Question

In the presence of excess thiocyanate ion, SCN-, the following reaction is first order in iron(III) ion, Fe3+. The rate constant is 1.27/s. Fe3+(aq) + SCN-(aq) → Fe(SCN)2-(aq) If 46.7% of the reaction is required to obtain a noticeable color from the formation of the Fe(SCN)2- ion, how many seconds are required?

Answer 1

The time required in seconds for the reaction to reach 46.7% completion and produce a noticeable color can be calculated using the first-order reaction equation, with a given rate constant of 1.27/s.

Step-by-step explanation:

To determine how many seconds are required for 46.7% of the reaction to occur, given that the reaction is first order in iron(III) ion, Fe3+, with a rate constant of 1.27/s, we can use the first-order reaction equation:

ln([A]0/[A]) = kt

Where:

• [A]0 is the initial concentration of Fe3+.
• [A] is the concentration of Fe3+ at time t.
• k is the rate constant.
• t is the time.

For the reaction to reach 46.7%, 53.3% of the reactant remains. So the ratio [A]0/[A] is 1/0.533. The time (t) can then be calculated:

ln(1/0.533) = (1.27/s) * t

t = ln(1/0.533) / 1.27

The calculated t is the time required in seconds for the reaction to reach the point where the noticeable color from the formation of the Fe(SCN)2- ion is observed.

Answer 2

0.60 s

Step-by-step explanation:

Our strategy to solve this question is based on the fact that the reaction is first order.

For a first order reaction:

ln [A]t / [A]₀ = - kt

where [A]t is the concentration after a time t,

[A]₀ is the original concentration of A,

k is the rate constant,

t is the time

Now we are told we need a 46.7 completion rate, therefore:

[A]t = 0.467 [A]₀

ln ( 0.467 [A]₀ / [A]₀ ) =

( -1.27/s ) t ⇒ t = ln ( 0.467 ) /(-1.27 ) s

= - 0.76/ (-1.27) s = 0.60 s