What is the free energy for the dissolution of solid sodium chloride in water at 25C?

A) What is the free energy for the dissolution of solid sodium
chloride in water at 25C?
NaCl(s) <-> Na+(aq) + Cl-(aq)

B) What is the solubility product constant for sodium chloride
in water at 25C?

Answer 1

A) Given the reaction:

#"NaCl"(s) stackrel("H"_2"O"(l)" ")(->) "Na"^(+)(aq) + "Cl"^(-)(aq)#
The #DeltaG_"rxn"^@# is as usual, and just like #DeltaH_"rxn"^@#:
#color(blue)(DeltaG_"rxn"^@) = sum_P nu_PDeltaG_(f,P)^@ - sum_R nu_RDeltaG_(f,R)^@#
#= [nu_("Na"^(+)(aq))DeltaG_(f,Na^(+)(aq))^@ + nu_("Cl"^(-)(aq))DeltaG_(f,Cl^(-)(aq))^@] - [nu_("NaCl"(s))DeltaG_(f,NaCl(s))^@]#
#= [(1)(-"261.9 kJ/mol") + (1)(-"131.2 kJ/mol")] - [(1)(-"384.0 kJ/mol")]#
#= -"261.9 kJ/mol" - "131.2 kJ/mol" + "384.0 kJ/mol"#
#= color(blue)(-"9.1 kJ/mol")#

It should be this small; that's fine, for dissolving solutes.

B)

The larger the #K_"sp"#, the more the equilibrium is skewed towards the aqueous products, and thus the more soluble the compound is in water. Obviously, #"NaCl"# is extremely soluble in water (#"359 g/L"#), so #K_"sp"# should be very large.
Since we have #DeltaG_"rxn"^@# for this process, we can realize that #DeltaG_"rxn" = 0# at equilibrium, so that:
#cancel(DeltaG_"rxn")^(0) = DeltaG_"rxn"^@ + RTlncancel(Q)^(K_"sp")#
#=> DeltaG_"rxn"^@ = -RTlnK_"sp"#
#=> color(blue)(K_"sp") = e^(-DeltaG_"rxn"^@"/"RT)#
#= e^(-(-"9.1 kJ/mol")"/"[("0.008314472 kJ/mol"cdot"K")("298.15 K")]#
#= color(blue)(39.29)#
And indeed, #K_"sp"# is fairly large. For poorly-soluble compounds, the #K_"sp"# is often less than #10^(-5)#.
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Answer 2

The standard free energy change ((\Delta G^\circ)) for the dissolution of solid sodium chloride ((NaCl)) in water at 25°C is approximately -385.92 kJ/mol.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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