Polymers and Biomolecules formulas for JEE Main & Advanced

13 formula entries for Polymers and Biomolecules, in the order the chapter builds them. Each shows the formula, when to use it and the first trap to avoid.

Degree of Polymerization (DP)

D P = \frac{M_{n}}{M_{0}}

When to use. When calculating the size or molecular weight of a polymer from its monomer.

Trap. Using weight-average molecular weight instead of number-average; DP uses $M_{n}$ .

Carbohydrates

General formula:

C_{n} (H_{2} O)_{n}

When to use. When identifying or classifying sugars and their reactions.

Trap. Assuming all carbohydrates follow $C_{n} (H_{2} O)_{n}$ ; deoxy sugars like deoxyribose do not.

Proteins

Peptide bond:

- C O - N H -

When to use. When studying protein structure, function, or denaturation.

Trap. Confusing peptide bond with disulfide bond; peptide bonds are between amino acids.

Nucleic Acids

Nucleotide = Nitrogenous base + Sugar + Phosphate

When to use. When studying genetics, replication, or transcription.

Trap. Confusing DNA and RNA; RNA has ribose and uracil, DNA has deoxyribose and thymine.

Number Average Molecular Weight ( $M_{n}$ )

M_{n} = \frac{\sum N_{i} M_{i}}{\sum N_{i}}

When to use. When calculating average molecular weight from number of chains.

Trap. Using $M_{n}$ when $M_{w}$ is needed; $M_{n}$ is lower than $M_{w}$ for polydisperse samples.

Weight Average Molecular Weight ( $M_{w}$ )

M_{w} = \frac{\sum N_{i} M_{i}^{2}}{\sum N_{i} M_{i}}

When to use. When assessing polymer properties affected by larger chains.

Trap. Confusing $M_{w}$ with $M_{n}$ ; $M_{w}$ uses $M_{i}^{2}$ in numerator.

Polydispersity Index (PDI)

P D I = \frac{M_{w}}{M_{n}}

When to use. When characterizing polymer uniformity or synthesis method.

Trap. Assuming PDI is always >1; it can be 1 for perfectly uniform polymers.

Mutarotation of Glucose

α

-D-glucose:

[α]_{D} = + 112 °

;

β

-D-glucose:

[α]_{D} = + 18.7 °

; equilibrium:

+ 52.5 °

When to use. When explaining optical rotation changes in sugar solutions.

Trap. Thinking mutarotation is only for glucose; it occurs for all reducing sugars.

Peptide Bond Formation

R - C O O H + H_{2} N - R^{'} \to R - C O - N H - R^{'} + H_{2} O

When to use. When understanding protein synthesis or hydrolysis.

Trap. Forgetting that water is lost when the peptide bond forms (a condensation), and that hydrolysis needs water to break it again.

Identifying Amino Acid from Structure

General structure:

H_{2} N - C H R - C O O H

When to use. When classifying or naming amino acids from their chemical structure.

Trap. Thinking all amino acids have the same R group; R varies (e.g., glycine has H, alanine has CH3).

Solving Polymer Molecular Weight Problems

M_{n} = \frac{\sum N_{i} M_{i}}{\sum N_{i}}

M_{w} = \frac{\sum N_{i} M_{i}^{2}}{\sum N_{i} M_{i}}

When to use. When given a table of polymer fractions with number of chains and molecular weights.

Trap. Forgetting to convert masses to consistent units (e.g., g/mol).

Solving Carbohydrate Hydrolysis Problems

(C_{6} H_{10} O_{5})_{n} + n H_{2} O \to n C_{6} H_{12} O_{6}

When to use. When calculating the amount of monosaccharides from a given polysaccharide mass.

Trap. Forgetting water is consumed; mass increases slightly.

Using Saponification for Lipid Analysis

Triglyceride + 3NaOH → Glycerol + 3RCOONa

When to use. When analyzing fats or producing soap.

Trap. Thinking saponification only works with NaOH; KOH also used.

Values to remember

$[α]_{D} = + 112 °$ Mutarotation of Glucose
$[α]_{D} = + 18.7 °$ Mutarotation of Glucose
$[α]_{D} = + 52.5 °$ Mutarotation of Glucose

Read the full chapter: Polymers and Biomolecules for JEE, with what JEE asks and the common traps.