Chemistry & Chemical Reactivity, Hybrid Edition (with OWLv2 24-Months Printed Access Card)
Chemistry & Chemical Reactivity, Hybrid Edition (with OWLv2 24-Months Printed Access Card)
9th Edition
ISBN: 9781285462530
Author: John C. Kotz, Paul M. Treichel, John Townsend, David Treichel
Publisher: Cengage Learning
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Chapter 10, Problem 105IL

You have a gas, one of the three known phosphorus-fluorine compounds (PF3, PF3, and P2F4). To find out which, you have decided to measure its molar mass.

  1. (a) First, yon determine that the density of the gas is 5.60 g/L at a pressure of 0.971 atm and a temperature of 18.2 °C. Calculate the molar mass and identify the compound.
  2. (b) To check the results from part (a), you decide to measure the molar mass based on the relative rales of effusion of the unknown gas and CO2. You find that CO2 effuses at a rate of 0.050 mol/min, whereas the unknown phosphorus fluoride effuses at a rate of 0.028 mol/min. Calculate the molar mass of the unknown gas based on these results.

(a)

Expert Solution
Check Mark
Interpretation Introduction

Interpretation:

 From the given set of gases the gas that matches with the molar mass obtained from the calculation using given set of conditions should be determined.

Concept introduction:

Ideal gas Equation:

Any gas is described by using four terms namely pressure, volume, temperature and the amount of gas. Thus combining three laws namely Boyle’s, Charles’s Law and Avogadro’s Hypothesis the following equation could be obtained. It is referred as ideal gas equation.

   nTPV = RnTPPV = nRTwhere,n = moles of gasP = pressureT = temperatureR = gas constant

Under some conditions gases don not behave like ideal gas that is they deviate from their ideal gas properties. At lower temperature and at high pressures the gas tends to deviate and behave like real gases.

Boyle’s Law:

At given constant temperature conditions the mass of given ideal gas in inversely proportional to its volume.

Charles’s Law:

At given constant pressure conditions the volume of ideal gas is directly proportional to the absolute temperature.

Avogadro’s Hypothesis:

Two equal volumes of gases with same temperature and pressure conditions tend to have same number of molecules with it.

The root mean square velocity μ is defined as the measure of velocity of particle in gas. It is the method to determine the single velocity value for particles.

Root mean square velocity can be determined,

                                                        μrms=(3RTM)1/2 (1)

  (gas constant)R=8.314JKmolM=Molarmass

Molar mass: The molar mass of a substance is determined by dividing the given mass of substance by the amount of the substance.

Average Kinetic energy: The kinetic energy for the gas is directly proportional to the kelvin temperature. The kinetic energy is equal to half of the multiplied value obtained by multiplication of mass of gas with rms velocity of the gas.

Answer to Problem 105IL

The molar mass for the gas is found to be 138g/mol and hence the gas is found to be P2F4

Explanation of Solution

Given:

  Density, D=5.60 g/LPressure, P=0.971 atmTemperature,T = 18.2oC = 273.15+18.2 = 291.35K

Using ideal gas equation the molar mass for the unknown gas is determined as follows,

  PV= nRTP = nRTVP = MassMolarmass×RTVMolarmass = MassV×RTP=5.60 g/L×0.0821×291.350.971[since MassV = D]=137.95g/mol=138 g/mol

From the above calculation it is clear that the molar mass for the given unknown gas is found to be 138 g/mol which actually equals to the molar mass of P2F4 from the given set of gases.

Therefore, the unknown gas is found to P2F4.

(b)

Expert Solution
Check Mark
Interpretation Introduction

Interpretation:

 From the given set of gases the gas that matches with the molar mass obtained from the calculation using given set of conditions should be determined.

Concept introduction:

Ideal gas Equation:

Any gas is described by using four terms namely pressure, volume, temperature and the amount of gas. Thus combining three laws namely Boyle’s, Charles’s Law and Avogadro’s Hypothesis the following equation could be obtained. It is referred as ideal gas equation.

   nTPV = RnTPPV = nRTwhere,n = moles of gasP = pressureT = temperatureR = gas constant

Under some conditions gases don not behave like ideal gas that is they deviate from their ideal gas properties. At lower temperature and at high pressures the gas tends to deviate and behave like real gases.

Boyle’s Law:

At given constant temperature conditions the mass of given ideal gas in inversely proportional to its volume.

Charles’s Law:

At given constant pressure conditions the volume of ideal gas is directly proportional to the absolute temperature.

