The degree of polymerization at t = 10 h of a polymer formed by a stepwise process with a polymerization rate constant of 3 × 10⁻² M⁻¹ s⁻¹ and an initial monomer concentration of 50 mM is

Concept:

• In polymer chemistry, polymerization is a process of reacting monomer molecules together in a chemical reaction to form polymer chains.
• The degree of polymerization \(\left\langle {\rm{N}} \right\rangle \) is given by,

\(\left\langle {\rm{N}} \right\rangle {\rm{ = kt}}\left[ {{{\rm{M}}_{\rm{o}}}} \right]{\rm{ + 1}} \)

Where, \(\left\langle {\rm{N}} \right\rangle \) is the degree of polymerization,

\(\left[ {{{\rm{M}}_{\rm{o}}}} \right]\) is the initial monomer concentration,

t is the time required for the polymerization and,

 k is the polymerization rate constant

Explanation:

For the given polymerization reaction,

 t = 10 h

\( = 10 \times 60 \times 60\;\sec \)

\({\rm{ = 36000\;sec}} \)

\(\left[ {{{\rm{M}}_{\rm{o}}}} \right]\) = 50 mM

\({\rm{ = 50 \times 1}}{{\rm{0}}^{{\rm{ - 3}}}}{\rm{M}}\)

k = 3 × 10−2 M−1 s−1 

Thus, the degree of polymerization (\(\left\langle {\rm{N}} \right\rangle \)) is,

\({\rm{ = 3 \times 1}}{{\rm{0}}^{{\rm{ - 2}}}}\;{{\rm{M}}^{{\rm{ - 1}}}}{\rm{.}}{{\rm{s}}^{{\rm{ - 1}}}}{\rm{ \times 36000\;sec \times 50 \times 1}}{{\rm{0}}^{{\rm{ - 3}}}}{\rm{M + 1}}\; \)

\( = 54 + 1 \)

\( = 55 \)

Conclusion:

Hence, the degree of polymerization is 55