**density** of the **gas** in g/L 5.4 **Gas** Mixtures and Partial Pressures Since **gas** molecules are so far apart, we can assume they behave independently. Dalton’s **Law**: in a **gas** mixture the total pressure is given by the sum of partial pressures of each component: Each **gas** obeys the **ideal** **gas** equation: Combining the equations we get: 5/

**density** of SO 2 at STP. 1 mole of any **gas** occupies 22.4 L at STP 88 **Ideal** **Gas** Equation 89 V P nT 90 V P nT atmospheres 91 V P / of the unknown **gas**. 126 Real Gases 127 **Ideal** **Gas** An **ideal** **gas** obeys the **gas** **laws**. –The volume the molecules of an **ideal** **gas** occupy is negligible compared to the volume of the **gas**. This is true at all temperatures and pressures. –The intermolecular attractions between the molecules of an **ideal** **gas** are negligible at/

**gas** **density**, which is the same as assuming that the **gas** is an **ideal** **gas**. Because momentum is conserved, the collisions the molecules make with each other have no / C V is assumed to be constant during the process All three variables in the **ideal** **gas** **law** (P, V, T ) can change during an adiabatic processAll three variables in the **ideal** **gas** **law** (P, V, T ) can change during an adiabatic process Equipartition of Energy With/

**Law** http://phet.colorado.edu/sims/**ideal**-**gas**/**gas**-properties.jnlp **Gas** **Laws** http://phet.colorado.edu/sims/**ideal**-**gas**/**gas**-properties.jnlp **Gas** **Laws** When we heat a **gas** at constant volume, what happens to the pressure? Why? Let’s do it! /= 2.1 m 3, This is the volume of 1kg of air on Everest **Density** = mass/volume = 1/2.1 = 0.48 kg.m -3. pV= constant T The equation of state of an **ideal** **gas** Experiment has shown us that pV = nR T p - pressure (Pa) V /

**Law** The **Gas** **Laws** Do Q1-3 page 71 The behaviour of gases- Pressure **Law** http://phet.colorado.edu/sims/**ideal**-**gas**/**gas**-properties.jnlp http://phet.colorado.edu/sims/**ideal**-**gas**/**gas**-properties.jnlp When we heat a **gas** at constant volume, what happens to the /= 2.1 m 3, This is the volume of 1kg of air on Everest **Density** = mass/volume = 1/2.1 = 0.48 kg.m -3. pV= constant T The equation of state of an **ideal** **gas** Experiment has shown us that pV = nR T p - pressure (Pa) V -/

**gas** particles are expelled (exhaling). **Gas** **Laws** Combined **Gas** **Law** Checking for understanding State the **law** Explain the **law** in your own words Write the formula(s) Boyle’s **Law** Charle’s **Law** Gay-Lussac’s **Law** Avogadro’s **Law** **Gas** Behavior – Diffusion/Effusion Diffusion is the movement of particles from regions of higher **density** to regions of lower **density**. The passage of **gas**/ **IDEAL** **GAS** **LAW** The **Ideal** **Gas** **Law** provides important information regarding reactions, like the combination of gases; stoichiometry, like the **gas**/

**gas** **laws**: Structure and Properties of Matter **IDEAL** **GAS** **LAW** **Ideal** **Gas** Equation: PV = nRT “R” is the universal **gas** constant. V ∝ (nT)/P replace ∝ with constant, R UNIVERSAL **GAS** CONSTANTS R = 0.08206 L atm mol K R = 62/ 125ºC. DETERMINING **DENSITY** This modified version of the **ideal** **gas** equation can also be used to solve for the **density** of a **gas**. PV = nRT bcomes D = PM RT DETERMINING **DENSITY** D = m = PMMor D = PMM V RT RT The **density** of gases is g/

**IDEAL** **GAS** **LAW** The **Ideal** **Gas** **Law** provides important information regarding reactions, like the combination of gases; stoichiometry, like the **gas** produced in a reaction; physical processes, like the mixing of gases; and thermodynamic processes, like the movement of matter toward disorder. The/

