How to tell between when to add solution or not?

[Sammy1024]

I've done a bunch of questions in acids and bases (and some other topics) where sometimes they will use the total solution amount and sometimes the "total solution amount".

I did the following question:

And calculated it to be exactly 3.0, but the answer is D because the total solution is 110 mL. I used a variation of the MV = MV equations where it was 10 mL on one side and 100 mL on the other. How do you tell when to use the total solution amount, which is 110 mL vs. 100 mL? Do you always use the total solution amount?

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[Czarcasm]

I've done a bunch of questions in acids and bases (and some other topics) where sometimes they will use the total solution amount and sometimes the "total solution amount".

I did the following question:

View attachment 184788

And calculated it to be exactly 3.0, but the answer is D because the total solution is 110 mL. I used a variation of the MV = MV equations where it was 10 mL on one side and 100 mL on the other. How do you tell when to use the total solution amount, which is 110 mL vs. 100 mL? Do you always use the total solution amount?

Whenever you are adding solvent to a solution, you should immediately recognize that it's a dilution problem. The scenario you are describing (the MV equation) can be useful in two situations. If you have say, 100mL of say, 10M Solution A and you want to know what the molarity is for 15mL of Solution A, you simply use M1V1=M2V2. Notice, these are two independent flasks of the same solutions with different concentrations. In this scenario, liquid is being added and based on what you know about molarity = moles/volume solvent, adding solvent will dilute the concentration. In this case, when using M1V1=M2V2 you must factor in the total volume to determine the final concentration. Notice the slight difference in the way we are using these equations. The first scenario, it's two flasks of solutions - we want to find concentration, but in this problem - we're considering initial and final conditions.

Personally, I prefer not to use the MV equation for this reason because I always make a careless mistake. Instead, I immediately solve for total moles. Then I find the total volume. From there, I calculate what the molarity will be. It's the same thing but you are more aware of what you're solving for (instead of route plugging and chugging). It avoids careless mistakes. So here, we're told pH = 2. Convert to molarity: 1x10^-2. Molarity = moles/volume. Volume initially is 10mL = 1x10^-3 L. Therefore, moles = MV = (1x10^-2)(1x10^-3L). Moles = 1x10^-5. The final volume: 10mL + 100mL = ~1x10^-1. So, final molarity=total moles/total volume> 1x10^-5 moles/1x10^-1 volume (L) = 10^-4 M. Convert this to pH: -log(1x10^-4), so pH =4 - a little less than 4 since we rounded volume to 0.1. (choice D). It seems like a lengthy process, but once you do this so many times, it becomes very straightforward. Hope this helps.

 

[Sammy1024]

Thanks for the detailed answer! This makes so much more sense! Thank you!

 

[Teleologist]

Whenever you are adding solvent to a solution, you should immediately recognize that it's a dilution problem.

Meh, adding solution to a solution is also dilution. What you're adding doesn't have to be pure solvent. I mention this because someone got screwed up by a question about what happens when they add NaCl solution to HCl solution or something like that.

 

[NextStepTutor_1]

I've done a bunch of questions in acids and bases (and some other topics) where sometimes they will use the total solution amount and sometimes the "total solution amount".

I did the following question:

View attachment 184788

And calculated it to be exactly 3.0, but the answer is D because the total solution is 110 mL. I used a variation of the MV = MV equations where it was 10 mL on one side and 100 mL on the other. How do you tell when to use the total solution amount, which is 110 mL vs. 100 mL? Do you always use the total solution amount?

To directly address your last 2 questions - it depends on the language they use in the question.
If they ask for the total or final conditions then you need to add the volumes of the solution in this example because the final condition depends on the absolute amount. However, if they wanted the change then you could subtract the two volumes.
Moral of the question: read the wording very carefully. Do not rush through it. Understand exactly what they ask.


Cheers!

 

[type12]

@Czarcasm and @NextStepTutor_1 are right: it's all in the wording. They added 100mL to the 10mL solution. You don't need to do the extensive math, as long as you catch that the final volume is over 100mLs. Why? because you are diluting the concentration by a little more than 10, but not more than 100, which lands you between the pHs of 3 and 4, but not exactly either.