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The heat of neutralisation of a strong acid and a strong alkali is 57.0 kJ mol157.0 \text{ kJ mol}^{-1}. The heat released when 0.5 mole of HNO30.5 \text{ mole of } HNO_{3} solution is mixed with 0.2 mole of KOH0.2 \text{ mole of } KOH is [KCET 1991; AIIMS 2002]:

A

57.0 kJ

B

11.4 kJ

C

28.5 kJ

D

34.9 kJ

Step-by-Step Solution

The enthalpy of neutralisation is defined as the heat change accompanying the reaction of one mole of H+H^{+} ions from an acid with one mole of OHOH^{-} ions from a base to form one mole of water. For strong acids and strong bases, this value is constant at approximately 57.3 kJ mol1-57.3 \text{ kJ mol}^{-1} (given here as 57.0 kJ mol157.0 \text{ kJ mol}^{-1}).

In the reaction between HNO3HNO_{3} and KOHKOH (HNO3+KOHKNO3+H2OHNO_{3} + KOH \rightarrow KNO_{3} + H_{2}O), both are strong electrolytes .

  1. Identify the moles of reactants: We have 0.5 mol0.5 \text{ mol} of H+H^{+} (from HNO3HNO_{3}) and 0.2 mol0.2 \text{ mol} of OHOH^{-} (from KOHKOH).
  2. Identify the limiting reagent: According to the sources, the reactant present in the least stoichiometric amount is the limiting reagent . Here, KOHKOH (0.2 mol0.2 \text{ mol}) is the limiting reagent.
  3. Calculate heat released: The amount of water formed is limited by the KOHKOH, resulting in 0.2 mol0.2 \text{ mol} of H2OH_{2}O. Heat released = (moles of water formed) ×\times (heat of neutralisation per mole) Heat released = 0.2 mol×57.0 kJ/mol=11.4 kJ0.2 \text{ mol} \times 57.0 \text{ kJ/mol} = 11.4 \text{ kJ}.

Thus, the total heat evolved is 11.4 kJ11.4 \text{ kJ}, which matches Option B.

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