problem with Topscore question.

[Smooth Operater]

what volume of HCl was added if 20 mL of 1 M NaOH is titrated with 1 M HCl to produce a pH = 2?

the answer is 20.4 mL accroding to topscore. But I am not how to claculate it even after seeing the solution. Can anyone explain step by step on how would you calculate this problem. Thanks1!!

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[denteng]

what volume of HCl was added if 20 mL of 1 M NaOH is titrated with 1 M HCl to produce a pH = 2?

the answer is 20.4 mL accroding to topscore. But I am not how to claculate it even after seeing the solution. Can anyone explain step by step on how would you calculate this problem. Thanks1!!

1) calculate how many mL of HCl needed to neutralize the NaOH, so that you reach a pH of 7. (0.020L)

2) Keep in mind HCl is a strong acid, and fully dissociates. Working backwards, you want a pH of 2, which means a 0.01mol/l solution of H+. Remember that you already have 40mL of solution from step 1, meaning that you need to add 4e-4 mol of H+ to reach a concentration of 0.01 (which gives you a pH of 2.0...). If you have trouble with this step, just set it up in an algebraic manner, where you know you need 0.01M = ???/0.040L which will give you 4e-4.

3) Knowing you need 4e-4 mol of H+, and you have a 1M solution of HCl, you calculate 0.0004L of the solution needs to be added.

4) Remember you added 20mL from step #1, and 0.4mL from step 3, you have your answer of 20.4mL

Hope it helps.

 

[denteng]

...just set it up in an algebraic manner, where you know you need 0.01M = ???/0.040L which will give you 4e-4.

3) Knowing you need 4e-4 mol of H+, and you have a 1M solution of HCl, you calculate 0.0004L of the solution needs to be added.

Thought I would point out that this is not entirely correct, as it is an assumption you have 40mL of existing solution to reach a pH of 2.0, where in fact you do not know the end solution amount (which really is slightly greater than 40mL -- i.e. 40mL + x).

However, since you're using a rather concentrated 1.0M HCl solution, you can make the assumption that the additional volume can be deemed to be almost negligible.

Keep in mind the DAT would never test you with multivariate problems of this nature, but thought I would mention the assumption being made for completeness' sake.

Hope it helps.