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Question: The standard heat of formation of sodium ions in aqueous solution from the following data. Heat of...

The standard heat of formation of sodium ions in aqueous solution from the following data.
Heat of formation of NaOH(aq)NaOH(aq) at 25∘C=−470.7kJ{25^ \circ }C = - 470.7kJ
Heat of formation of OH−(aq)O{H^ - }(aq) at 25∘C=−228.8kJ{25^ \circ }C = - 228.8kJ
A. -251.9kJ
B. 241.9kJ
C. -241.9kJ
D. 251.9kJ

Explanation

Solution

Standard heat of formation is the amount of heat absorbed or evolved when one mole of a substance is formed from its constituent components. We are given standard heats of formation of Sodium hydroxide and Hydroxide ion. Sodium hydroxide decomposes into sodium ion and hydroxide ion. To find the standard heat of formation of sodium ion subtract the heat of formation of Hydroxide ion from heat of formation of Sodium hydroxide.

Step by step answer: We are given the heats if formation of sodium hydroxide and hydroxide ions.
We have to use this information and find the heat of formation of Sodium ions.
Sodium hydroxide in aqueous solution decomposes into sodium ion and hydroxide ion.
NaOH→Na++OH−NaOH \to N{a^ + } + O{H^ - }
The standard heat of formation of NaOHNaOH is the sum of standard heat of formation of Na+N{a^ + } and standard heat of formation of OH−O{H^ - }

ΔHfNaOH=ΔHfNa++ΔHfOH−\Delta {H_{fNaOH}} = \Delta {H_{fN{a^ + }}} + \Delta {H_{fO{H^ - }}}
Heat of formation of NaOH(aq)NaOH(aq) at 25∘C=−470.7kJ{25^ \circ }C = - 470.7kJ
Heat of formation of OH−(aq)O{H^ - }(aq) at 25∘C=−228.8kJ{25^ \circ }C = - 228.8kJ

ΔHfNaOH=ΔHfNa++ΔHfOH− →ΔHfNa+=ΔHfNaOH−ΔHfOH− →ΔHfNa+=−470.7−(−228.8) →ΔHfNa+=−470.7+228.8 ∴ΔHfNa+=−241.9kJ  \Delta {H_{fNaOH}} = \Delta {H_{fN{a^ + }}} + \Delta {H_{fO{H^ - }}} \\\ \to \Delta {H_{fN{a^ + }}} = \Delta {H_{fNaOH}} - \Delta {H_{fO{H^ - }}} \\\ \to \Delta {H_{fN{a^ + }}} = - 470.7 - \left( { - 228.8} \right) \\\ \to \Delta {H_{fN{a^ + }}} = - 470.7 + 228.8 \\\ \therefore \Delta {H_{fN{a^ + }}} = - 241.9kJ \\\

Therefore, the standard heat of formation of sodium ions in aqueous solution is -241.9kJ.

The correct option is Option C, -241.9kJ.

Note: When the given heats of formations are negative, then the formation of the compound is exothermic which means energy is released and when it is positive, then the formation of the compound is endothermic which means it absorbs energy. In exothermic reactions, the amount of energy to break the bonds is less than the amount of energy that is released to make the bonds and in endothermic it is vice-versa.