Chemistry: The Molecular Nature of Matter and Change - Standalone book
Chemistry: The Molecular Nature of Matter and Change - Standalone book
7th Edition
ISBN: 9780073511177
Author: Martin Silberberg Dr., Patricia Amateis Professor
Publisher: McGraw-Hill Education
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Chapter 17.5, Problem 17.10AFP

(a)

Interpretation Introduction

Interpretation:

The equilibrium concentrations of [I2] and [I] at 600 K for the given halogen decomposition reaction has to be calculated.

Concept Introduction:

Equilibrium constant (Kc) is the ratio of the rate constants of the forward and reverse reactions at a given temperature.  In other words it is the ratio of the concentrations of the products to concentrations of the reactants.  Each concentration term is raised to a power, which is same as the coefficients in the chemical reaction.

Consider the reaction where A reacts to give B.

    aAbB

    Rate of forward reaction = Rate of reverse reactionkf[A]a=kr[B]b

On rearranging,

    [B]b[A]a=kfkr=Kc

Where,

    kf is the rate constant of the forward reaction.

    kr is the rate constant of the reverse reaction.

    Kc is the equilibrium constant.

(a)

Expert Solution
Check Mark

Explanation of Solution

Given data:

The decomposition reaction of halogen is,

  I2(g)  2I(g)

The equilibrium constant for the above reaction is Kc = 2.94×1010. For the above to reaction to occur 0.50 mol of I2 was heated in a 2.5 L vessel at 600 K.

Determination of concentration at equilibrium:

From the balanced equation, it is known that one mole of I2 decomposes to give two moles of iodine gas.

Calculate the initial concentration of I2 using the given moles.

  [I2]initial = moles of I2Volume =0.50 mol2.5 L =0.20 M

Determine the concentration of all reactants and product using the below table.

Conc. (M) I2(g)   2I(g)Initial 0.20 0Change -x +2xEquilibrium 0.20-x 2x¯

The equilibrium expression for the given reaction is,

  Kc  [I]2[I2]

Solve for x using the above expression and obtain the concentration of all reactants and products.

         Kc[I]2[I2]2.94×1010=[2x]2[0.20 - x]Assume x is negligible and 0.20 - x0.202.94×1010=[2x]2[0.20]             4x2 = (2.94×1010)(0.20) x=3.834×106 3.8×106

Check the assumption by calculating the % error.

  [Change][Initial]×1003.8×1060.20×100 =0.0019%

The above value is smaller than 5%.  Thus the assumption is valid.

At equilibrium,

  [I]eq  = 2x =2(3.834×106) =7.668×106 =7.7×106 M[I2]eq =0.20 - x =0.20 - 3.834×106 =0.199996 0.20 M

Therefore, the equilibrium concentrations of [I2] and [I] is,

[I]eq  7.7×106 M[I2]eq =0.20 M

(b)

Interpretation Introduction

Interpretation:

The equilibrium concentrations of [I2] and [I] at 2000 K for the given halogen decomposition reaction has to be calculated.

Concept Introduction:

Equilibrium constant (Kc) is the ratio of the rate constants of the forward and reverse reactions at a given temperature.  In other words it is the ratio of the concentrations of the products to concentrations of the reactants.  Each concentration term is raised to a power, which is same as the coefficients in the chemical reaction.

Consider the reaction where A reacts to give B.

    aAbB

    Rate of forward reaction = Rate of reverse reactionkf[A]a=kr[B]b

On rearranging,

    [B]b[A]a=kfkr=Kc

Where,

    kf is the rate constant of the forward reaction.

    kr is the rate constant of the reverse reaction.

    Kc is the equilibrium constant.

(b)

Expert Solution
Check Mark

Explanation of Solution

Given data:

The decomposition reaction of halogen is,

  I2(g)  2I(g)

The equilibrium constant for the above reaction is Kc = 0.209 .  For the above to reaction to occur 0.50 mol of I2 was heated in a 2.5 L vessel at 2000 K.

Determination of concentration at equilibrium:

From the balanced equation, it is known that one mole of I2 decomposes to give two moles of iodine gas.

Calculate the initial concentration of I2 using the given moles.