**Ideal** **gas** **law** calculations **gas** **densities** partial pressures mole fractions for the reaction: CH 4(g) + 2 O 2(g) CO 2(g) + 2 H 2 O (g) **Ideal** **Gas** Equation Example 2 2.80 L CH 4 35.0 L O 2 25 o/P = nRT V = 8(0.082)(300) 4.00 = 49.2 atm according to van der Waals: = 29.5 atm (49.2 atm from **ideal** **gas** **law**) The Atmosphere P 1 atm (thus PV = nRT applies) but the chemistry is very complex Atmospheric Problems Ozone depletion Smog Acid rain Pressure and Mean /

**gas** at STP. **Density** at STP The Molar mass of a **gas** can be determined by the **density** of the **gas**. d= mass = m = MM Volume V 22.4 L Examples: **Density** at STP Calculate the **density** of oxygen **gas**, O 2, at STP. Calculate the **density** of methane **gas**,CH 4, at STP. **Density**/take up space and they do interact with each other (especially polar molecules). Need to add correction factors to the **ideal** **gas** **law** to account for these. Volume Correction The actual volume (container volume) free to move in is less because of /

**ideal** **gas** **law** describes the physical behavior of an **ideal** **gas** in terms of pressure, volume, temperature, and amount. SECTION 13.2 The **Ideal** **Gas** **Law** The **Ideal** **Gas** **Law** (cont.) SECTION 13.2 The **Ideal** **Gas** **Law** The **Ideal** **Gas** **Law**—Molar Mass and **Density** Molar mass and the **ideal** **gas** **law** SECTION 13.2 The **Ideal** **Gas** **Law** The **Ideal** **Gas** **Law**—Molar Mass and **Density** (cont.) **Density** and the **ideal** **gas** **law** SECTION 13.2 The **Ideal** **Gas** **Law** Real Versus **Ideal** Gases **Ideal** gases follow the assumptions of/

**Ideal** **gas** **law** calculations are favored at low pressures and high temperatures Let’ Try It! Example: If we had 1.0 mol of **gas** at 1.0 atm of pressure at 0°C (STP), what would be the volume? PV = nRT V = nRT/P **Gas** **Density** and Molar Mass D = m/V Let M stand for molar/

**Ideal** **Gas** **Law**? Combining Boyle’s **Law**, Charles’ **law** & Avogadro’s **Law** we derive the **Ideal** **Gas** **Law**: P V = n R T P = Pressure (atm) V = Volume (L) n = # moles (mol) R = **Gas** Constant (0.0821 L atm /mol K) T = Temperature (K) **Ideal** **gas** **law** calculations are favored at low pressures /1.0 mol)(0.0821 L atm/mol K)(273 K)/(1.0 atm) V = 22.41 L 1 mole of ANY **gas** at STP will occupy 22.4 Liters of volume **Gas** **Density** and Molar Mass D = m/V Let M stand for molar mass M = m/n n = m/M PV = nRT/

**Ideal** **Gas** **Law** If you know any three variables, you can solve for the fourth: You can solve for n (number of moles) Combined **gas** **law**, you cannot. You can use **ideal** **gas** **law** allows you to solve for molar mass and **density**, if mass is known n (number of/ 0.0821 L*atm/mol*K Step1: Convert T to Kelvin Tk = Tc+273 Tk = 273 Molar Mass Problem Use **density** form of **ideal** **gas** **law** M = DRT/P Substitute known values: M = (1.40 g/L)(0.0821 L*atm/mol*K)(273K) 1 atm M = 31/

**density** of N2 at 125°C and 755 mmHg Molar Mass of a **Gas** One of the methods chemists use to determine the molar mass of an unknown substance is to heat a weighed sample until it becomes a **gas**, measure the temperature, pressure, and volume, and use the **ideal** **gas** **law** Calculate the molar mass of a **gas** with mass 0 Calculate/

**gas**? What would be the volume of the dry hydrogen **gas** at STP? G. Solving for **Density** and /or Molar Mass of a **gas** using the **Ideal** **Gas** **Law** 1. **Density** (units are g/L) Use the **Ideal** **Gas** **Law** to find moles (n), convert n to grams OR use the **Ideal** **Gas** **Law** to find the volume. Divide n (in grams) by the/

