Problem 92 - A Complete Resource Book in Chemistry for JEE Main

Question

In DNA molecule, \(\mathrm{A}+\mathrm{T} / \mathrm{G}+\mathrm{C}\) ratio is \(0.9\) if the number of moles of cytosine in the molecule of DNA is 300,000 . The number of moles of thymine in the molecule is (a) 240,000 (b) 150,000 (c) 120,000 (d) 270,000

Step-by-Step Solution

Answer

The number of moles of thymine is 270,000.

Step 1: Understand the Base Pair Rule

In a DNA molecule, the bases form pairs: Adenine (A) pairs with Thymine (T) and Guanine (G) pairs with Cytosine (C). Thus, the amount of A is equal to T, and G is equal to C.

Step 2: Set Up the Initial Equation

We know that the ratio \( \frac{A + T}{G + C} = 0.9 \). Given \(C = 300,000\), then \(G = 300,000\) since G pairs with C.

Step 3: Calculate Total G+C

Calculate \(G + C = 300,000 + 300,000 = 600,000\).

Step 4: Use the Ratio to Find A + T

Using the ratio equation: \( \frac{A + T}{600,000} = 0.9 \). Rearrange to find \(A + T = 0.9 \times 600,000 = 540,000\).

Step 5: Determine the Moles of Thymine

Since A pairs with T, \(A = T\). We know \(A + T = 540,000\), thus \(2T = 540,000\). Solve for \(T\) to find \(T = \frac{540,000}{2} = 270,000\).

Key Concepts

DNA Structure

DNA, or deoxyribonucleic acid, is the hereditary material in all living organisms. It carries genetic instructions crucial for development, functioning, and reproduction. Structurally, DNA is composed of two strands that coil around each other to form a double helix. These strands are composed of smaller units called nucleotides.
A nucleotide consists of three components:

• A sugar molecule (deoxyribose in the case of DNA)
• A phosphate group
• A nitrogenous base

There are four different nitrogenous bases in DNA: Adenine (A), Thymine (T), Guanine (G), and Cytosine (C). The nitrogenous bases pair in a very specific way: Adenine always pairs with Thymine, and Guanine always pairs with Cytosine. This specific pairing is essential for DNA replication and transcription processes, as it ensures the genetic information is conserved when cells divide.

Nucleotide Ratios

The concept of nucleotide ratios is crucial for understanding DNA structure and genetic information organization. The base pairing rules (A with T, and G with C) lead to predictable ratios within DNA strands. For any given DNA molecule, the amount of Adenine (A) equals the amount of Thymine (T), and the amount of Guanine (G) equals that of Cytosine (C).
This understanding allows us to set up equations based on given ratios, such as the ratio \(\frac{A+T}{G+C}\). In many problems, like the one considered here, knowing the ratio and one quantity can lead us to calculate unknown values. For instance, if G and C each equal 300,000, the sum \(G+C=600,000\), allowing predicted calculations for \(A+T\). Such ratios are not just academic; they play a role in modern genetics and biotechnology by offering insight into the DNA's stability and the structure of genetic material across different species.

Genetics Calculations

Genetic calculations provide a powerful toolset for determining unknown variables in DNA problems by leveraging known relationships and ratios. Consider the problem where the sum \(A+T\) is determined using a known ratio and a given value for \(G+C\). With \(\frac{A+T}{G+C} = 0.9\) and knowing \(G+C = 600,000\), we calculated \(A+T = 540,000\).
Since \(A = T \, \A+T \ = \ 2T\), determining the number of moles of thymine is straightforward: \(T = \frac{540,000}{2} = 270,000\). Such calculations, while seemingly simple, illustrate foundational principles of genetics that help scientists uncover gene sequences and understand complex genetic traits.
By mastering these types of calculations, students can apply quantitative problem-solving techniques to a wide range of genetic issues, from basic botanical genetics experiments to advanced genetic engineering and forensic analysis.