  [I2]initial = moles of I2Volume =0.50 mol2.5 L =0.20 M

Determine the concentration of all reactants and product using the below table.

Conc. (M) I2(g)   2I(g)Initial 0.20 0Change -x +2xEquilibrium 0.20-x 2x¯

The equilibrium expression for the given reaction is,

  Kc  [I]2[I2]

Solve for x using the above expression and obtain the concentration of all reactants and products.

        Kc[I]2[I2]0.209=[2x]2[0.20 - x]Assume x is negligible and 0.20 - x0.200.209=[2x]2[0.20]             4x2 = (0.209)(0.20) x=0.102225 0.102

Check the assumption by calculating the % error.

  [Change][Initial]×1000.1020.20×100 =51%

The above value is larger than 5% so the assumption is not valid.  Thus, solve using quadratic equation.

  [2x]2[0.20-x] =0.2094x2 + 0.209x - 0.0418 = 0 x =0.209±(0.209)24(4)(0.0418)2(4) =0.0793857 (or) 0.1316

Choose the positive root value, x = 0.0793857

At equilibrium,

  [I]eq  = 2x =2(0.0793857) =0.1587714 0.16 M[I2]eq =0.20 - x =0.20 - 0.0793857 =0.1206143 0.12 M

Therefore, the equilibrium concentrations of [I2] and [I] is,

  [I]eq  0.16 M[I2]eq =0.12 M

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Chapter 17 Solutions

Chemistry: The Molecular Nature of Matter and Change - Standalone book

Ch. 17.5 - Prob. 17.6AFPCh. 17.5 - Prob. 17.6BFPCh. 17.5 - Prob. 17.7AFPCh. 17.5 - Prob. 17.7BFPCh. 17.5 - Prob. 17.8AFPCh. 17.5 - Prob. 17.8BFPCh. 17.5 - Prob. 17.9AFPCh. 17.5 - Prob. 17.9BFPCh. 17.5 - Prob. 17.10AFPCh. 17.5 - Prob. 17.10BFPCh. 17.5 - An inorganic chemist studying the reactions of...Ch. 17.5 - A chemist studying the production of nitrogen...Ch. 17.6 - In a study of glass etching, a chemist examines...Ch. 17.6 - Prob. 17.12BFPCh. 17.6 - Prob. 17.13AFPCh. 17.6 - Prob. 17.13BFPCh. 17.6 - Prob. 17.14AFPCh. 17.6 - Should T be increased or decreased to yield more...Ch. 17.6 - Prob. 17.15AFPCh. 17.6 - Prob. 17.15BFPCh. 17.6 - Many metabolites are products in branched...Ch. 17 - Prob. 17.1PCh. 17 - When a chemical company employs a new reaction to...Ch. 17 - If there is no change in concentrations, why is...Ch. 17 - Prob. 17.4PCh. 17 - Prob. 17.5PCh. 17 - Prob. 17.6PCh. 17 - Prob. 17.7PCh. 17 - Prob. 17.8PCh. 17 - Prob. 17.9PCh. 17 - Does Q for the formation of 1 mol of NO from its...Ch. 17 - Does Q for the formation of 1 mol of NH3 from H2...Ch. 17 - Balance each reaction and write its reaction...Ch. 17 - Prob. 17.13PCh. 17 - Prob. 17.14PCh. 17 - Prob. 17.15PCh. 17 - At a particular temperature, Kc = 1.6×10−2...Ch. 17 - Prob. 17.17PCh. 17 - Balance each of the following examples of...Ch. 17 - Balance each of the following examples of...Ch. 17 - Balance each of the following examples of...Ch. 17 - Balance each of the following examples of...Ch. 17 - Prob. 17.22PCh. 17 - Prob. 17.23PCh. 17 - Prob. 17.24PCh. 17 - When are Kc and Kp equal, and when are they not? Ch. 17 - A certain reaction at equilibrium has more moles...Ch. 17 - Prob. 17.27PCh. 17 - Determine Δngas for each of the following...Ch. 17 - Prob. 17.29PCh. 17 - Prob. 17.30PCh. 17 - Prob. 17.31PCh. 17 - Prob. 