**ideal** **gas** **law** can be used to calculate molar mass if grams of **gas**, and P,V, T are known: 1. Calculate moles of **gas**, n = PV / RT 2. Use moles, n and mass, g to calculate M n, moles = mass, g molar mass, M = mass, g molar mass, M n, moles Widely used **Gas** **Laws** : **Density**/, Molar Mass Chloroform is a common liquid which vaporizes readily. If the pressure of the vaporized liquid is 195mm Hg at 25 o C, and the **density** of the **gas** is 1.25 g/L, what is the molar /

**laws**! Or we can just use the **Ideal** **Gas** **Law**! Combined **Gas** **Law** Cont. Ex: A 2.3L sample of **gas** has a pressure of 1.2atm at 200.K. If the pressure is raised to 1.4atm and the / 1.52mol CO2 Use STP conditions & stoichiometry: At STP 1mol = 22.4L 1.52mol x (22.4L/1mol) = 34.1L CO2 Can double check using **ideal** **gas** **law** **Gas** **Density** and Molar Mass Recall: D = m/V Let mmolar stand for molar mass mmolar = m/n so n = m/mmolar PV = nRT solve for n/

**ideal** **gas** **law** * The **Ideal** **Gas** **Law** (cont.) SECTION13.2 The **Ideal** **Gas** **Law** The **Ideal** **Gas** **Law** (cont.) The **Ideal** **Gas** **Law**—Molar Mass and **Density** SECTION13.2 The **Ideal** **Gas** **Law** The **Ideal** **Gas** **Law**—Molar Mass and **Density** Molar mass and the **ideal** **gas** **law** The **Ideal** **Gas** **Law**—Molar Mass and **Density** (cont.) SECTION13.2 The **Ideal** **Gas** **Law** The **Ideal** **Gas** **Law**—Molar Mass and **Density** (cont.) **Density** and the **ideal** **gas** **law** Real Versus **Ideal** Gases SECTION13.2 The **Ideal** **Gas** **Law** Real Versus **Ideal** Gases **Ideal** gases follow/

**ideal** **gas** **law** (P, V, T ) can change during an adiabatic process Equipartition of Energy With complex molecules, other contributions to internal energy must be/ plane of the paper Mean Free Path The mean free path is related to the diameter of the molecules and the **density** of the **gas** We assume that the molecules are spheres of diameter d No two molecules will collide unless their paths are less than/

**ideal** **gas** **law** Working Session 100 g/h of ethylene (C2H4) flows through a pipe at 120oC and 1.2 atm and 100 g/h of butene (C4H8) flows through a second pipe at the same pressure and temperature. Which of the following quantities differ for the two gases; (a) the volumetric flowrate (b) specific molar volume (L/mol) (c) mass **density** (g/

**densities** than liquids and solids. Exerts pressure on its surroundings. Physical Characteristics of Gases Copyright©2000 by Houghton Mifflin Company./ 1 P V V nT P V = constant x = R nT P P R is the **gas** constant PV = nRT Copyright©2000 by Houghton Mifflin Company. All rights reserved. 24 **Ideal** **Gas** **Law** PV = nRT R = proportionality constant = 0.08206 L atm mol P = pressure in/

**Ideal** **Gas** **Law** b Can be used to calculate the molar mass of a **gas** and the **density** b Substitute this into **ideal** **gas** **law** b And m/V = d in g/L, so GIVEN: P = 1.50 atm T = 27°/ dRT/P MM=(1.95)(0.08206)(300.)/1.50 g/L L atm/mol K K atm MM = 32.0 g/mol Applications of **Ideal** **Gas** **Law** Applications of **Ideal** **Gas** **Law** b The **density** of a **gas** was measured at 1.50 atm and 27 ° C and found to be 1.95 g/L. Calculate the molar mass of the/

