[Big-Daddy]

In an acid-base problem, given the Kw of the solution and the current concentration of [H₃O⁺], how does one work out the true value of [H2O] at equilibrium in the solution?

This value is assumed to be around 55.35 M when [H₃O⁺] is taken as 0 (and [OH^-] is also taken as 0). But how can [H₂O] be accurately calculated as a relation to [H₃O⁺] and Kw, e.g. in a solution where it is significantly below 55.35 M?

[Borek]

If it is significantly different the exact doesn't matter much, as activity coefficients are far from unity.

Technically you should take into account solution density, calculate the solution mass, subtract masses of all ions present, whatever is left is water - and knowing volume you can calculate concentration.

[Big-Daddy]

If it is significantly different the exact doesn't matter much, as activity coefficients are far from unity.

Technically you should take into account solution density, calculate the solution mass, subtract masses of all ions present, whatever is left is water - and knowing volume you can calculate concentration.

So would the correct process to go about be: find the mass of the solution (number of moles of everything * Mr), find the density (mass/volume), and then ... the problem is that I don't know how many moles of H2O there are yet, and I can't work out the solution mass without that information.

e.g. let's say I add 20M HCl to water. (Assume HCl is strong, water is pure, the form of the H⁺ ion in water is indeed H₃O⁺, Kw = 1.00*10^-14). And yes, I know the pH of this is impossible to work out by theoretical means. But since H₃O⁺ can be worked out easily, [H₂O] should also be possible to find?) how can I find the [H₂O] after addition of HCl then?

[Borek]

e.g. let's say I add 20M HCl to water

To how much water? You don't know how much water? Than you can't calculate anything.

Problem - as worded now - is incomplete.

[Big-Daddy]

0.6 dm³ of water, which has a density of 1gcm^-3 as per normal. As for the quantity of HCl, let's go with 0.2 dm³. Is that enough information to complete the problem?

[Borek]

Yes, now it is not a problem, but you still need density of the solution - that has to be checked in tables.

You start with 600 g of water plus 0.2L of 20 M HCl solution. You can easily calculate mass of HCl in the solution, check density and you will be able to calculate total mass of the HCl solution and mass of water there. Now mix these solutions - mass of HCl doesn't change, total mass of water is just a sum of masses. Assume all HCl is dissociated - that gives you number of moles of H₃O⁺, as you knew number of moles of H₂O you are just a subtraction away from the answer. If you need to convert it to concentration - you will need density tables again, preferably based on %w/w concentration, as that's what you can easily calculate from known masses.

[Big-Daddy]

Yes, now it is not a problem, but you still need density of the solution - that has to be checked in tables.

You start with 600 g of water plus 0.2L of 20 M HCl solution. You can easily calculate mass of HCl in the solution, check density and you will be able to calculate total mass of the HCl solution and mass of water there. Now mix these solutions - mass of HCl doesn't change, total mass of water is just a sum of masses. Assume all HCl is dissociated - that gives you number of moles of H₃O⁺, as you knew number of moles of H₂O you are just a subtraction away from the answer. If you need to convert it to concentration - you will need density tables again, preferably based on %w/w concentration, as that's what you can easily calculate from known masses.

OK, please tell me where to go from where I am:

Mass of HCl = 0.2dm3*20moldm-3*(1+35.5)gmol-1=142 g
Mass of H2O original = 600g
Mass of HCl solution = 600g+142g=742g

Where do I go from there?

[Borek]

Mass of HCl = 0.2dm3*20moldm-3*(1+35.5)gmol-1=142 g

OK

Mass of H2O original = 600g

OK

Mass of HCl solution = 600g+142g=742g

No. You have ignored water that was present in the 20M HCl solution.

Note that typical commercially available HCl is around 12 M (about 38% w/w), so you may have problems finding the density of the 20 M solution.

Density of stock solutions is around 1.18 g/mL.

[Big-Daddy]

Mass of HCl = 0.2dm3*20moldm-3*(1+35.5)gmol-1=142 g

OK

Mass of H2O original = 600g

OK

Mass of HCl solution = 600g+142g=742g

No. You have ignored water that was present in the 20M HCl solution.

Note that typical commercially available HCl is around 12 M (about 38% w/w), so you may have problems finding the density of the 20 M solution.

Density of stock solutions is around 1.18 g/mL.

I see - so there is no way of calculating the mass of the new solution, or [H₂O] in the original HCl, and this value must simply be taken from a table listing these values (experimentally determined I presume?) for HCl?

[Borek]

I see - so there is no way of calculating the mass of the new solution, or [H₂O] in the original HCl, and this value must simply be taken from a table listing these values (experimentally determined I presume?) for HCl?

Calculating mass of the final solution is not a problem if you know mass (or density) of the initial solution. But in general yes, you need density tables as I was telling you from the very beginning.

[Big-Daddy]

I see - so there is no way of calculating the mass of the new solution, or [H₂O] in the original HCl, and this value must simply be taken from a table listing these values (experimentally determined I presume?) for HCl?

Calculating mass of the final solution is not a problem if you know mass (or density) of the initial solution. But in general yes, you need density tables as I was telling you from the very beginning.

You already have the mass, and the volume for the initial solution (both for water and HCl). After you combine them, if you were given the volume of the new solution, and seeing as you already have the mass, could you then calculate density and proceed without using the tables?