Which relation is wrong

Options

A. `10^(-pH)+10^(-pOH)=10^(-14)`
B. `pH alpha(1)/([H^(+)])`
C. `K_(w) prop T`
D. dissociation constant of water `K=1.8 xx 10^(-16)`

Explanation

To determine which relation is wrong, we need to analyze the information provided in the question and the video transcript.

### Step-by-Step Solution:

1. **Identify the Constants**:
- The transcript mentions \( K_w \) (the ion product of water) and \( K_b \) (the base dissociation constant). Recall that \( K_w = [H^+][OH^-] \) at a given temperature.

2. **Understand the Relationship**:
- The relationship between \( K_w \) and \( K_b \) can be expressed as:
\[ K_w = K_a \cdot K_b \]
- Here, \( K_a \) is the acid dissociation constant. This relationship holds true at a specific temperature.

3. **Analyze the Values Provided**:
- The transcript mentions values such as \( 10^{-7} \) and \( 1.003 \). We need to clarify if these values are consistent with known constants at room temperature (25°C), where \( K_w \) is approximately \( 1.0 \times 10^{-14} \).

4. **Check for Errors**:
- The statement that both \( K_w \) and \( K_b \) are equal to \( 10^{-7} \) is incorrect. At 25°C, \( K_w \) should be \( 1.0 \times 10^{-14} \), and \( K_b \) cannot be \( 10^{-7} \) unless it is for a very weak base.

5. **Conclusion**:
- The incorrect relation is the assumption that \( K_w \) and \( K_b \) can both be \( 10^{-7} \). This is not valid as it contradicts the established relationship between these constants.

### Final Answer:
The wrong relation is the assumption that \( K_w = K_b = 10^{-7} \).