**gas**. Chemistry, 2nd Canadian Edition ©2013 John Wiley & Sons Canada, Ltd. Chapter 5 **Density** and the **Ideal** **Gas** **Law** Easy to manipulate **ideal** **gas** **law** to determine the **density**. Chemistry, 2nd Canadian Edition ©2013 John Wiley & Sons Canada, Ltd. Chapter 5 Chemistry, 2nd Canadian Edition ©2013 John Wiley & Sons/

**Ideal** **Gas** **Law** Units 2 Slides 3-6 give some background on bubbles in magmas and discuss how bubbles are intimately related to magma flow /and the equation for viscous drag is generally for turbulent flow, rather than laminar flow. (a) Use the **ideal** **gas** **law** to calculate the change in **density** of the atmosphere as a function of height from sea-level (0 m) to 30 km (approximately the /

**gas** in moles. **Ideal** **Gas** **Law** **Ideal** **Gas** **Law** How many moles of a **gas** at 100oC does it take to fill a 1.00L flask to a pressure of 1.5atm? Lifting Power of Gases For a **gas** to be used to inflate lighter-than-air craft like balloons and blimps, the **gas** must have a **density** lower than air. The lower the/

**ideal** **gas** **laws** (working backwards from our derivation) Use of **Ideal** **Gas** **Law** Equation to determine the **density** of a **gas**; r is difficult to measure directly. [The only instrument that can do this is the “direct detection” lidar which measures backscatter from molecules/

**Ideal** **Gas** **Law** PVM=mRT If you are given the mass of a **gas**, you can use this equation instead of converting mass to moles first. mass molar mass **Ideal** **Gas** **Law** d=PM/RT If you are given the molar mass of a **gas**, you can use this equation to find the **density** molar mass **density** GIVEN: P = ? atm n = 0.412/

**Ideal** **Gas** **Law** A child’s lungs can hold 2.20 L. How many grams of air do her lungs hold at a pressure of 102 kPa and a body temperature of 37/ all the lakes and oceans would tend to evaporate. Water in the Solid State When the temperature of water falls below 4 º C, the **density** of water actually starts to decrease. Below 4 º C, water no longer behaves like a typical liquid. Hydrogen bonds hold the water molecules in/

**density** and molar mass for liquids and solids. 16 Gases in Chemical Reactions Use the stoichiometric factors to relate the amount of a **gas** to amounts of other reactants or products. Use the **ideal** **gas** equation to relate the amount of **gas** to volume,temperature and pressure. **Law** of combining volumes can be modified with the other/

**Ideal** **Gas** Constant Using the **Ideal** **Gas** **Law** What volume does 9.45g of C 2 H 2 occupy at STP? What volume does 9.45g of C 2 H 2 occupy at STP? /V} 2) What is the **density** of laughing **gas**(N 2 O 4 ) released at 25°C and 1.02 atm? Try These 5 problems 3) A 0.519 g **gas** has a volume of 200 ml at STP. Is this **gas** propane (C 3 H 8 ), butane (C 4 H 10 ) or something else? Using the **Ideal** **Gas** **Law** PV = mRT/M /

**Density** O 2 at STP = 32.00 g O 2 = 1.43 g/L 22.4 L (STP) Chapter 11 Slide 51 of 77 Chapter 11 Gases The **Ideal** **Gas** **Law** Copyright © 2008 by Pearson Education, Inc. Publishing as Benjamin Cummings Chapter 11 Slide 52 /11 Slide 60 of 77 1. Determine the given properties. P = 0.85 atm, V = 5.0 L, T = 293 K, n ( or g =?) 2. Rearrange the **ideal** **gas** **law** for n (moles). n = PV RT = (0.85 atm)(5.0 L)(mol K) = 0.18 mol O 2 (0.0821atm L)(293 K) 3. Convert moles to /

**Ideal** **Gas** **Law**”, PV=nRT –Includes all the variables in one equation –Reduces to named **gas** **laws** with omitted variables 9 Gases & **Gas** **Laws** **Gas** **laws** with 2 variables –Boyle’s **law**, Charles’ **law**, Avagadro’s **Law** Combined **gas** **law** with 3 variables –PV/T=constant **Ideal** **Gas** **Law** with all 4 variables –PV=nRT Applications –**Density** and Lift –Air Bags, etc. **Gas** Pressure Pressure Units of Measure –Air pressure is/

