sig figs

[sam0001]

A student wishes to determine the purity of a sample of calcium carbonate. The student dissolves a 1.15g same of calcium carbonate in water in a 250ml flask, and adds 50.0ml of 1.00M HCl. The student then adds deionized water up till the mark. A 20.00ml aliquot of this solution is pipetted into a conical flask. The mixture is titrated with a .100M standard solution of NaOH. The average titre was 22.33 ml. What is the percentage purity of the calcium carbonate?

bit iffy with the sig figs here. what are you guys getting as an answer?

[thushan]

A student wishes to determine the purity of a sample of calcium carbonate. The student dissolves a 1.15g same of calcium carbonate in water in a 250ml flask, and adds 50.0ml of 1.00M HCl. The student then adds deionized water up till the mark. A 20.00ml aliquot of this solution is pipetted into a conical flask. The mixture is titrated with a .100M standard solution of NaOH. The average titre was 22.33 ml. What is the percentage purity of the calcium carbonate?

bit iffy with the sig figs here. what are you guys getting as an answer?

n(HCl)excess,aliquot = 0.100 x 0.02233 = 0.00223 mol
(0.002233, use this value. quote answer to 3 sf as 0.100 is 3 sf and 0.002233 is 4sf)

n(HCl)excess,volumetric = n(HCl)excess,aliquot x 250/20.00 = 0.0279 mol
(0.0279125. quoted answer to 3 sf as 0.00223 is 3 sf, 250 is 3sf and 20.00 is 4 sf)

n(HCl)react = n(HCl)added - n(HCl)excess,volumetric
                  = 1.00 x 0.0500 - 0.0279
                  = 0.0500 - 0.0279
                  = 0.0221 mol
(0.0220875. quoted answer to 4 DECIMAL PLACES as 0.0500 is to 4 dp and 0.0279 is to 4 dp. When subtracting, your answer is to the least number of DECIMAL PLACES)

%(CaCO3) = (0.0221/2 x (40.1 + 12.0 + 48.0))/1.15
                 = (0.0221/2 x 100.1)/1.15
                 = 0.961 (96.1%)

(0.961286413. Put to 3 sf as 0.0221 is to 3 sf, 2 is an exact value, 100.1 is to 4 sf and 1.15 is to 3 sf)

Did that make sense?

[sin0001]

will a mark be deducted if your final answer is off by 0.01 or whatever, but you have the right amount of sig figs

[thushan]

Yeah :/ most likely, unfortunately.

[sam0001]

Yep! Thankyou!

I got 96.13, will a mark be deducted for that?

[thushan]

if it were the qn where sig figs were audited, then yes :/

[sin0001]

what if a question didn't instruct you to 'give your answer with the appropriate number of sig figs,' would a mark still be deducted? And in an exam question, the lowest number of sig figs were 3, and there were three titres given (10.12, 10.18, 9.98), why is the average titre (10.09) given in 4 sig figs and not 3 sig figs? And plus, in the solutions, to work out the average titre, they have took an average of all three titres, but 9.98 is not concordant with the other two?

[charmanderp]

It depends on how tight the examiner is.

The reasoning behind using the fewest significant to give your final answer is that we can only produce a result which is as accurate as our least accurate piece of data. For example, 3.01 could be something like 3.0139999, which would give us a very different answer. Burette's can supply a reasonably reliable volume to two decimal places. Note that it could easily be three significant figures if your titre was less than 10ml. But above you've supplied four. If later in our experiment we find a piece of data to be given to three sig figs, that applies only to any calculations which involve that information, which an average titre does not.

[thushan]

It depends on how tight the examiner is.

The reasoning behind using the fewest significant to give your final answer is that we can only produce a result which is as accurate as our least accurate piece of data. For example, 3.01 could be something like 3.0139999, which would give us a very different answer. Burette's can supply a reasonably reliable volume to two decimal places. Note that it could easily be three significant figures if your titre was less than 10ml. But above you've supplied four. If later in our experiment we find a piece of data to be given to three sig figs, that applies only to any calculations which involve that information, which an average titre does not.

Careful guys - when adding or subtracting, we consider the least number of DECIMAL PLACES, NOT SIG FIGS. It's only in multiplication and division that we consider the least number of sig figs.

[Somye]

This is a question that's been bugging me for a while now,
Do you use Molar masses in calculations of sig figs?

[thushan]

This is a question that's been bugging me for a while now,
Do you use Molar masses in calculations of sig figs?

Yup, you do. But when you add molar masses, remember adding means decimal places, your final molar mass will be to one decimal place too.

[ligands]

ah thushan might of been answered but what do you mean when you add or substract you consider the least amount of decimal places and with multiplying you consider the least number of sig figs? :s

[Destiny]

0.1110 has 4 decimal places and 4 significant figures.
1.10 has 3 significant figures, 2 decimal places.
0.01 has two decimal places, 1 significant figure.
Correct me if I'm wrong.
Instead of SF we look at the fewest decimal places in an addition/subtraction problem.

[ligands]

ok thankyou

[thushan]

0.1110 has 4 decimal places and 4 significant figures.
1.10 has 3 significant figures, 2 decimal places.
0.01 has two decimal places, 1 significant figure.
Correct me if I'm wrong.
Instead of SF we look at the fewest decimal places in an addition/subtraction problem.

that's right!