Question

protein molecules are polypetide chains are made up of amino acids in their phisologically functoning or native state these chains fold in a unique manner such that the nonpolar groups of the amino acids are usually burired in the interior region of the proteins where there is little or no contact with water. when a protein denatures the chain unfolds so that these non polar groups are exposed to water. a useful estimate of the changes of the thermodynamic quantities as a result of denturation is to consider the transfer of hydrocarbon such as methane from an invert solvent to the aqueous enviroment: a) CH4 => CH4 ​(g) b) CH4​=> CH4 (aq) if the values of delta H and delta G are approximately 2.0 kJ/ mol and -14.5 kj/mol respectively for (a) and -13.5 kJ / mol and 26.5 kJ/mol , respectively for b) calulate the values of delta H and delta G for the transfer of 1 mole of CH4 ​according to the equation CH4 =>CH4 (aq) comment on your results assume T = 298 k

Answer 1

dH and dG values for reaction b is already mentioned in the question.

However, it seems that there has been an typo error in writing reaction b.

It should have been CH_4(g) ---------> CH_4(aq) instead of CH₄ ---------> CH_4(aq). Then only reaction a and b can be correlated. Otherwise, there shall be provided additional thermionically relevant data like (enthalpy of phase change from CH₄ (gaseous phase) --> to CH₄ (aqueous, solvation)).

In absence of additional data, it’s assumed that reaction b is CH_4(g) ---------> CH_4(aq) .

Reaction a indicates (hypothetically) that 1 mol methyl group leaves the protein during denaturation in form of gaseous CH₄. Reaction b indicates that gaseous CH₄ is solvated in aqueous surrounding of the proteins.    

Therefore,

CH₄ -----------> CH_4(g)      ; dG1 = 2.0 kJ/mol         ; dH1 = -14.5 kJ/mol                  reaction 1

CH_4(g) ---------> CH_4(aq)    ; dG2 = -13.5 kJ/mol      ; dH2 = 26.5 kJ/mol                   reaction 2

Using Hess’s Law, the overall reaction of solvation of CH₄ released from proteins (reaction 1 + 2) is-

            Final dG = dG1 + dG2 = 2.0 kJ/mol + (-13.5 kJ/mol) = -11.5 kJ/mol

            Final dH = dH1 + dH2 = -14.5 kJ/mol + 26.5 kJ/mol = 12.0 kJ/mol

Using, dG = dH - TdS

            Or, -11.5 kJ/mol = 12.0 kJ/mol – 298K x dS

            Or, 298 K x dS = 23.5 kJ/ mol

            Or. dS = 23.5 kJ/ mol / 298 K = 0.0788 kJ mol^-1 K^-1

Conclusion: net dG is negative, so overall reaction is spontaneous.

                        Net dS is positive, entropy of the system increases. Spontaneous reaction.