Question

The number average molecular weight (M\(_n\)) of a polymer is 1500. In this polymer, 800 molecules of molar mass 1000, 100 molecules of molar mass 2000 and x molecules of molar mass 5000 are present. What is the value of x?

• A. 200
• B. 400
• C. 100
• D. 50

Hint:

In polymer chemistry, the number average molecular weight is a useful tool to describe the average size of the molecules in the polymer sample.

Answer 1

The Correct Option is C

The number average molecular weight is calculated using the formula: \[ M_n = \frac{\sum (N_i M_i)}{\sum N_i} \] where \( N_i \) is the number of molecules of molar mass \( M_i \). Substituting the given values: \[ 1500 = \frac{(800 \times 1000) + (100 \times 2000) + (x \times 5000)}{800 + 100 + x} \] Simplifying the equation: \[ 1500 = \frac{800000 + 200000 + 5000x}{900 + x} \] Multiplying both sides by \( 900 + x \): \[ 1500(900 + x) = 1000000 + 5000x \] \[ 1350000 + 1500x = 1000000 + 5000x \] Solving for \( x \): \[ 350000 = 3500x \] \[ x = \frac{350000}{3500} = 100 \] Thus, the value of \( x \) is 100.