Question

Which equation is used to determine the amount of time required for the initial concentration to decrease by 45% if the rate constant has units of s⁻¹?A) t = ln 2/kB) Rate = k[A]C) ln([A]/[A]₀) = -ktD) [A] = [A]₀ - ktE) 1/[A] = 1/[A]₀ + kt

Answer 1

The equation used to determine the amount of time required for the initial concentration to decrease by 45% if the rate constant has units of s⁻¹ is option A) t = ln 2/k.

Step-by-step explanation:

The equation used to determine the amount of time required for the initial concentration to decrease by 45% if the rate constant has units of s⁻¹ is option A) t = ln 2/k. This equation is derived from the integrated rate law for a first-order reaction, which states that the concentration of reactant A decreases exponentially with time.

Answer 2

The correct equation to find the time for a 45% decrease in initial concentration with a first-order rate constant (s−¹) is ln([A]/[A]₀) = -kt.

Step-by-step explanation:

The equation used to determine the amount of time required for the initial concentration to decrease by 45% if the rate constant has units of s−¹ is C) ln([A]/[A]₀) = -kt.

For first-order reactions, where the rate constant 'k' has units of s−¹, the relationship between the concentration of reactant [A] at time 't' and the initial concentration [A]₀ can be expressed using an exponential decay formula: [A] = [A]₀e−kt. Taking the natural logarithm of both sides, we obtain the logarithmic form of the first-order integrated rate law, which is ln([A]/[A]₀) = -kt.

To find the time required for a 45% decrease, we set [A] to be 55% of [A]₀ (since 100% - 45% = 55%) and solve for 't' using the equation:

ln(0.55[A]₀/[A]₀) = -kt

Simplifying, we get:

ln(0.55) = -kt

Thus, the time 't' can be found by:

t = -ln(0.55) / k