**density** of air at s.t.p. is 1.3 kg m -3 and the atmospheric pressure is 1.01 x 10 5 Pa. Calculate a) the means square speed, and/ amount finally 1.2 + 0.93 = n A + n B = p = 1.37x10 ⁵Pa pV = nRT For two containers of equal volume **Ideal** **gas** a **gas** that obeys **gas** **laws**, PV=nRT at all T, p and V Assumptions Point molecules Elastic collision Large Number Duration of collision No intermolecular forces u -u kinetic theory N = /

**Gas** **Laws** Combined **Gas** **Law** Checking for understanding State the **law** Explain the **law** in your own words Write the formula(s) Boyle’s **Law** Charle’s **Law** Gay-Lussac’s **Law** Avogadro’s **Law** **Gas** Behavior – Diffusion/Effusion Diffusion is the movement of particles from regions of higher **density** to regions of lower **density**. The passage of **gas**/ The combined **gas** **law** expresses the relationship between pressure, volume and temperature of a fixed amount of **gas**. **Ideal** **Gas** **Law** Calculation How many moles of **gas** are contained in/

**Gas** **Laws** 1. Individual **Gas** **Laws** Combine to Form the **Ideal** **Gas** **Law**. 2. **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). 3. **Density** of Gases Ideas & Calculations Can use **Ideal** **Gas** **Law** here (or memorize variant) 1 Prentice Hall ©2004 Ppt17b Important Comment In all/

**gas** **density**, This expression is known by various names such as the **ideal** **gas** **law**, the general **gas** **law**, or the perfect **gas** **law**. This equation has limited practical value since no known **gas** behaves as an **ideal** **gas**; however, the equation does describe the behavior of most real gases at low pressure and gives a/

**Density** Buoyant force Buoyantly of floating objects Pressure Pascals principle Pressure and depth Temperature Fluid flow continuity equation Bernoullis principle **Ideal** **gas** **law** What is a Fluid? So far/in the United States. Fahrenheit is the units for temperature in the United States. **Ideal** **Gas** **Law** The **ideal** **gas** **law** varies slightly for physics versus chemistry. The **ideal** **gas** **law** varies slightly for physics versus chemistry. That is due to Boltzmann’s Constant (k /

**Ideal** **gas** **law** MW = g R T = PV Remember **density** = The **Ideal** **gas** **law** can also be used with **density** of a **gas** gVgV MW = d R T P If the **density** of a **gas** is 1.75 _g_ L at 740 torr and 300 K, what is its MW? MW = g R/ T P V 740 torr ( 1 atm ) (760 torr) The **Ideal** **gas** **law** MW = d R T P If **density** of a **gas** = 1.75 g_ L at 740 torr and 300 K, What is its MW? 1.75g MW = 1.75 g (.0821 L atm)( 300 K) L/

**gas** molecules. The **Gas** **Laws** 25 The Quantity-Volume Relationship: Avogadro’s **Law** The **Gas** **Laws** 27 Consider the three **gas** **laws**. We can combine these into a general **gas** **law**: 6.3 & 6.4 The **Ideal** **Gas** Equation Boyle’s **Law**: Charles’s **Law**: Avogadro’s **Law**: 28 If R is the constant of proportionality (called the **gas** constant), then The **ideal** **gas** equation is: R = 0.08206 L·atm/

**Ideal** **Gas** **Law** 5. The **Ideal** **Gas** **Law** #1 Equation: P x V = n x R x T R = 0.08206 L x atm) / (mol x K) The other units must match the value of the constant, in / is 63.0°C? 0.572 g/L NH 3 0.572 g/L NH 3 The **density** of a **gas** was found to be 2.0 g/L at 1.50 atm and 27°C. What is the molar mass of the **gas**? The **density** of a **gas** was found to be 2.0 g/L at 1.50 atm and 27°C. What/

