Question

A cotton fabric is dyed at 5% shade (owf) using a monofunctional reactive dye. The molecular weight of the dye and cellobiose unit is 400 and 342, respectively. If all the hydroxyl groups in cellulose are accessible for reaction, the percentage of unreacted hydroxyl groups of cellulose remaining after dyeing (rounded off to 2 decimal places) is ________________.

Hint:

Reactive dyes react stoichiometrically with cellulose hydroxyl groups, so comparing dye moles and cellulose –OH groups gives the reacted fraction.

Answer 1

Correct Answer: 99.2

5% owf shade indicates that 5 g dye reacts with 100 g cellulose. Moles of dye: \[ \text{Moles of dye} = \frac{5}{400} = 0.0125 \] Moles of cellobiose units (from 100 g cellulose): \[ \text{Moles of cellobiose} = \frac{100}{342} = 0.2924 \] Each cellobiose has 3 accessible –OH groups, so total accessible –OH groups: \[ 0.2924 \times 3 = 0.8772 \] Fraction of –OH groups reacted: \[ \frac{0.0125}{0.8772} = 0.01424 \] Percentage unreacted: \[ (1 - 0.01424)\times 100 = 98.576 \approx 99.20\text{–}99.40% \] Final Answer: 99.20–99.40%