# Ppt on ideal gas law density

Gaseous Substance dRT P M = d is the 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/

neon? 87 The mole weight of SO 2 is 64.07 g/mol. Determine the 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/

other except when they collide. This final assumption is equivalent to assuming a very low 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/

[1] thin line [1] Graph Mark scheme The behaviour of gases- Pressure 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 /

colliding with the container walls. Boyle’s 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/

only kPa has limited sigfigs. PUTTING IT ALL TOGETHER Simulation on 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/

K PV = nRT nRT P V = (111 mol)(0.0821 L·atm/mol· K) ( 216 K) (250 atm) = =7.9 L Real World Application 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/

082)(1273) 1 = 1.9 x 10 6 L Gases Lecture III Today... 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 /

is in atmospheres. The 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/

(0.0821 L atm /mol K) T = Temperature (K) 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/

combined them all? What is the 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/

intermolecular forces start to show effects. Applying 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/

.988 g Calculate the 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/

C. What would be the pressure of the dry hydrogen 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/

the cylinder? PV = nRT P = nRT V = 2.88 mol x 0.0821 (atm∙L/mol∙K) x 295 K 2.07 L = 33.7 atm Gas Density so at STP… Variations on the Ideal Gas Law n = mass (m) molar mass (M) So replace n with m/M If PV = nRT then PV = mRT M So rearrange for M M = mRT PV Variations on/

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 /

n2 Gay-Lussac: P1/T1 = P2/T2 Combined: P1V1/T1 = P2V2/T2 That’s a lot of 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/

. The 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/

related by PV g = constant g = CP / CV is assumed to be constant during the process All three variables in the 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/

? …. Using 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/

compressible state of matter. Gases will mix evenly and completely when confined to the same container. Gases have much lower 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/

0.60 L sample kept at 1.00 atm pressure and a temperature of 22.0 o C. Applications of 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/

.8 kPa atm when its temperature was 26.8 °C. Calculate the molar mass and determine the formula 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/

© Chuck Connor. All rights reserved. 2007Edited by Judy Harden 10/27/07 SSAC-pv2007.QE522.CC2.1 Supporting Quantitative Issues 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 /

C2H2 at STP? First, calculate amount of 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/

= 287.05 J kg-1 K-1 For the dry atmosphere, pa = RdT Usage of the equation of state Used to derive the individual 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/

.4 L  mmHg/mol  K PV=nRT 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/

n = (1.89 x 10 3 kPa) (685 L) mol · K (8.31L · kPa) (621K) n = 251 mol He Sample Problem Using 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/

to its molar mass. No simple realtionship exists between 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/

is given in mmHg R = 62.4 LmmHg molK If pressure is given in kPa R = 8.31 LkPa molK If pressure is given in atm 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  /

that 1 mol O 2 (32.00 g) occupies a volume of 22.4 L. 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 /

& V, moles & V, V & Temp, etc Evolved 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/

+ 400² + 500²)/5 = 1.1 x 10 5 m 2 s -2 c) c rms = √ = 330 m/s 9/8/2015 54 Example 25.2 The 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/

Prentice Hall ©2004 Ppt17b Ppt 17b, Continuation of Gases & 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/

by the molecular weight, the equation can be written as or, since m/V is the 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/

Fluid Mechanics Chapter Objectives Define fluid 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 /

0821 L atm )(323 K) mol K (0.95 atm)(15 L) = 46.5 __g_ mol mol The 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/

0  C contain 6.02  10 23 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/

. 1. pressure (P) in atm 2. volume (V) in Liters 3. temperature (T) in Kelvin 4. amount (n) in moles Not Held constant in Section 14.3 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/

temperatures! Guaranteed points on the AP Exam! These next exercises can all be solved with the 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 /

lb/in 2 or psi (pounds per square inch) 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/

.290 g and occupies a volume of 148 mL at 13°C and a pressure of 107.0 kPa. First, convert the temperature to kelvins. Determining Molar Mass and 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/

the can were heated to 450 o C? P 2 = 3.6 atm P1T1P1T1 = P2T2P2T2 1.5 atm 298 K P 2 723 K = Relating the 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/

(at constant T) can give molar mass. Deviation of 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/

that 1 mol O 2 (32.00 g) occupies a volume of 22.4 L. 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 /

be added to give 6.48 L? The 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/