Avogadro’s Hypothesis:

Two equal volumes of gases with same temperature and pressure conditions tend to have same number of molecules with it.

The root mean square velocity μ is defined as the measure of velocity of particle in gas. It is the method to determine the single velocity value for particles.

Root mean square velocity can be determined,

                                                        μrms=(3RTM)1/2 (1)

  (gas constant)R=8.314JKmolM=Molarmass

Molar mass: The molar mass of a substance is determined by dividing the given mass of substance by the amount of the substance.

Average Kinetic energy: The kinetic energy for the gas is directly proportional to the kelvin temperature. The kinetic energy is equal to half of the multiplied value obtained by multiplication of mass of gas with rms velocity of the gas.

Answer to Problem 105IL

The molar mass for the given gas is 140g/mol.

Explanation of Solution

Using the effusion rate of the unknown gas compared with the known  CO2 gas the above calculation is verified as follows,

  r1r2=M2M1where,r1=Effusion rate for CO2r2=Effusion rate for unknown gasM2=Molar mass of unknown gasM1=Molar mass for CO20.050 mol/min0.028 mol/min(M244.01)1/2M2=140g/mol

The above calculation shows that the molar mass for unknown gas is found to be 140g/mol. Therefore, it verifies the answer in the part a since the molar mass obtained from both the calculation matches.

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Chapter 10 Solutions

Chemistry & Chemical Reactivity, Hybrid Edition (with OWLv2 24-Months Printed Access Card)

