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Ppt 17b, Continuation of Gases & Gas Laws . Individual Gas Laws Combine to Form the Ideal Gas Law . Ideal Gas Law Problems-I Find one variable if the other three are known (“one state” problem) Problems in which the state of a gas changes (“two state” problem).
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Ppt 17b, Continuation of Gases & Gas Laws • Individual Gas Laws Combine to Form the Ideal Gas Law. • Ideal Gas Law Problems-I • Find one variable if the other three are known (“one state” problem) • Problems in which the state of a gas changes (“two state” problem). • Density of Gases Ideas & Calculations • Can use Ideal Gas Law here (or memorize variant) Ppt17b
Important Comment • In all previous laws, the proportionality constant, k , is not a fundamental constant of nature; it would depend on the conditions [the values of the other variables being held constant] Ppt17b
The Ideal Gas Law • Ideal gases obey an equation incorporating the laws of Charles, Boyle, and Avogadro: • The gas constant R = 0.08206 L·atm·K–1·mol–1 • STP conditions are 273.15 K and 1 atm pressure • 1 mole of an ideal gas occupies 22.41 Lat STP(molar volume = V of 1 mol) [same for all gases, conditions] Ppt17b
The Ideal Gas Law No “before and after” kind of problem (1 state) • Sulfur hexafluoride (SF6) is a colorless, odorless, very unreactive gas. Calculate the pressure (in atm) exerted by 1.82 moles of the gas in a steel vessel of volume 5.43 L at 69.5°C. • What is the volume (in liters) occupied by 7.40 g of CO2 at STP? (Recall: STP is P = 1 atm; T = 0°C) Ppt17b
What if a variable changes? (2 “states”!) A “before and after” kind of problem (2 states) • Oxygen gas is normally sold in 49.0 L steel containers at a pressure of 150.0 atm. What volume would the gas occupy if the pressure was reduced to 1.02 atm and the temperature raised from 20oC to 35oC? Ppt17b
Example #2 • An inflated balloon with a volume of 0.55 L at sea level, where the pressure is 1.0 atm, is allowed to rise to a height of 6.5 km, where the pressure is about 0.40 atm. • 1) Assuming that the temperature remains constant, what is the final volume of the balloon? • 2) Assuming that the temperature at sea level is 22°C and the temperature at 6.5 km is -28°C, what is the final volume of the balloon? Ppt17b
Gases Worksheet-I Practice • Proportional relationships / calculations Ppt17b
The Ideal Gas Law—Applications Recall: At the same T and P, equal volumes of gases contain equal numbers of molecules. V n (P, T constant) • Implication? • The concentration of gas particles is “fixed” at a given T and P! = a fixed value (at a givenP & T, for any gas!) Ppt17b
At the same T & P, [gas] is “fixed” (sample size does not matter)(identity of the gas does not matter) Same T & P … He H2 He …same number of particles per L Ar Ppt17b
Density of a gas at fixed T and P does depend on gas identity (molar mass)! • Density is “number density” x mass per particle • Which equals concentration x molar mass! This slide is intended to make a conceptual connection, not give you another equation to memorize! • One could substitute in for n/V here to get an equation that relates d, P, T, and MM, • but I don’t think it’s really “worth it” (see answer key comments)
Summary (of prior few slides): At the same T&P, concentrationis constant, but density varies with MM Same # particles / L, but… He H2 He …different densities for different gaseous substances, because mass Ar Greatest density b/c greatest MM per particle (and thus per mole) varies!
Practical Application: Will gases (or balloons filled with them) float or sink (in air)? MM is the key! • Air is about 80% N2 and 20% O2 MM(air) 29 g/mol Quiz: Would a neon balloon float or sink? Argon? Ppt17b
The bottom line? Density of a gas depends on molar mass, T, & P, but not on “amount” Since amount does not matter, I prefer to PICK A CONVENIENT AMOUNT* to solve problems that relate to gas density and molar mass! No need to memorize or derive separate equations (although if you want to do so, more power to you!) * 1 L of gas, if density is given; 1 mol of gas, if molar mass (or formula) is given Ppt17b
The Ideal Gas Law—Applications (Examples) What is the molar mass of a gas with a density of 4.07 g/L at a pressure of 3.42 atm and 35°C? What is the density of uranium hexafluoride, UF6, (MM = 352 g/mol) under conditions of STP? To what temperature must a sample of CO2 be raised at 1.97 atm in order for the density to become 3.38 g/L? Ppt17b