Question

Half-life equation for first-order reactions:

t1/2=0.693k t1/2=0.693k
where t1/2t1/2 is the half-life in seconds (s), and kk is the rate constant in inverse seconds (s⁻¹)
To calculate the half-life, plug the value for kk into the half-life equation and solve.What is the half-life of a first-order reaction with a rate constant of 2.10×10⁻⁴ s⁻¹?

Answer 1

The half-life of a first-order reaction with a rate constant of 2.10× 10^-4 s^-1 is calculated using the equation t1/2 = 0.693/k, yielding a half-life of 3,300 seconds.

Step-by-step explanation:

The half-life of a first-order reaction expresses the time it takes for the concentration of a substance to reduce to half of its initial amount. For first-order reactions, the half-life (t1/2) is given by the equation t1/2 = 0.693/k, where k is the rate constant. This equation signifies the inverse relationship between the half-life and the rate constant; a larger rate constant correlates with a shorter half-life, indicative of a faster reaction. When solving for the half-life of a substance with a rate constant of 2.10× 10^-4 s^-1, we substitute the value of k into the equation to obtain the half-life.

To calculate the half-life for the given rate constant, we plug the value into the half-life equation:

t1/2 = 0.693 / (2.10 × 10^-4 s^-1)

Carrying out the division:

t1/2 = 3,300 s

Therefore, the half-life of this first-order reaction is 3,300 seconds.