Unformatted text preview: Using the Ideal Gas Law The balloon used by Jacques Charles in his historic flight in 1783 was filled with about 2626 g of H2. If the temperature of the gas was 23°C and its pressure was 750 mm Hg, what was the volume of the balloon?
Slide 1 of 26 CHM 25 SP07 LU The General Gas Equation
R= P1V1 PV = 22 n 1T 1 n 2T 2 If we hold the amount and volume constant: P1 T1 = P2 T2 Slide 2 of 26 CHM 25 SP07 LU EXAMPLE
Helium-filled balloons are used to carry scientific instruments high into the atmosphere. Suppose a balloon is launched when the temperature is 22.5 °C and the barometric pressure is 754 mm Hg. If the balloon’ volume s is 4.19 x 103 L (and no helium escapes), what will the volume be at a height of 20 miles, where the pressure is 76.0 mm Hg and the temperature is -33.0°C?
Slide 3 of 26 CHM 25 SP07 LU Applications of the Ideal Gas Equation Molar Mass Determination PV = nRT PV = M=
Slide 4 of 26 and m RT M m RT PV n= m M CHM 25 SP07 LU Gas Densities
PV = nRT and PV = d= m m , n= M V EXAMPLE
You are trying to determine, by experiment, the empirical formula of a gaseous compound to replace chlorofluorocarbons in air conditioners. Your results give an empirical formula of CHF2. Now you need the molar mass of the compound to find the molecular formula. You conduct another experiment and find that a 0.100 g sample of the compound exerts a pressure of 75.00 mm Hg in a 256 mL container at 22.3°C. What is the molar mass of the compound? What is its molecular formula?
Slide 6 of 26 CHM 25 SP07 LU m RT M m MP =d= V RT Slide 5 of 26 CHM 25 SP07 LU CHM 25 SP07 LU 1 Gases in Chemical Reactions Stoichiometric factors relate gas quantities to quantities of other reactants or products. Ideal gas equation relates the amount of a gas to volume, temperature and pressure. Law of combining volumes can be developed using the gas law. EXAMPLE 2 H2O2(liq) → 2 H2O(g) + O2(g)
Decompose 1.1 g of H2O2 in a flask with a volume of 2.50 L. What is the pressure of O2 at 25 °C? Of H2O?
Bombardier beetle uses decomposition of hydrogen peroxide to defend itself. Slide 7 of 26 CHM 25 SP07 LU Slide 8 of 26 CHM 25 SP07 LU Dalton’ Law of Partial Pressures s
2 H2O2(liq) ---> 2 H2O(g) + O2(g) 0.32 atm 0.16 atm Dalton’ Law of Partial Pressure s What is the total pressure in the flask? Ptotal in gas mixture = PA + PB + ...
Therefore, Ptotal = P(H2O) + P(O2) = 0.48 atm Dalton’ Law: total P is sum of s PARTIAL pressures.
Slide 9 of 26 CHM 25 SP07 LU Slide 10 of 26 John Dalton 1766-1844 CHM 25 SP07 LU Kinetic Molecular Theory Particles are point masses in constant, random, straight line motion. Particles are separated by great distances. Collisions are rapid and elastic. No force between particles. Total energy remains constant.
Slide 11 of 26 CHM 25 SP07 LU Kinetic Molecular Theory
Because we assume molecules are in motion, they have a kinetic energy. KE = (1/2)(mass)(speed)2
At the same T, all gases have At the same T, all gases have the same average KE. the same average KE.
As T goes up for a gas, KE also As T goes up for a gas, KE also increases — and so does speed. increases — and so does speed.
Slide 12 of 26 CHM 25 SP07 LU CHM 25 SP07 LU 2 Kinetic Molecular Theory
Maxwell’ equation s where u is the speed and M is the molar mass. speed INCREASES with T speed DECREASES with M
Slide 13 of 26 Distribution of Gas Molecule Speeds
Boltzmann plots Named for Ludwig Boltzmann doubted the existence of atoms. This played a role in his suicide in 1906. u2 3RT M root mean square speed CHM 25 SP07 LU Slide 14 of 26 CHM 25 SP07 LU Velocity of Gas Molecules
Molecules of a given gas have a range of speeds. Velocity of Gas Molecules
Average velocity decreases with increasing mass. Slide 15 of 26 CHM 25 SP07 LU Slide 16 of 26 CHM 25 SP07 LU GAS DIFFUSION AND EFFUSION GAS EFFUSION DIFFUSION is the gradual mixing of molecules of different gases. EFFUSION is the movement of molecules through a small hole into an empty container. Slide 17 of 26 CHM 25 SP07 LU Slide 18 of 26 CHM 25 SP07 LU CHM 25 SP07 LU 3 GAS DIFFUSION AND EFFUSION Graham’ Law s
Graham’ law governs s effusion and diffusion of gas molecules. Molecules effuse thru holes in a rubber balloon, for example, at a rate (= moles/time) that is proportional to T inversely proportional to M. Therefore, He effuses more rapidly than O2 at same T.
Slide 19 of 26 He Rate for A Rate for B M of B M of A
Thomas Graham, 1805-1869. Professor in Glasgow and London. Rate of effusion is Rate of effusion is inversely proportional inversely proportional to its molar mass. to its molar mass.
CHM 25 SP07 LU Slide 20 of 26 CHM 25 SP07 LU Gas Diffusion
relation of mass to rate of diffusion relation of mass to rate of diffusion Using KMT to Understand Gas Laws Recall that KMT assumptions are Gases consist of molecules in constant, random motion. P arises from collisions with container walls. No attractive or repulsive forces between molecules. Collisions elastic. Volume of molecules is negligible.
Slide 22 of 26 CHM 25 SP07 LU HCl and NH33 diffuse HCl and NH diffuse from opposite ends of from opposite ends of tube. tube. Gases meet to form Gases meet to form NH44Cl NH Cl HCl heavier than NH33 HCl heavier than NH Therefore, NH44Cl forms Therefore, NH Cl forms closer to HCl end of tube. closer to HCl end of tube.
Slide 21 of 26 CHM 25 SP07 LU Deviations from Ideal Gas Law Real molecules have Deviations from Ideal Gas Law
Account for volume of molecules and intermolecular forces with volume. There are VAN DER WAALS’ s EQUATION.
Measured P Measured V = V(ideal)
2 intermolecular forces. Otherwise a gas could not become a liquid.
Slide 23 of 26 CHM 25 SP07 LU ( P na + ----2 V ) V - nb nRT vol. correction intermol. forces
Slide 24 of 26 J. van der Waals, 1837-1923, Professor of Physics, Amsterdam. Nobel Prize 1910.
CHM 25 SP07 LU CHM 25 SP07 LU 4 Deviations from Ideal Gas Law
Measured P P + n2 a ----V2 Measured V = V(ideal) V nb nRT vol. correction intermol. forces Cl2 gas has a = 6.49, b = 0.0562 For 8.0 mol Cl2 in a 4.0 L tank at 27 oC. P (ideal) = nRT/V = 49.3 atm
Slide 25 of 26 P (van der Waals) = 29.5 atm CHM 25 SP07 LU CHM 25 SP07 LU 5 ...
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