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Chapter 8: Q10P (page 183)

Including activity coefficient, find [Hg22+]in saturated Hg2Br2in localid="1654854633986" 0.00100MKBr .

Short Answer

Expert verified

The concentration of Hg22+in saturated Hg2Br2in 0.00100MKBr is7脳10-17M

Step by step solution

01

Step 1:Finding the activity coefficient of aqueous solution (Hg22+) and (Br-).

In the given problem, we need to find the activity coefficient along with concentration of Hg22+in saturated in Hg2Br2in0.00100MKBr.

The solubility of is not quite expressed. So we will assume that,

渭=0.001M=cBr-

From the Table 8-1, we can know that the values are,

渭Hg2+=0.867渭Br-=0.964

02

Finding the concentration of (Hg22+) using equilibrium constant equation.

Now, we will use equilibrium constant equation,

Ksp=5.6脳10-23Ksp=cHg22+渭Hg2+脳c2Br-5.6脳10-23=cHg22+脳0.867脳0.0012脳0.9642cHg22+=7脳10-17M

Thus, the concentration ofHg22+in saturatedHg2Br2in localid="1654855580714" 0.00100MKBris7脳10-17M

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Most popular questions from this chapter

Solubility with Activity: Find the concentration of the major species in a saturated aqueous solution of LiF. Consider these reactions:

LiFs謴Li++F-Ksp=Li+纬Li+F-纬F-LiFs謴LiFaqKionpair=LiFaq纬尝颈贵aqF-+H2O謴HF+OH-Kb=KwKaforHFH2O謴KwH++OH-Kw=H+纬H+OH-纬OH-

  1. Look up the equilibrium constants in the appendixes and write their pK values. The ion pair reaction is the sum of localid="1654945209684" LiFs謴Li++F-from the Appendix FandLi+謴LiFaqfrom Appendix J. write the equilibrium constant expressions and the charge and mass balance.
  2. Create a spreadsheet that uses activities to find the concentration of all species and the ionic strength. Use pH and pOH as independent variables to estimate. It does not work to choose pH and pLi because their concentration fixes that of the other through the relation Ksp=Li+纬Li+F-纬F-

Systematic treatment of equilibrium for ion pairing. Let鈥檚 derive the fraction of ion pairing for the salt in Box 8-1, which are 0.025FNaCI,Na2SO4,MgCI2,MgSO4. Each case is somewhat different. All of the solutions will be near neutral pH because hydrolysis reactions of Mg2+,SO2-4,Na+,CI-have small equilibrium constants. Therefore, we assume that H+=OH-and omit these species from the calculations. We work MgCI2as an example and then you asked to work each of the others. The ion-pair equilibrium constant, Kipcomes from Appendix J.

Pertinent reaction:

Mg2+CI-謴MgCI+aqKip=MgCI+aq纬MgCI+Mg2+纬Mg2+CI-纬CI-logKip=0.6.pKip=-0.6鈫�A

Charge balance (omitting H+,OH-whose concentrations are both small in comparison with Mg+,MgCI+,CI-:

role="math" localid="1655088043259" 2Mg2-+MgCI+=CI-鈫�B

Mass balance:

Mg2-+MgCI+=F=0.025M鈫�CCI-+MgCI+=2F=0.050M鈫�D

Only two of the three equations (B),(C) and (D) are independent. If you double (c) and subtract (D) , you will produce (B). we choose (C) and (D) as independent equations.

Equilibrium constant expression : Equation (A)

Count : 3 equations (A,C,D) and 3 unknowns Mg2+,MgCI+,CI-

Solve: We will use Solver to find

numberofunknowns-numberofequiliberia=3-1=2unknown concentrations.

The spreadsheet shows the work. Formal concentration F=0.0025Mappears in cell G2. We estimate pMg2+,pCI-in cell B8and B9. The ionic strength in cell B5is given by the formula in cell H24. Excel must be set to allow for circular definitions as described on page role="math" localid="1655088766279" 179. The sizes of role="math" localid="1655088853561" Mg2+,CI-are from Table 8-1and the size of MgCI+is a guess. Activity coefficient are computed in columns E,F. Mass balance b1=F-Mg2+-MGCI+,b2=2F-CI--MgCI+appears in cell H14,H15, and the sum of squares b21+b22 appears in cell H16. The charge balance is not used because it is not independentof the two mass balances.

Solver is invoked to minimizes b21+b22in cell H16be varying pMg2+,pCI-in cells B8and B9. From the optimized concentration, the ion-pair fraction =MgCI+F=0.0815is computed in cell D15.

The problem: Create a spreadsheet like the one for MgCI+to find the concentration, ionic strength, and ion pair fraction in 0.025MNaCI. The ion pair formation constant from Appendix J is log Kip=10-0.5for the reaction Na++CI-謴NaCIaq. The two mass balances are Na++NaCIaq=F,Na+=CI-Estimate pNa+,pCI- for input and then minimizes the sum of square of the two mass balances.

(a) Following the example of Mg(OH)2 in Section 8-5, write the equations needed to find the solubility of Ca(OH)2. Include activity coefficients where appropriate. Look up the equilibrium constants in Appendixes F and I.

(b) Suppose that the size of CaOH+= Ca(H2O)5(OH)+ is 500 pm. Including activity coefficients, compute the concentrations of all species, the fraction of hydrolysis (= [CaOH+]/{[Ca2+] + [CaOH+]}), and the solubility of Ca(OH)2 in g/L. The Handbook of Chemistry and Physics lists the solubility of Ca(OH)2 as 1.85 g/L at 00C and 0.77 g/L at 1000C

Calculate the activity coefficient of AI3+when role="math" localid="1654836623327" 渭=0.083Mby using linear interpolation in Table 8-1 .

Using activities, calculate the pH of a solution containing 0.010 M NaOH plus 0.012 0 M LiNO3 . What would be the pH if you neglected activities?
See all solutions

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