**ideal** **gas** **law**. BUT, you can use another if you like! Exercise 6 **Ideal** **Gas** **Law** I A sample of hydrogen **gas** (H 2 ) has a volume of 8.56 L at a temperature of 0º C / is the approximate molar mass of air? _________ The **density** of air is approximately _______ g/L. List 3 gases that float in air: List 3 gases that sink in air: Exercise 14 **Gas** **Density**/Molar Mass The **density** of a **gas** was measured at 1.50 atm and 27º C and/

**Law** - Charles’ **Law** & - Avogadro’s **Law** **Ideal** **Gas** **Law** 4 An equation of state for a **gas**. 4 “state” is the condition of the **gas** at a given time. PV = nRT An **Ideal** **Gas** is a hypothetical substance. **Ideal** **Gas** **Law** is an empirical equation. **Ideal** **Gas** **Law** PV = nRT R = proportionality constant R = proportionality constant = **ideal** **gas**/ What is the average molar mass of the air? Solution **Density** = (molar mass) x P R T Therefore, Molar Mass = **Density** x R x T P Solution Molar Mass = **Density** x R x T P Molar Mass = 1.225 g /

**Gas** **Laws** **Gas** **law** EquationVariablesConstant(s) Boyle’s **law** Charles’s **law** Avogadro’s **law** Combined **gas** **law** **Ideal** **gas** **law** P- pressureT- temperatureR- universal **gas** constant V- volumen- number of moles Boyle’s **Law**: P-V relationship Robert Boyle, 1662 : Boyle’s **Law** –For a given amount of **gas** at a constant temperature, the volume of the **gas** varies inversely with its pressure. V 1 / P V/

**Density** Next, solve the **ideal** **gas** **law** equation for M, the molar mass. Finally, substitute values and calculate the value of M. Notice that you must use the value of R that uses kilopascals as/

**Ideal**-**Gas** Equation and the **Gas** **Laws** When the quantity of **gas** is held constant, n has fixed values. = nR = constant PV = nRT PV T P1V1T1P1V1T1 P2V2T2P2V2T2 = An inflated balloon has a volume of 6.0/-1 d = 1.8 g L -1 d = 2.91 g L -1 N2ON2O Cl (a)Calculate the **density** of NO 2 **gas** at 0.970 atm and 35 o C. (b) Calculate the molar mass of a **gas** if 2.50 g occupies 0.875 L at 685 torr and 35 o C. PM RT d = 0.97 x/

**Density** from **Ideal** Plotting data of ρ/P vs. P (at constant T) can give molar mass. Dalton’s **Law**: in a **gas** mixture the total pressure is given by the sum of partial pressures of each component: Each **gas** obeys the **ideal** **gas** equation: **Ideal** **Gas** Mixtures and Partial Pressures **Density**? Partial Pressures and Mole Fractions Let n i be the/

**Density** O 2 at STP = 32.00 g O 2 = 1.43 g/L 22.4 L (STP) Chapter 11 Slide 56 of 89 Chapter 11 Gases The **Ideal** **Gas** **Law** Copyright © 2008 by Pearson Education, Inc. Publishing as Benjamin Cummings Chapter 11 Slide 57 /11 Slide 65 of 89 1. Determine the given properties. P = 0.85 atm, V = 5.0 L, T = 293 K, n ( or g =?) 2. Rearrange the **ideal** **gas** **law** for n (moles). n = PV RT = (0.85 atm)(5.0 L)(mol K) = 0.18 mol O 2 (0.0821atm L)(293 K) 3. Convert moles to /

**Gas** **Laws** **Ideal** **Gas**: A **gas** whose behavior follows the **gas** **laws** exactly. The physical properties of a **gas** can be defined by four variables: Ppressure (atm) Ttemperature (calculation must be in Kelvin) Vvolume (L) nnumber of moles The **Ideal** **Gas** **Law**, PV = nRT, - models the behavior of **ideal** gases. Other **gas** **laws** can be derived from the **Ideal** **Gas** **Law** for either one set of conditions or for/

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