Chemistry & Chemical Reactivity
Chemistry & Chemical Reactivity
10th Edition
ISBN: 9781337399074
Author: John C. Kotz, Paul M. Treichel, John Townsend, David Treichel
Publisher: Cengage Learning
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Question
Chapter 10, Problem 102IL
Interpretation Introduction

Interpretation:

The percent composition by mass of Na2CO3 and NaHCO3 in the mixture should be calculated.

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.

Expert Solution & Answer
Check Mark

Answer to Problem 102IL

The percent composition by mass of Na2CO3 in the mixture is 57.6% and the weight percentage for NaHCO3 in the mixture is 42.4%.

Given:

  Total amount of the mixture = 2.50 gVolume of CO2=665mL=665×10-3LPressure of CO2=735mmHg=735mmHg760mmHg=0.967atmTemperature of CO2= 25oC = 273.15K+25=289.15K

Explanation of Solution

The balanced chemical equation for the reaction of the two given gases with HCl is as follows,

  NaHCO3+HClNaCl+H2O+CO2Na2CO3+HCl2NaCl+H2O+CO2

First using the ideal gas equation the moles of CO2 produced is calculated as follows,

Here, we carry an extra significant figure throughout this calculation to limit rounding errors.

   nCO2=PVRT =(0.967atm)(665×10-3L)(0.0821L.atmK.mol)(289.15)K=0.02709molCO2

From the balanced chemical equation it is clear that one mole of both the gases gives rise to one mole of CO2 hence, the total calculated amount of 0.02709molCO2 should be then produced by 0.02709mol of gases present in the given mixture.

Hence, there exists 1:1 mole ratio between CO2 and both reactants (Na2COand MgCO3), which show that 0.02709 of the mixture must have reacted.

molNa2CO3+molNaHCO3=0.02709mol

Let x be the mass of Na2CO3 in the mixture, then (2.50- x) is the mass of NaHCOin the mixture.    (xgNa2CO3×1molNa2CO3105.99gNa2CO3)+[(2.50-x)gMgCO3×1molNaHCO384.007gNaHCO3]=0.08436mol

  9.4349×10-3x+(2.50-x)0.012 = 0.027099.435×10-3x+0.03-0.012x = 0.02709-2.565×10-3x = -3.7×10-3x = 1.44gx = 1.44 g = mass of Na2CO3 in the mixture

The mass of the remaining NaHCO3 in the mixture is determined by subtracting the amount of Na2CO3 from the total amount of the mixture as follows gives the mass of the other gas present in the mixture.

  2.50g1.44g=1.66g

Determine the percent composition by mass of Na2CO3 in the mixture as follows,

  mass%Na2CO3=massNa2CO3massofmixture×100%=1.44 g2.50 g×100%=57.6%

Similarly, the weight percentage for the other gas in the mixture is as follows,

  mass%NaHCO3=massNaHCO3massofmixture×100%=1.06 g2.50 g×100%=42.4%

The percent composition by mass of Na2CO3 in the mixture is calculated using the ratio between massNa2CO3 and mass of mixture.  The mass of Na2CO3 in the mixture is

  33.1%Na2CO3

Conclusion

The percent composition by mass of two given gases in the mixture was calculated by using the ideal gas equation and the expression used for moles calculation.

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Chapter 10 Solutions

Chemistry & Chemical Reactivity

Ch. 10.6 - Prob. 10.11CYUCh. 10.7 - Prob. 10.12CYUCh. 10.8 - Prob. 1.1ACPCh. 10.8 - Prob. 1.2ACPCh. 10.8 - At sea level, atmospheric pressure is 1.00 atm....Ch. 10.8 - Prob. 2.2ACPCh. 10.8 - To stay aloft, a blimp must achieve neutral...Ch. 10.8 - Nitrogen gas is produced not only by NaN3...Ch. 10.8 - Prob. 3.2ACPCh. 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. What is the...Ch. 10 - A flask is first evacuated so that it contains no...Ch. 10 - Prob. 20PSCh. 10 - Prob. 21PSCh. 10 - Prob. 22PSCh. 10 - Forty miles above Earths surface, the temperature...Ch. 10 - Prob. 24PSCh. 10 - A gaseous organofluorine compound has a density of...Ch. 10 - Prob. 26PSCh. 10 - A 1 007-g sample of an unknown gas exerts a...Ch. 10 - A 0.0130-g sample of a gas with an empirical...Ch. 10 - A new boron hydride, BxHy, has been isolated. 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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