I have $100\ \mathrm{L}$ of water in a tank with an mixer inside and want to know how fast the tank mixes at a given rpm-setting. I am adding $50\ \mathrm{mL}$ of $2\ \mathrm{N}\ \ce{HCl}$ and see how long the $\ce{pH}$ goes to down to an equilibrium. Then I add $50\ \mathrm{mL}$ of $2\ \mathrm{N}\ \ce{NaOH}$ to the solution and wait for the $\ce{pH}$ to come to an equilibrium $\ce{pH}$. I feel like the 2 times should be the same, but acid mixes much faster than base in all cases. Why?

The time for $\ce{pH}$ to change from $7$ to $4$ is always less than time for $\ce{pH}$ to change from $4$ to $7$ in the same tank at the same rpm.

Any theories regarding why?

  • $\begingroup$ How do you test the pH change? Also, what is "eve"? $\endgroup$ – SendersReagent May 5 '16 at 0:10
  • $\begingroup$ pH probes are being used fr monitoring pH.. Not sure what you mean by "eve" .. RPM= rotations per min of the impeller/mixer $\endgroup$ – Suresh May 5 '16 at 11:24
  • $\begingroup$ You had "eve" as one of your tags. It has apparently been edited out. If you were doing chemical analysis of pH, I would have guessed a slower base reaction than acid reaction. Don't know enough about pH meters to know if that's a possibility. $\endgroup$ – SendersReagent May 5 '16 at 11:34
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    $\begingroup$ The analysis is slightly skewed. Please do the confirmation experiment of adding $50~\mathrm{ml}\ 2~\mathrm{M}\ \ce{NaOH}$ to $100~\mathrm{ml}$ of water and compare that time to adding $50~\mathrm{ml}\ 2~\mathrm{M}\ \ce{HCl}$. $\endgroup$ – Jan May 5 '16 at 12:03
  • $\begingroup$ Could it simply be that you are adding 50 mls of acid to 100 mls of water and then 50 mls of base to 150 mls of solution? Time for mixing in a larger volume? Do as @Jan says, and time base into water, followed by acid into the solution and compare your times.. $\endgroup$ – Leeser May 5 '16 at 18:10

You cannot compare the rate of first mixing acid with water with the rate of mixing the base with the diluted acid. You should compare the rate of mixing the acid with water with the rate of mixing the base with water instead.

The reason is that adding the base to the diluted acid will neutralize portions of the base during the mixing process resulting in lower concentration gradients that make the mixing slower.

A simple gedankenexperiment will show this. Consider a cylindrical tank with water of volume 1 with a mixing rod along the axis. Now put an amount of 1 acid into the tank along its axis. When the acid has made half the way to the wall of the tank the concentration in the inner volume is 4. The gradient is 4.

Now think of adding an amount of 1 base to the completely mixed diluted acid. When the base has made half the way to the wall of the tank, 1/4 of the base has already been neutralized. The concentration in the inner volume is 3. The gradient is only 3 compared to 4 before.

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  • $\begingroup$ For those of us not inclined towards sesquipedalianism, "gedankenexperiment" just means "thought experiment". $\endgroup$ – gsurfer04 May 6 '16 at 11:46
  • $\begingroup$ Thank you for all the responses. A few important things -- 1. We are adding very little acid/base to a lot of water 2. The mixing is completely impeller driven and not acid/base dispersion driven. We add the acid - it mixes 100% in 5 mins wait for 30 while the impeller turned on, then add the base do the same.. $\endgroup$ – Suresh May 6 '16 at 12:57

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