Ch. 10.3 - Prob. 1CYUCh. 10.3 - At 1.00 atm and 25 C, the density of dry air is...Ch. 10.3 - A 0.105-g sample of a gaseous compound has a...Ch. 10.3 - Which gas has the greatest density at 25 and 1.00...Ch. 10.3 - Prob. 2RCCh. 10.3 - Prob. 3RCCh. 10.4 - Prob. 1CYUCh. 10.4 - Diborane reacts with O2 to give boric oxide and...Ch. 10.4 - 2. If you mix 1.5 L of B2H6 with 4.0 L of O2, each...Ch. 10.5 - The halothane-oxygen mixture described in this...Ch. 10.5 - Prob. 1RCCh. 10.6 - Prob. 1CYUCh. 10.6 - What is the rms speed of chlorine molecules at...Ch. 10.6 - 2. The species identified with each curve in the...Ch. 10.7 - Prob. 1CYUCh. 10.7 - In Figure 10.17, ammonia gas and hydrogen chloride...Ch. 10.8 - Prob. 1RCCh. 10.8 - At sea level, atmospheric pressure is 1.00 atm....Ch. 10.8 - Prob. 2QCh. 10.8 - To stay aloft, a blimp must achieve neutral...Ch. 10 - Pressure (See Section 10.1 and Example 10.1.) The...Ch. 10 - The average barometric pressure at an altitude of...Ch. 10 - Indicate which represents the higher pressure in...Ch. 10 - Put the following in order of increasing pressure:...Ch. 10 - Prob. 5PSCh. 10 - Prob. 6PSCh. 10 - You have 3.5 L of NO at a temperature of 22.0 C....Ch. 10 - Prob. 8PSCh. 10 - Prob. 9PSCh. 10 - You have a sample of CO2 in flask A with a volume...Ch. 10 - You have a sample of gas in a flask with a volume...Ch. 10 - A sample of gas occupies 135 mL at 22.5 C; the...Ch. 10 - One of the cylinders of an automobile engine has a...Ch. 10 - A helium-filled balloon of the type used in...Ch. 10 - Nitrogen monoxide reacts with oxygen to give...Ch. 10 - Ethane bums in air to give H2O and CO2. 2 C2H6(g)...Ch. 10 - A 1.25-g sample of CO2 is contained in a 750.-mL...Ch. 10 - A balloon holds 30.0 kg of helium. 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To...Ch. 10 - Acetaldehyde is a common liquid compound that...Ch. 10 - Iron reacts with hydrochloric acid to produce...Ch. 10 - Silane, SiH4, reacts with O2 to give silicon...Ch. 10 - Prob. 33PSCh. 10 - The hydrocarbon octane (C8H18) bums to give CO2...Ch. 10 - Prob. 35PSCh. 10 - A self-contained underwater breathing apparatus...Ch. 10 - What is the total pressure in atmospheres of a gas...Ch. 10 - A cylinder of compressed gas is labeled...Ch. 10 - A halothane-oxygen mixture (C2HBrCIF3 + O2) can be...Ch. 10 - A collapsed balloon is filled with He to a volume...Ch. 10 - You have two flasks of equal volume. Flask A...Ch. 10 - Equal masses of gaseous N2 and Ar are placed in...Ch. 10 - If the rms speed of an oxygen molecule is 4.28 ...Ch. 10 - Prob. 44PSCh. 10 - Place the following gases in order of increasing...Ch. 10 - Prob. 46PSCh. 10 - In each pair of gases below, tell which will...Ch. 10 - Prob. 48PSCh. 10 - Prob. 49PSCh. 10 - A sample of uranium fluoride is found to effuse at...Ch. 10 - Prob. 51PSCh. 10 - Prob. 52PSCh. 10 - In the text, it is stated that the pressure of...Ch. 10 - You want to store 165 g of CO2 gas in a 12.5-L...Ch. 10 - Consider a 5.00-L tank containing 325 g of H2O at...Ch. 10 - Consider a 5.00-L tank containing 375 g of Ar at a...Ch. 10 - Complete the following table:Ch. 10 - On combustion, 1.0 L of a gaseous compound of...Ch. 10 - You have a sample of helium gas at 33 C, and you...Ch. 10 - Prob. 60GQCh. 10 - Butyl mercaptan, C4H9SH, has a very bad odor and...Ch. 10 - Prob. 62GQCh. 10 - The temperature of the atmosphere on Mars can be...Ch. 10 - If you place 2.25 g of solid silicon in a 6.56-L...Ch. 10 - What volume (in liters) of O2, measured at...Ch. 10 - Nitroglycerin decomposes into four different gases...Ch. 10 - Ni(CO)4 can be made by reacting finely divided...Ch. 10 - Ethane bums in air to give H2O and CO2. 2 C2H6(g)...Ch. 10 - You have four gas samples: 1. 1.0 L of H2 at STP...Ch. 10 - Propane reacts with oxygen to give carbon dioxide...Ch. 10 - Iron carbonyl can be made by the direct reaction...Ch. 10 - Prob. 72GQCh. 10 - There are five compounds in the family of...Ch. 10 - A miniature volcano can be made in the laboratory...Ch. 10 - The density of air 20 km above Earths surface is...Ch. 10 - Prob. 76GQCh. 10 - Chlorine dioxide, ClO2, reacts with fluorine to...Ch. 10 - A xenon fluoride can be prepared by heating a...Ch. 10 - Prob. 79GQCh. 10 - Prob. 80GQCh. 10 - Prob. 81GQCh. 10 - Carbon dioxide, CO2, was shown lo effuse through a...Ch. 10 - Prob. 84GQCh. 10 - Prob. 85GQCh. 10 - Prob. 86GQCh. 10 - You are given 1.56 g of a mixture of KClO3 and...Ch. 10 - A study of climbers who reached the summit of...Ch. 10 - Nitrogen monoxide reacts with oxygen to give...Ch. 10 - Ammonia gas is synthesized by combining hydrogen...Ch. 10 - Nitrogen trifluoride is prepared by the reaction...Ch. 10 - Chlorine trifluoride, ClF3, is a valuable reagent...Ch. 10 - Prob. 93GQCh. 10 - Prob. 94GQCh. 10 - You have a 550.-mL tank of gas with a pressure of...Ch. 10 - Prob. 96ILCh. 10 - Prob. 97ILCh. 10 - Group 2A metal carbonates are decomposed to the...Ch. 10 - One way to synthesize diborane, B2H6, is the...Ch. 10 - You are given a solid mixture of NaNO2 and NaCl...Ch. 10 - You have 1.249 g of a mixture of NaHCO3 and...Ch. 10 - Prob. 102ILCh. 10 - Many nitrate salts can be decomposed by heating....Ch. 10 - You have a gas, one of the three known...Ch. 10 - Prob. 106ILCh. 10 - A 1.0-L flask contains 10.0 g each of O2 and CO2...Ch. 10 - If equal masses of O2 and N2 are placed in...Ch. 10 - You have two pressure-proof steel cylinders of...Ch. 10 - Prob. 110SCQCh. 10 - Prob. 111SCQCh. 10 - Each of four flasks is filled with a different...Ch. 10 - Prob. 113SCQCh. 10 - The sodium azide required for automobile air bags...Ch. 10 - Prob. 115SCQCh. 10 - Prob. 116SCQ
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