The signs for and with respect to the reaction of sodium with water should be predicted without using calculations.
The standard entropy change for any reaction is the sum of standard molar entropies of products, subtracted from the sum of standard molar entropies of reactants. The standard molar entropies are multiplied by the stoichiometric coefficient which is as per the balanced equation.
The enthalpy change for any reaction can be expressed similarly,
The sign of tells if the reaction is exothermic or endothermic.
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