Introduction

DNA denaturation is a thermally induced process where the double helix separates into single strands. The enthalpy change (ΔH) of this process depends on temperature and can be estimated if the heat capacity change (ΔCp) is known or assumed constant.

Given ΔH values at two temperatures, one can estimate ΔH at another temperature using thermodynamic relations assuming ΔCp is temperature-independent.

Given Data

• ΔH at 70°C (343 K) = 80 kcal/mole

• ΔH at 80°C (353 K) = 90 kcal/mole

• Estimate ΔH at 37°C (310 K)

• Assume ΔCp is constant and independent of temperature.

Thermodynamic Relation

The temperature dependence of enthalpy change is given by:

ΔH(T)=ΔH(Tref)+ΔCp(T−Tref)ΔH(T)=ΔH(Tref)+ΔCp(T−Tref)

Using two known enthalpy values, ΔCp can be calculated as:

ΔCp=ΔH(T2)−ΔH(T1)T2−T1ΔCp=T2−T1ΔH(T2)−ΔH(T1)

Where:

• T1=343 KT1=343K (70°C)

• T2=353 KT2=353K (80°C)

• ΔH(T1)=80 kcal/molΔH(T1)=80kcal/mol

• ΔH(T2)=90 kcal/molΔH(T2)=90kcal/mol

Step 1: Calculate ΔCp

ΔCp=90−80353−343=1010=1 kcal/mol\cdotpKΔCp=353−34390−80=1010=1kcal/mol\cdotpK

Step 2: Calculate ΔH at 310 K (37°C)

Using $T=310K$ and reference Tref=343 KTref=343K:

ΔH(310)=ΔH(343)+ΔCp(310−343)ΔH(310)=ΔH(343)+ΔCp(310−343)$$\Delta H(310)=80+1\times (310-343)=80-33=47\text{kcal/mol}$$

Interpretation

The enthalpy change for DNA denaturation decreases as temperature decreases, consistent with the positive ΔCp. The estimated ΔH at 37°C is 47 kcal/mole.

Summary Table of Options

Conclusion

Assuming constant ΔCp, the enthalpy change of DNA denaturation at 37°C is approximately 47 kcal/mole based on given ΔH values at 70°C and 80°C.

Keywords

DNA denaturation, enthalpy change, ΔH temperature dependence, heat capacity change, ΔCp, thermal melting of DNA, DNA melting enthalpy calculation, thermodynamics of DNA, DNA stability, temperature effect on DNA denaturation

Final answer:
(3) 47