Which of the following statement is incorrect?

Options

A. Unit of rate of disapearence is `Ms^(-1)`
B. Unit if rate of reaction is `Ms^(-1)`
C. Unit of rate constant k depends upon order
D. Unit of k for first order reaction is `Ms^(-1)`

Answer

To determine which statement is incorrect among the given options, we will analyze each statement step by step.

### Step 1: Analyze the first statement
**Statement:** The unit of rate of disappearance is moles per second inverse.

**Analysis:**
- The rate of disappearance refers to how quickly a reactant is consumed in a reaction.
- The general expression for the rate of disappearance of a reactant A in a reaction can be written as:
\[ \text{Rate} = -\frac{1}{n_1} \frac{d[A]}{dt} \]
- Here, \([A]\) is the concentration of A in moles per liter (Molarity), and \(t\) is time in seconds.
- Therefore, the unit of the rate of disappearance is indeed moles per second (mol/s).

**Conclusion:** This statement is **correct**.

### Step 2: Analyze the second statement
**Statement:** The unit of rate of reaction is mole second inverse.

**Analysis:**
- The rate of reaction is defined similarly to the rate of disappearance. It can be expressed as:
\[ \text{Rate} = \frac{d[\text{Products}]}{dt} \quad \text{or} \quad -\frac{d[\text{Reactants}]}{dt} \]
- The unit of rate of reaction is also moles per second (mol/s).

**Conclusion:** This statement is also **correct**.

### Step 3: Analyze the third statement
**Statement:** The unit of rate constant \(K\) depends on the order \(n\).

**Analysis:**
- The unit of the rate constant \(K\) varies with the order of the reaction. For a reaction of order \(n\):
\[ K = \frac{\text{moles}}{\text{liters}^{(1-n)} \cdot \text{time}} \]
- This shows that the unit of \(K\) indeed depends on the reaction order \(n\).

**Conclusion:** This statement is **correct**.

### Step 4: Analyze the fourth statement
**Statement:** The unit of \(K\) for first order is mole second inverse.

**Analysis:**
- For a first-order reaction (\(n = 1\)):
\[ K = \frac{\text{moles}}{\text{liters}^{(1-1)} \cdot \text{time}} = \frac{\text{moles}}{\text{liters}^0 \cdot \text{seconds}} = \frac{\text{moles}}{\text{seconds}} = \text{mol/s} \]
- However, the statement claims the unit is "mole second inverse," which is typically written as "mol/s" or "moles per second."

**Conclusion:** This statement is **incorrect** because it misrepresents the unit of \(K\) for first-order reactions.

### Final Answer
The incorrect statement is: **The unit of \(K\) for first order is mole second inverse.**

---