For the reaction
`CH_4(g) +2O_2(g) hArr CO_2(g) +2H_2O(I)`
`Delta_rH=-170.8 kJ mol ^(-1)`
Which of the following statements is not true ?

Options

A. At equilibrium , the concentration of `CO_2(g) and H_2O(I)` are not equal
B. The equilibrium constant for the reaction is
given by `K_p =([CO_2])/([CH_4][O_2])`
C. Addition of `CH_4(g) or O_2(g)` at equilibrium will cause a shift to the right
D. The reaction is exothermic

Answer

To determine which statement is not true regarding the reaction:

\[ \text{CH}_4(g) + 2\text{O}_2(g) \rightleftharpoons \text{CO}_2(g) + 2\text{H}_2\text{O}(l) \]
with \(\Delta_rH = -170.8 \, \text{kJ mol}^{-1}\), we will analyze each statement one by one.

### Step 1: Analyze the first statement
The first statement suggests that the concentrations of \(\text{CO}_2\) and \(\text{H}_2\text{O}\) at equilibrium are not equal.

**Analysis:**
- Initially, we have 1 mole of \(\text{CH}_4\) and 2 moles of \(\text{O}_2\), with 0 moles of \(\text{CO}_2\) and \(\text{H}_2\text{O}\).
- At equilibrium, if \(x\) moles of \(\text{CH}_4\) react, then:
- \(\text{CH}_4\) will be \(1 - x\)
- \(\text{O}_2\) will be \(2 - 2x\)
- \(\text{CO}_2\) will be \(x\)
- \(\text{H}_2\text{O}\) will be \(2x\)

Since the moles of \(\text{CO}_2\) and \(\text{H}_2\text{O}\) are \(x\) and \(2x\) respectively, they are not equal. Thus, this statement is true.

### Step 2: Analyze the second statement
The second statement claims that the expression for \(K_p\) for this reaction is incorrect.

**Analysis:**
- The equilibrium constant \(K_p\) is defined as:
\[ K_p = \frac{P_{\text{CO}_2}}{P_{\text{CH}_4} \cdot (P_{\text{O}_2})^2} \]
- The stoichiometric coefficients from the balanced equation dictate the powers in the expression. Here, the powers are correct as per the reaction stoichiometry.

Thus, this statement is not true.

### Step 3: Analyze the third statement
The third statement suggests that adding \(\text{CH}_4\) or \(\text{O}_2\) at equilibrium will shift the equilibrium to the right.

**Analysis:**
- According to Le Chatelier's principle, if we increase the concentration of reactants, the equilibrium will shift to the right to produce more products. Therefore, this statement is true.

### Step 4: Analyze the fourth statement
The fourth statement claims that the reaction is exothermic.

**Analysis:**
- The given \(\Delta_rH\) is negative (\(-170.8 \, \text{kJ mol}^{-1}\)), indicating that heat is released during the reaction. This confirms that the reaction is exothermic, making this statement true.

### Conclusion
The statement that is not true is the second one regarding the expression for \(K_p\).

### Final Answer
The statement that is not true is: **"The Kp expression for this reaction is correct."**