Questions: 4 Fe^2+ + O2 + 2 H2 O -> 4 Fe^3+ + 4 OH^- rate = k[Fe^2+][OH^-]^2[O2] What are the units for the rate constant? M^-1 * t^1, t^1, M^-2 * t^1, M^-1 * t^1

Transcript text: Acellus | Student om/student/3/work/5TAkN6eQGXL6hwza8AN7qQ Rate Laws and Order of Reactions \[ \begin{array}{c} 4 \mathrm{Fe}^{2+}+\mathrm{O}_{2}+2 \mathrm{H}_{2} \mathrm{O} \rightarrow 4 \mathrm{Fe}^{3+}+4 \mathrm{OH}^{-} \\ \text {rate }=k\left[\mathrm{Fe}^{2+}\right]\left[\mathrm{OH}^{-}\right]^{2}\left[\mathrm{O}_{2}\right] \end{array} \] What are the units for the rate constant? \[ \begin{array}{ll} M^{-1} \cdot t^{1} & t^{1} \\ M^{-2} \cdot t^{1} & M^{-1} \bullet t^{1} \end{array} \]

Solution

Solution Steps

Step 1: Determine the Overall Order of the Reaction

The rate law for the reaction is given by:

\[ \text{rate} = k[\mathrm{Fe}^{2+}][\mathrm{OH}^{-}]^2[\mathrm{O}_2] \]

To find the overall order of the reaction, sum the exponents of the concentration terms:

Order with respect to \([\mathrm{Fe}^{2+}]\) is 1.
Order with respect to \([\mathrm{OH}^{-}]\) is 2.
Order with respect to \([\mathrm{O}_2]\) is 1.

Overall order = \(1 + 2 + 1 = 4\).

Step 2: Determine the Units of the Rate Constant

The rate of reaction is typically expressed in units of concentration per unit time, such as \(M \cdot t^{-1}\), where \(M\) is molarity and \(t\) is time.

For a reaction of overall order \(n\), the units of the rate constant \(k\) are given by:

\[ \text{Units of } k = M^{1-n} \cdot t^{-1} \]

Substituting \(n = 4\) (the overall order of the reaction):

\[ \text{Units of } k = M^{1-4} \cdot t^{-1} = M^{-3} \cdot t^{-1} \]

Step 3: Match the Units with the Given Options

The given options for the units of the rate constant are:

\(M^{-1} \cdot t^{1}\)
\(t^{1}\)
\(M^{-2} \cdot t^{1}\)
\(M^{-1} \bullet t^{1}\)

None of these options directly match \(M^{-3} \cdot t^{-1}\). It seems there might be a typographical error in the options provided, as they do not align with the expected units for a fourth-order reaction.