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Chapter 25: Problem 52

Assume the energy of hydrogen bonds per base pair to be \(10 \mathrm{~kJ} / \mathrm{mol}\). Given two complementary strands of DNA containing 10 base pairs each, estimate the ratio of two separate strands to hydrogen-bonded double helix in solution at \(300 \mathrm{~K}\). The ratio for a single base pair is given by the formula \(\exp (-\Delta E / R T)\) where \(\Delta E\) is the energy of hydrogen bond per base pair, \(R\) is the gas constant, and \(T\) is the temperature in kelvins.

Short Answer

Expert verified
The ratio of two separate strands to hydrogen-bonded double helix in solution at 300 K is approximately 1.15E-54

Step by step solution

01

Substitution of values

First, substitute the given values into the formula for the ratio of a single base pair. The energy of hydrogen bond per base pair, \( \Delta E \) is given as 10 kJ/mol. So, convert it to joules (1 kJ = 1000 J) to be consistent with the SI unit of R. It becomes 10000 J/mol. The gas constant, \( R \), is 8.3145 J/(mol.K) and the temperature, \( T \), is 300 K. The formula becomes \(\exp (-10000 / (8.3145 * 300))\).
02

Calculate the ratio for a single base pair

Calculate the expression in the formula to get the ratio for a single base pair. The resulting ratio is approximately 2.08E-06.
03

Calculate the overall ratio for all base pairs

Since there are 10 base pairs, the overall ratio is given by the ratio for a single base pair raised to the power of the number of base pairs. So, it's \((2.08E-06)^{10}\). Calculate this expression to get the overall ratio.

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Most popular questions from this chapter

Why is sickle cell anemia called a molecular disease?

The "melting point" of a DNA molecule is the temperature at which the double- helical strand breaks apart. Suppose you are given two DNA samples. One sample contains 45 percent C-G base pairs while the other contains 64 percent C-G base pairs. The total number of bases is the same in each sample. Which of the two samples has a higher melting point? Why?

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