The experiment was to take 7 test tubes, put 5mL of HCl and 5mL of H2O in the fi

Question

The experiment was to take 7 test tubes, put 5mL of HCl and 5mL of H2O in the first test tube, then 9mL of water for the initial in test tubes 2-7. Pour 1 mL of test tube 1 into 2, then pour 1mL from test tube 2 to 3, and so fourth. Then the following question is asked,

The pH of the test tube can be calculated by knowing the concentration of hydrogen ions (or hydronium molecules) in solution. The pH = -log10([H+]). For example, the 0.1 M stock of HCl has a pH = -log10(0.1) = 1. Based on the dilution, what is the pH of tube 7? Choose the closest answer.

Explanation / Answer

In the test tube No1 you are diluting 0.1M HCl with an equal quantity of water. This halves the concentration. You now have 0.05M HCl. because HCl dissociates completely, [H+] = 0.05M
pH = - log [H+]
pH = -log 0.05
pH = 1.30

You are then diluting the contents of test tube 1 10 fold successively: This has the effect of 1) reducing the concentration to 1/10th of the preceding test tube, 2) increasing the pH by 1 unit in each tube.
You can make the following table without any further calculations

Test tube 1 concentration = 0.05M , pH = 1.30
Test tube 2 concentration = 0.005M , pH = 2.30
Test tube 3 concentration = 0.0005M , pH = 3.30
Test tube 4 concentration = 0.00005M , pH = 4.30
Test tube 5 concentration = 0.000005M , pH = 5.30
Test tube 6 concentration = 0.0000005M , pH = 6.30
Test tube 7 concentration = 0.0000005M , pH = 7.0

The only tube to be careful with is tube 7 - the pH cannot be 7.3 as the pattern suggests An acid solution cannot have pH > 7.0. There is a very complex calculation and theory about what the pH of this solution will be, but I think that it is well beyond your undestanding at this stage. You can accept that it is just below 7.00 pH.

Bromothymol blue is an indicator that is yellow in a solution where pH <6.0, and blue where pH > 7.6 . Between these two values it is changing from yellow green to green blue. Therefore in tubes 1 - 5 it will be yellow and tubes 6&7 it will be green/ blue.

If you have to repeat this with NaOH, I think that you should be able to do this yourself, remember that the pOH of 0.05M soltion of NaOH will be 1.30 and the pH will be 14.00-1.30 = 12.70.
The final tube 7 will have pH just above 7.00 and pOH just below 7.00.

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