`K_w` for water at `25^(@)C` is equal to `10^(-14)`. What is its value at `90^@C`-

Options

A. `10^(-15)`
B. `10^(-17)`
C. `10^(-14)`
D. `10^(-12)`

Answer

To determine the value of \( K_w \) (the ionic product of water) at \( 90^\circ C \), we can follow these steps:

### Step 1: Understand the Ionic Product of Water
The ionic product of water (\( K_w \)) is defined as the product of the concentrations of hydrogen ions (\( [H^+] \)) and hydroxide ions (\( [OH^-] \)) in water:
\[ K_w = [H^+][OH^-] \]

### Step 2: Analyze the Given Information
At \( 25^\circ C \), we know that:
\[ K_w = 10^{-14} \]
This means that at this temperature, the concentrations of \( [H^+] \) and \( [OH^-] \) are both \( 10^{-7} \) M.

### Step 3: Consider the Effect of Temperature on \( K_w \)
As the temperature increases, the dissociation of water increases, which leads to an increase in the concentrations of both \( [H^+] \) and \( [OH^-] \). Therefore, \( K_w \) will also increase with temperature.

### Step 4: Estimate \( K_w \) at \( 90^\circ C \)
While we do not have the exact value of \( K_w \) at \( 90^\circ C \) without experimental data, we can conclude that it will be greater than \( 10^{-14} \).

### Step 5: Evaluate the Options
Given the options, we need to find a value of \( K_w \) that is greater than \( 10^{-14} \). The potential options provided are:
- \( 10^{-15} \) (less than \( 10^{-14} \))
- \( 10^{-17} \) (less than \( 10^{-14} \))
- \( 10^{-14} \) (equal to the value at \( 25^\circ C \))
- \( 10^{-12} \) (greater than \( 10^{-14} \))

### Conclusion
Since \( K_w \) at \( 90^\circ C \) must be greater than \( 10^{-14} \), the only correct option is:
\[ K_w = 10^{-12} \]

### Final Answer:
The value of \( K_w \) at \( 90^\circ C \) is \( 10^{-12} \).

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