For a reaction of order n, the unit of the rate constant is
(a) mol^(1-n) L^(1-n) s
(b) mol^(1-n) L^

Q: Why is the unit of rate always $\text{mol L}^{-1}\text{s}^{-1}$?

Rate is defined as the change in concentration per unit time. Since concentration is measured in molarity ($\text{mol L}^{-1}$) and time in seconds ($\text{s}$), the unit of rate is fixed regardless of the reaction order.

Q: Can the order of reaction $n$ be a fraction or negative?

Yes, the order of a reaction is an experimental quantity and can be an integer, zero, a fraction, or even negative. The formula for the unit of $k$ holds true for all these cases.

Q: What if the time is given in minutes instead of seconds?

If time is in minutes, simply replace $\text{s}^{-1}$ with $\text{min}^{-1}$ in the final formula. The concentration part ($\text{mol}^{1-n}\text{L}^{n-1}$) remains exactly the same.

Q: How do I quickly find the unit for a second-order reaction?

Just substitute $n=2$ into the general formula $\text{mol}^{1-n}\text{L}^{n-1}\text{s}^{-1}$. You will get $\text{mol}^{-1}\text{L}^{1}\text{s}^{-1}$, which is often written as $\text{L mol}^{-1}\text{s}^{-1}$.

Q: Is this formula applicable to gaseous reactions where pressure is used instead of concentration?

For gaseous reactions, if rate is expressed in terms of partial pressure (e.g., $\text{atm s}^{-1}$), the unit of $k$ would be $\text{atm}^{1-n}\text{s}^{-1}$. The logic remains identical!

Question

For a reaction of order $n$, the unit of the rate constant is

Options:

(A) $	ext{mol}^{1-n}	ext{L}^{1-n}	ext{s}$

(B) $	ext{mol}^{1-n}	ext{L}^{2n}	ext{s}^{-1}$

(C) $	ext{mol}^{1-n}	ext{L}^{n-1}	ext{s}^{-1}$

(D) $	ext{mol}^{1-n}	ext{L}^{1-n}	ext{s}^{-1}$

Sigma Percentile · Accepted Answer

### The Foundation: Rate Law Equation

Every journey in chemical kinetics begins with the rate law. For a general reaction of order $n$, the rate of the reaction is directly proportional to the concentration of the reactants raised to the power of $n$.

Mathematically, we express this as:
$$ 	ext{Rate} = k [	ext{Reactant}]^n $$

Here, $k$ is our star of the show—the rate constant. To find its unit, our first logical step is to isolate it. By rearranging the equation, we get:
$$ k = \frac{	ext{Rate}}{[	ext{Reactant}]^n} $$

### Substituting the Standard Units

Now, let's bring in the physical units. The rate of a reaction is defined as the change in concentration over time. Therefore, its unit is always $	ext{mol L}^{-1} 	ext{s}^{-1}$.

The concentration of the reactant is simply molarity, which is $	ext{mol L}^{-1}$. Substituting these into our rearranged equation gives us the raw setup:
$$ k = \frac{	ext{mol L}^{-1} 	ext{s}^{-1}}{(	ext{mol L}^{-1})^n} $$

### The Magic of Exponents

This is where basic algebra saves the day. We need to simplify the fraction using the laws of exponents. Let's break it down element by element.

For the unit of moles ($	ext{mol}$), we have a power of $1$ in the numerator and a power of $n$ in the denominator. Subtracting the denominator's power from the numerator's gives us $	ext{mol}^{1-n}$.

For the unit of liters ($	ext{L}$), we have a power of $-1$ in the numerator and $-n$ in the denominator. Subtracting these gives $-1 - (-n)$, which simplifies beautifully to $	ext{L}^{n-1}$.

The unit of time ($	ext{s}^{-1}$) remains untouched as there is no time component in the denominator.

### The Final Master Formula

Combining all these simplified parts, we arrive at the universal formula for the unit of the rate constant for an $n^{	ext{th}}$ order reaction:
$$ \mathbf{k = 	ext{mol}^{1-n} 	ext{L}^{n-1} 	ext{s}^{-1}} $$

This elegant formula is a powerful tool. Instead of memorizing the units for zero, first, and second-order reactions individually, you can simply plug in the value of $n$ into this master equation. For instance, if $n=1$ (first-order), the units of $	ext{mol}$ and $	ext{L}$ become zero, leaving only $	ext{s}^{-1}$. It's a foolproof way to ensure you never make a unit mistake in kinetics again!

Animated Solution for Chemistry - Chemical Kinetics: For a reaction of order $n$ , the unit of the rate constant is

Select Answer:

Visualized Solution

\text{Rate Law Equation}

\text{Expression for } k

\text{Substituting Units}

\text{Simplifying the Expression}

\text{Final Unit of } k

\text{Checking for Specific Orders}

The Sigma Insight: Order and Molecularity

The Foundation

Substituting the Standard Units

The Magic of Exponents

The Final Master Formula

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Animated Solution for Chemistry - Chemical Kinetics: .math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } For a reaction of order n, the unit of the rate constant is