17.32PCh. 17 - Prob. 17.33PCh. 17 - The following molecular scenes depict the aqueous...Ch. 17 - At 425°C, Kp = 4.18 × 10−9 for the...Ch. 17 - At 100°C, Kp = 60.6 for the reaction 2NOBr(g) ⇌...Ch. 17 - The water-gas shift reaction plays a central role...Ch. 17 - In the 1980s, CFC-11 was one of the most heavily...Ch. 17 - For a problem involving the catalyzed reaction of...Ch. 17 - What is the basis of the approximation that avoids...Ch. 17 - Prob. 17.41PCh. 17 - Gaseous ammonia was introduced into a sealed...Ch. 17 - Prob. 17.43PCh. 17 - Prob. 17.44PCh. 17 - Prob. 17.45PCh. 17 - Prob. 17.46PCh. 17 - Prob. 17.47PCh. 17 - Prob. 17.48PCh. 17 - Prob. 17.49PCh. 17 - Nitrogen dioxide decomposes according to the...Ch. 17 - Hydrogen iodide decomposes according to the...Ch. 17 - Compound A decomposes according to the...Ch. 17 - In an analysis of interhalogen reactivity, 0.500...Ch. 17 - A toxicologist studying mustard gas, S(CH2CH2Cl)2,...Ch. 17 - Prob. 17.55PCh. 17 - A key step in the extraction of iron from its ore...Ch. 17 - What does “disturbance” mean in Le Châtelier’s...Ch. 17 - Prob. 17.58PCh. 17 - Prob. 17.59PCh. 17 - Prob. 17.60PCh. 17 - Le Châtelier’s principle is related ultimately to...Ch. 17 - An equilibrium mixture of two solids and a gas, in...Ch. 17 - Consider this equilibrium system: CO(g) + Fe3O4(s)...Ch. 17 - Sodium bicarbonate undergoes thermal decomposition...Ch. 17 - Prob. 17.65PCh. 17 - Prob. 17.66PCh. 17 - Predict the effect of decreasing the container...Ch. 17 - Prob. 17.68PCh. 17 - Prob. 17.69PCh. 17 - Prob. 17.70PCh. 17 - Prob. 17.71PCh. 17 - Prob. 17.72PCh. 17 - Prob. 17.73PCh. 17 - The formation of methanol is important to the...Ch. 17 - Prob. 17.75PCh. 17 - The oxidation of SO2 is the key step in H2SO4...Ch. 17 - A mixture of 3.00 volumes of H2 and 1.00 volume of...Ch. 17 - You are a member of a research team of chemists...Ch. 17 - For the following equilibrium system, which of the...Ch. 17 - Prob. 17.80PCh. 17 - Prob. 17.81PCh. 17 - Prob. 17.82PCh. 17 - Prob. 17.83PCh. 17 - Prob. 17.84PCh. 17 - Prob. 17.85PCh. 17 - Prob. 17.86PCh. 17 - Prob. 17.87PCh. 17 - Prob. 17.88PCh. 17 - When 0.100 mol of CaCO3(s) and 0.100 mol of CaO(s)...Ch. 17 - Prob. 17.90PCh. 17 - Prob. 17.91PCh. 17 - Prob. 17.92PCh. 17 - Highly toxic disulfur decafluoride decomposes by a...Ch. 17 - A study of the water-gas shift reaction (see...Ch. 17 - Prob. 17.95PCh. 17 - Prob. 17.96PCh. 17 - Prob. 17.97PCh. 17 - Prob. 17.98PCh. 17 - Prob. 17.99PCh. 17 - Prob. 17.100PCh. 17 - The molecular scenes below depict the reaction Y ⇌...Ch. 17 - For the equilibrium H2S(g) ⇌ 2H2(g) + S2(g) Kc =...Ch. 17 - Prob. 17.103PCh. 17 - Prob. 17.104PCh. 17 - The kinetics and equilibrium of the decomposition...Ch. 17 - Isopentyl alcohol reacts with pure acetic acid to...Ch. 17 - Isomers Q (blue) and R (yellow) interconvert. They...Ch. 17 - Glauber’s salt, Na2SO4·10H2O, was used by J. R....Ch. 17 - Prob. 17.109PCh. 17 - Synthetic diamonds are made under conditions of...
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