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The rate for the reaction OH-Aq+NH4+Aq→H2Ol+NH3Aq is first order in both OH2 and NH4- concentrations, and the rate constant k at 20°C is 3.4 × 1010 L mol21 s21 . Suppose 1.00 L of a 0.0010 M NaOH solution is rapidly mixed with the same volume of 0.0010 M NH4Cl solution. Calculate the time (in seconds) required for the OH2 concentration to decrease to a value of 1.0 × 10-5M.

Short Answer

Expert verified

The time required for the decrease of hydroxide ion concendration is2.9×106s

Step by step solution

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01

Concendration of  NaOH:

1.00L volume of 0.0010M is mixed with 1.00L of 0.0010M of NH4Cl,the volume of the solution becomes double (2.00L),

InitialconcendrationofNaOHC0=0.0010M2C0=0.0005M

01

Rate expression:

Integrated rate expression for the seacond order reaction in which both the reactents are of first order is given by

1ϑ=1C0-1Ct=kt.........1

Where C0 is the initial concendration and Ct is the final concendration ,k is the rate constant ,t is the time in seaconds.

02

Concendration of  NaOH:

1.00L volume of 0.0010M is mixed with 1.00L of 0.0010M of NH4Cl,the volume of the solution becomes double (2.00L),so the initial concendration of NaOH is

InitialconcendrationofNaOHC0=0.0010M2C0=0.0005M

03

Time required for the reaction:

According to given data

InitialconcendrationC0=0.0005MC0=0.0005molL-1FinalconcendrationCt=1.0×10-5MCt=1.0×10-5molL-1k=3.4×1010Lmols-1νOH-,NH4+=1Substitutingthesevaluesinequation-11ϑ=1C0-1Ct=kt.........111=11.0×10-5molL-1-10.0005molL-1=kt.........111=11.0×10-5-10.00051molL-1=3.4×1010Lmols-1×tt=0.29100000-2000×10-10st=2.9×10-6s

Therefore time required for the reaction to occur is2.9×10-6s

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