Question

If the complete reaction with 0.8642 (plus or minus 0.0005) g of sodium carbonate (FW= 105.9884 plus or minus 0.0007) required 42.36 (plus or minus 0.04) mL of acid, what is the molarity of the acid. Report the value with its absolute uncertainty

Answer 1

If the acid is a dibasicbasic acid like H2SO4 then the balanced chemical reaction will be

Na2CO3 + H2SO4 ----- > Na2SO4 + CO2 + H2O

1 mol -------1 mol ------------- 1 mol ----

Given the volume of the acid, V = (42.36 +/- 0.04) mL =  (42.36 +/- 0.040) x 10^-3 L

Let the molarity of the acid be 'M'

Hence moles of the acid required = MxV =  (42.36 +/- 0.040) x 10^-3 xM mol

Given the mass of Na2CO3 = (0.8642 +/- 0.0005) g

Formulae mass of Na2CO3 = (105.9884 +/- 0.0007) g/mol

Hence moles of Na2CO3 = mass / molecular mass =  (0.8642 +/- 0.0005) g / (105.9884 +/- 0.0007) g/mol

= 0.008154 +/- (0.8642/105.9884) x underroot[(0.0005/0.8642)²+(0.0007/105.9884)²]

= (0.00815 +/- 0.00005) mol

Now moles of acid(dibasic) required = moles of Na2CO3

=> (42.36 +/- 0.040) x 10^-3 xM mol =  (0.00815 +/- 0.00005) mol

=> (0.04236 +/- 0.00004)xM mol = (0.00815 +/- 0.00005) mol

=> M = (0.00815 +/- 0.00005) / (0.04236 +/- 0.00004)

=> M = 0.1924 +/- (0.00815/0.04236) x underroot[(0.00005/0.00815)²+(0.00004/0.04236)²]

= (0.192 +/- 0.001) molar (answer)

If the acid is a monobasic acid like HCl, then M = 2x(0.192 +/- 0.001) molar = (0.384 +/- 0.002) molar (answer)