
1 atm = 101,300 Pa = 101.3 kPa = 14.7 psi = 760 torr = 760 mm Hg
• Convert 0.75 atm into mm Hg.
• Convert 32.0 psi into kPa.
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The Gas Laws• Robert Boyle (1627 – 1691)• An English scientist whose work revolved around
trying to discover the relationship between the pressure and volume of a gas.
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The Gas Laws• Boyle’s Law• If the pressure exerted on a gas increases, the
volume of the gas will proportionally decrease.
• What is the relationshipbetween the pressure exerted ona gas and its volume?
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The Gas Laws• Boyle’s Law• The product of the pressure and volume of a gas
must always be a constant as long as the temperature and # of moles of gas remain constant.
Pressure x Volume = constant
Pressure(initial) x Volume(initial) = Pressure(final) x Volume (final)
P1V1 = P2V2
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The Gas Laws• Boyle’s Law• Initially, a 3.0 L expandable tank of gas is under a
pressure of 13 atm. What would be the volume of the tank if the pressure inside the tank is reduced to 5.0 atm. The temperature and # of moles of gas remain constant.
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The Gas Laws• Jacques Charles (1746 – 1823)• A French scientist, inventor, and avid balloonist.• He was interested in discovering the affect that the
temperature had on the volume of a gas.
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The Gas Laws• Charles’ Law
• The volume of a gas divided by its Kelvin temperature must remain constant. As long as the pressure and # moles of gas does not change.
Volume = constant Temperature
Volume(initial) = Volume(final)
Temperature(initial) Temperature(final)
V1 = V2
T1 T2
Temperature must be in Kelvins!
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The Gas Laws• Charles’ Law
• This is how absolute zero was determined. Is it possible?
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The Gas Laws• Charles’ Law Problem• A balloon has a volume of 1.0 L at 23.0°C. What is
the volume of the balloon if the temperature decreases to -10.0°C? Assume that the pressure and # of moles of gas particles remains constant.
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The Gas Laws• Combined Gas Law (Boyle’s and Charles’ Law)
P1.V1 = P2.V2
T1 T2
• The number of moles of gas must remain constant.
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The Gas Laws• Combined Gas Law (Boyle’s and Charles’ Law)
• A 2.0 L balloon initially at Standard Temperature and Pressure (STP) is heated to 100.0 °C and pressurized to 1.5 atmospheres. Calculate the new volume of the balloon.
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The Gas Laws• Joseph Louis Gay-Lussac (1778 – 1850)• French Chemist and Physicist who discovered th
relationship between the pressure and the temperature of a gas.
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The Gas Laws• Joseph Louis Gay-Lussac (1778 – 1850)• Gay-Lussac’s Law
P1 = P2
T1 T2
• The volume and number of moles of gas must remain constant.
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The Gas Laws• Gay-Lussac’s Law
• Initially, a sample of gas has a temperature of 10.0°C. It is then pressurized from 740. mm Hg to 800. mm Hg. What will be the new temperature of the gas if the volume and number of moles of gas remain constant?
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The Gas Laws• The Ideal Gas Law
• The only gas law that incorporates moles into it.
PV = nRTP = Pressure (atm or kPa)V = Volume (L)n = # of moles of gas particlesR = The Gas Law Constant (0.0821 L.atm)
mol.KT = Temperature (K)
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The Gas Laws• The Ideal Gas Law
• What volume would 44.01 grams of CO2 occupy at 0.00°C and 1.00 atmosphere?
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The Gas Laws• The Ideal Gas Law
• What is pressure of 10.0 grams of NH3 in a 5.0 L tank at 50.0°C?
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The Gas Laws• Using the Ideal Gas Law to Relate Molar Mass
and Density of Gas;
We can rearrange the Ideal Gas Law to get the following equation -
P.V = nRT ==== n = P V RT
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The Gas Laws• Using the Ideal Gas Law to Relate Molar Mass
and Density of Gas;
• If we multiply both sides of the Ideal Gas Law by molar mass, we have the following –
(molar mass) n = P (molar mass) V RT
Mass = P (molar mass)Volume RT
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The Gas Laws• Using the Ideal Gas Law to Relate Molar Mass
and Density of Gas;
Mass = P (molar mass)Volume RT
Density = P (molar mass) RT
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The Gas Laws• Using the Ideal Gas Law to Relate Molar Mass
and Density of Gas;
Density = P (molar mass) RT
Calculate the density of nitrogen gas at a pressure of 1.5 atm and a temperature of -10.0°C.
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The Gas Laws• Using the Ideal Gas Law to Relate Molar Mass
and Density of Gas;
Density = P (molar mass) RT
Calculate the molar mass of a gas that has a density of 0.029 g / L when it is at a pressure of 800. kPa and 25.0°C.
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The Gas Laws• Using the Ideal Gas Law with Gas Stoichiometry;
How many grams of hydrogen gas is needed to fill a 100.0 L vessel with ammonia gas at 1.2 atm at a temperature of -25.0°C?
N2(g) + 3H2(g) 2NH3(g)
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The Gas Laws• Using the Ideal Gas Law with Gas Stoichiometry;
Automobile airbags are inflated with nitrogen gas using the following chemical reaction;
2NaN3(s) 2Na(s) + 3N2(g)
How many grams of NaN3 must decompose in order to fill a 40.0 L airbag with nitrogen gas at 30.0°C and 1.0 atm?
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The Gas Laws• John Dalton (1766-1844)• What did he not do?
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The Gas Laws• Dalton’s Law of Partial Pressures
• The partial pressure (pgas X) of a gas is the pressure that the gas exerts when it is part of a mixture of gases.
• Right now, the room that we are sitting in contains nitrogen gas, oxygen gas, water vapor, and trace amount of other gases.
0.21 atm O2 + 0.78 atm N2 + 0.05 atm CO2 +
0.05atm trace gases = 1.0 atm (atmospheric pressure)
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The Gas Laws• Dalton’s Law of Partial Pressures
• The total pressure of a mixture of gases is equal to the sum of all of the partial pressures of the gases that make up the gas mixture.
p gas 1 + p gas 2 + p gas 3 + ……… = P total
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The Gas Laws• Graham’s Law of Effusion
• Grahams Law Describes the relative speed (velocity) at which gas particles will move, or diffuse.
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The Gas Laws• Graham’s Law of Effusion
• Effusion – The movement of a gas molecule through a small hole so its velocity may be measured.
• Diffusion – The movement of gas particles from an area of high concentration to an area of low concentration.
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The Gas Laws• Graham’s Law of Effusion
• What is diffusion?
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The Gas Laws• Graham’s Law of Effusion
• A heavier gas particle will travel slower than a lighter gas particle.
• KE = ½ mass x velocity2
• If the kinetic energy is the same for a heavy and a light gas particle, then the velocity of the heavier one will be less than the velocity of the lighter one.
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The Gas Laws• Graham’s Law of Effusion
• Ammonia and hydrogen chloride gas will form the white precipitate ammonium chloride;
NH3(g) + HCl(g) NH4Cl(s)
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The Gas Laws• Graham’s Law of Effusion
• Ammonia and hydrogen chloride gas will form the white precipitate ammonium chloride;
NH3(g) + HCl(g) NH4Cl(s)
Which end contains theammonia?
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The Gas Laws• Graham’s Law of Effusion
• Which molecule will diffuse faster, H2 or O2? How many times faster will the ‘faster’ molecule diffuse compared to the slower one?