A typical back titration involves the deliberate addition of excess reagent. Here we add the impure sample of limestone (calcium carbonate) to excess HCl. The reaction proceeds according to the equation below. The excess amount of HCl can be determined very accurately.
Next step is to now titrate
the solution with a base to determine how much acid remained unreacted.
This way we can work out exactly how much acid did react. We can then use
stoichiometry to determine the amount of calcium carbonate present.
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We titrate the solution with a known sodium carbonate solution of accurately known concentration.
The reaction takes place according to the equation above. A suitable indicator is used to give a colour change at the end point.
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Solution
Step 1  Work out the equations for all the reactions taking place.
The equation for
the reaction betweenHCl with the limestone is given below.
Equation 1
The equation for
the reaction between HCl and sodium carbonate is given below.
Equation 2
Step 2  From equation 2 we can work out the mole of HCl left unreacted.
Step 3  Work out how much HCl did react. Subtract the amount in excess from the amount originally added.
Amount originally
added  amount in excess = amount reacted.
(0.15 X 0.91)  0.0504 = 0.0861 mole of HCl reacted.
Step 3  Using equation
1 calculate the amount of caclium carbonate present.
Mole of HCl /2 = mole of calcium carbonate = 0.0861/2 = 0.043 mole.
Step 4  Calculate the mass of calcium carbonate present.
0.043 X formula mass
= 0.043X 100 = 4.3 grams
Step 4 Calculate the percentage
(mass of calcium carbonate
/ mass of sample) X 100 = %
4.3/5.00 X100 = 86%
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Volumetric analysis Backtitration exercise 2 

5.00g sample of impure limestone is treated with 150.0mL of 0.910M HCl. The reaction takes place according to the equation below. After the reaction is complete it is found that 18.10mls of a 1.40M sodium carbonate is required to neutralise the unreacted acid. Calculate the percentage of calcium carbonate in the sample. (Ca =40.0, C= 12.0, O=16.0, CL =35.5, H =1.0) Click for more detail. 

