Question

The second picture is the aforementioned Equation 2 that needs to be derived. Thanks in advance!

Equation 2 on page 2 is simply a specialized form of the van't Hoff equation. It shows how the melting temperature of DNA depends on the initial DNA concentration. Derive equation 2. [Hints: When T = Tm [A B]e [A]eq = [B]eq 2 [A B]o C. Use this fact to write K (dissociation constant, Kp) in terms of the initial DNA concentration (C). Substitute this expression into the van't Hoff equation and rearrange the equation. Clearly show every step of the derivation.

Answer 1

van't Hoff equation usually relates the change in equilibrium with change in temperature and the enthalpy change associated with it.
Under standard candihons : Van't Hoff equchon is: a en keq = AHO RT2 - In- nahral logarithms R- ideal gas constant On integrating: dhe rear = - op In here -40® ( ) equilbrium constant at absolute temperatus 291 K₂ - equilibrium constant at absolute temperature Tz

+ = - Bln C+ os t Rhoz 40 Oto - Giver equchon showing the melting temperakroe (Tm) of DNA which depends on the wihal DNA in contrabon. Van't Hoff equchon on equching or developing from thermodynamics? Go=oHo ToS Gibbs free energy s- entropy of system, We have: G = -RT In Keg, (Gibbs free energy 150 theon equation. we obtain: linkan : .- At tas o

On rearranging the above equehors: RT we get ; 2H0 - In keq, + see — On seaquangang: $. - rlokep + $5°xR – On reagrangan eal DH XR SH - Given when P = Tm [A. B Jean = [A Jaq, = [BJq = 12 [AB] = 1/2 C. equehon ③ will be: = - R lnct aso SHO OHO

It is givers that when To Tm, [A, B]eq = [A]aq - [B]q = 1/2 [A, B] - YC Dissociation constant to can write in terms of inhal DNA concentraban; keq = Ź C. - ④. We con equate is equchon ③ ln keq = - + 150 0 lm (+ C) = ln C) = (lnc- ln 2) = - 1 + AS SH -lac + loa + 45 RT R RT R T= Tm

I = - R loc tras t ROH R lna DHO Tim OH I m = -R Inc + 05 +R lona DHO SHO