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Author Topic: Problem of the week - 25/02/2013  (Read 1751 times)

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Borek

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Problem of the week - 25/02/2013
« on: February 25, 2013, 02:01:07 AM »

Silver nitrate solution was added to 10 mL of sodium sulfate solution. Assuming concentrations of both solutions were high enough to produce a precipitate, at what volume of the AgNO3 added amount of solid is at its maximum?
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SinkingTako

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Re: Problem of the week - 25/02/2013
« Reply #1 on: March 02, 2013, 05:21:38 AM »

this Is probably wrong, but Is it 20ml?
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Borek

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Re: Problem of the week - 25/02/2013
« Reply #2 on: March 02, 2013, 06:47:18 AM »

Please show how you got this result.
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SinkingTako

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Re: Problem of the week - 25/02/2013
« Reply #3 on: March 02, 2013, 02:33:33 PM »

Let [Ag] and [SO4] be the initial concentration of the 2 ions in the various solutions.

Let the amount of AgNO3 solution added be Xml

When combined, [tex][Ag]new= \frac{x[Ag]}{x+10}[/tex], [tex][SO_4]new= \frac{10[SO_4]}{x+10}[/tex]

Thus, [tex]Ksp = \frac{10x^2[Ag]^2[SO_4]}{(x+10)^3}[/tex]

[Ag]2[SO4]=1.2x10-5 (Actually specific value doesn't matter)

Sub this into the Ksp equation, then max X is when [tex]\frac{d}{dx}  \frac{10x^2×1.2×10^{-5} }{(x+10)^3}=0[/tex]

Solving, X=20.
« Last Edit: March 02, 2013, 10:57:16 PM by Borek »
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Borek

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Re: Problem of the week - 25/02/2013
« Reply #4 on: March 02, 2013, 10:57:02 PM »

Perfect!

Funny how the result doesn't depend on the initial concentrations nor the Ksp. Also, while the differential looks rather unpleasant, finding the maximum is quite simple - it is enough to compare the numerator to zero and it is just x(x-20)=0.

I am correcting a typo in your LaTeX - 10^(-5) is not equivalent to 10^{-5}.
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Re: Problem of the week - 25/02/2013
« Reply #5 on: March 03, 2013, 12:13:00 AM »



I am correcting a typo in your LaTeX - 10^(-5) is not equivalent to 10^{-5}.

Thanks! Was actually trying to figure out why the ^-5 couldn't be displayed correctly, but couldn't find the problem.
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Re: Problem of the week - 25/02/2013
« Reply #6 on: March 03, 2013, 12:55:51 AM »

In LaTeX {} are used for grouping of symbols, () are treated like every other character.
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