Question

Suppose a reaction with a single reactant is first order in that reactant. As a first-order reaction, the concentration of the reactant will decrease exponentially with time, and its half-life will be constant. Does the fraction of molecules that react per unit time change as the reaction progresses? Justify your answer.

please justify with words and not just equations.

Answer 1

Does not change

Explanation

For first order reaction

t_1/2 = 0.693/k

where, k is rate constant

so,

rate constant, k = 0.693/t_1/2

Integrated form first order equation is

ln[A]_t = -kt + ln[A₀]

where,

[A]₀ = Initial concentration of reactant

[A]_t = Concentration at time t

ln([A]₀/[A]_t) = kt

half life is not changing,

so, at half life

ln([A]₀/[A]_t) = kt_1/2

the term, kt_1/2 = constant

Therefore,

[A]₀/[A]_t = Constant

the ratio between Concentration A at initial and Concentration of A at half life is not changing

Therefore,

Fraction of molecules that react per unit time will not change

as the reaction progress