# Homework Help: Ksp of Calcium Hydroxide - A Percentage Error of 480%?

1. Jan 4, 2009

### Celer

Ksp of Calcium Hydroxide - A Percentage Error of 480%??

1. The problem statement, all variables and given/known data

I did a titration between HCl and Ca(OH)2. I use the indicator Phenopthalein I did most of my calculations and thru repeated checking cannot find any significant error in my calculations.

However, upon calculating the percentage error of this experiment, I got a whooping 488% error! I have no idea what kind of errors would cause such as huge percentage. I have never seen such a huge percentage myself.

2. Relevant equations

C = n/v to first calculate moles of HCl (C = 0.05 M)
Mole ratios to find moles of Ca(OH)2
C= n/v again to find concentration of Ca(OH)2
that would also be concentration of Ca2+ ions
x2 of concentration to find concentration of OH- ions
Ksp = [Ca][OH]^2

3. The attempt at a solution
These are my calculations and the data...

19 ml of HCl with concentration of 0.05 M
25 ml of Ca(OH)2

Setting up a titration between them using phenolpthalein in Ca(OH)2. HCl is dripped into the flask till pink color of pheno appears.

So calculations, I find out HCl moles is = 9.75 x 10^-4 mols
and thru stoichiometry, we find out Ca(OH)2 has half of that, 4.875 x 10^-4

and calculating that, concentraition of Ca(OH)2 is 0.01948 M

So Ca2+ concentration is 0.0198M
and
OH- concentration is double that, so 0.0389M

Setting up Ksp = [Ca][OH]^2
Ksp = 2.95 x 10^-5

Accepted Value* for Ksp of Ca(OH)2: 5.02 x 10-6

% error = ((experimental value – accepted value) / (accepted value)) x 100%
= 488%

What possible errors would cause such a huge percentage?

Acid or base was left on the sides of the flask, or at the tip of the burette used, measurement errors, air bubbles etc. should be relatively minor errors right?

2. Jan 4, 2009

### Staff: Mentor

Re: Ksp of Calcium Hydroxide - A Percentage Error of 480%??

You should account for ionic strength and activity coefficients, your error will be much smaller then.

See ionic strength & activity coefficients.

3. Jan 4, 2009

### Celer

Re: Ksp of Calcium Hydroxide - A Percentage Error of 480%??

I tried reading it, but I don't think my teacher have taught up to there yet...

Is there another way to talk about ionic strength, and activity coefficients so that they kind of make sense in the context of this question?

Thanks.

4. Jan 4, 2009

### Staff: Mentor

Re: Ksp of Calcium Hydroxide - A Percentage Error of 480%??

You may try to google other sites, perhaps other way of explaining the problem will better suit you.

Basically in all expressions for equilibrium constants - like Ka, Kb, Kso and so on - you should use not concentrations, but activities. Page I have linked to shows how to calculate activity. First, you have to calculate ionic strength of the solution. In this case it will be just

$$I = \frac 1 2 (2^2[Ca^{2+}]+1^2[OH^-])$$

Then it is just a matter of putting I and charges into Debye-Huckel equation to calculate logs of activity coefficients (different one for Ca2+ and different one for OH-, that's because they are function of both ionic strength and charge of ion). You have to calculate f1 - activity coefficient for all singly charged ions (regardless of whether they are positively or negatively charged) and f2 - activity coefficient for all double charged ions.

And as activity of an ion is just a concentration times activity coefficients, Kso looks like

$$K_{so} = f_2 [Ca^{2+}] (f_1[OH^-])^2$$

Here comes tricky part, as ionic strength is calculated using concentrations, which can be calculated once you know activity coefficients, which you can calculate when you know ionic strength, which you can calculate when you know concentration... and so on. Best approach is as follows:

Assume activity coefficients equal 1.

repeat:
{
Calculate concentrations from Kso.

Calculate ionic strength.

Calculate activity coefficients.
} until results between actual and previous step are almost identical.

Most likely it will be enough to do the calculations twice or thrice. That'll give you real concentrations - ones that are determined by titration.

5. Jan 5, 2009

### chemisttree

Re: Ksp of Calcium Hydroxide - A Percentage Error of 480%??

Huh? It should have been real pink at the start and the color should have faded when you added the HCl. Are you sure you titrated using HCl and not an unknown solution of Ca(OH)2? Think about the kind of error you might see if you had this backwards...

6. Jan 10, 2009

### Rami.makhlout

Re: Ksp of Calcium Hydroxide - A Percentage Error of 480%??

the error is in the indicator u should use black T or methyl orange
since u r using a weak base
phenolphthalaien does not work

Last edited: Jan 10, 2009
7. Jan 10, 2009

### chemisttree

Re: Ksp of Calcium Hydroxide - A Percentage Error of 480%??

Ca(OH)2 has a pH of around 12-13 in water. Phenolphthalein is appropriate to use as an indicator.

8. Jan 10, 2009

### Staff: Mentor

Re: Ksp of Calcium Hydroxide - A Percentage Error of 480%??

Ca(OH)2 has low solubility, but it is a strong base - ie its total concentration is not high, but whatever is dissolved it is fully dissociated.

9. Jan 11, 2009

### Rami.makhlout

Re: Ksp of Calcium Hydroxide - A Percentage Error of 480%??

then the error wil be in the dissolved amount. if not all the solid was dissolved then the experiment will give this error

10. Jan 11, 2009

### Staff: Mentor

Re: Ksp of Calcium Hydroxide - A Percentage Error of 480%??

I am afraid you are wrong again. Assuming solution was not saturated, measured Kso should be lover than expected, not 5 times higher.