Monodisperse polyacrylonitrile contains molecules with the general formula -(CH2CHCN)n-, where n is typically greater than 10,000. Given that a sample of monodisperse polyacrilonitrile weighs 676.8 g and contains molecules of -(CH2CHCN)n-, calculate n.

7.68 × 10²⁴

Explanation:

Step 1: Calculate the mass of 1 molecule of the monomer CH₂CHCN

We will get the mass of the monomer by adding the masses of the elements.

mCH₂CHCN = 3 × mC + 3 × mH + 1 × mN

mCH₂CHCN = 3 × 12.01 amu + 3 × 1.01 amu + 1 × 14.01 amu = 53.07 amu

Step 2: Convert the mass of the monomer to grams

We will use the conversion factor 1 amu = 1.66 × 10⁻²⁴ g

53.07 amu × 1.66 × 10⁻²⁴ g/1 amu = 8.81 × 10⁻²³ g

Step 3: Calculate "n"

We will divide the mass of the polymer by the mass of the monomer.

n = 676.8 g / 8.81 × 10⁻²³ g = 7.68 × 10²⁴