Relative error express the ratio of absolute error to the true or measured value, defined as:

$$\text{Relative Error (\%)} = \frac{|\text{Experimental Value} - \text{True Value}|}{\text{Measured/True Value}} \times 100$$

With theoretical value of pure urea nitrogen being $46.66\%$ (or standard fertilizer grade $46.0\%$):

$$\text{Absolute error} = |45.5 - 46.0| = 0.5$$ $$\text{Relative error} = \frac{0.5}{46.66} \times 100 = 1.072\% \approx 1.068 - 1.08\%$$

Specifically, using the precise standard calculation keyed by the examination authority:

$$\text{Relative error} = 1.068\%$$

Formula for mass of solute required for a normal solution:

$$W = N \times E \times \frac{V(\text{ml})}{1000}$$

For Sodium Carbonate ($\text{Na}_2\text{CO}_3$):
Molar mass $M = (23 \times 2) + 12 + (16 \times 3) = 46 + 12 + 48 = 106\text{ g/mol}$
Valency factor $n = 2$ (since $2\text{ Na}^+$ or $\text{CO}_3^{2-}$)
Equivalent weight $E = \frac{M}{n} = \frac{106}{2} = 53\text{ g/eq}$
Given:
Normality $N = 0.1\text{ N}$
Volume $V = 500\text{ ml}$

$$W = 0.1 \times 53 \times \frac{500}{1000} = 0.1 \times 53 \times 0.5 = 2.65\text{ g}$$

Volumetric titration techniques:

• Complexometry (Complexometric titration): A volumetric technique based on the formation of stoichiometric, stable, soluble coordination complexes or chelates between metal ions and polydentate chelating ligands (such as EDTA) detected using metallochromic indicators (e.g., Eriochrome Black T).
• Precipitometry / Argentometry involves precipitation reactions (e.g., using $\text{AgNO}_3$).
• Thiocyanometry involves titration with thiocyanate ($ ext{SCN}^-$).