If the ionic product of water is `1.96 xx 10^(-14)` at `35^(0)C`,What is the value at `10^(0)C`

Options

A. `2.95 xx 10^(-14)`
B. `1.96 xx 10^(-7)`
C. `2.95 xx 10^(-15)`
D. `3.9 xx 10^(-12)`

Answer

To find the ionic product of water (Kw) at 10°C given that Kw is 1.96 x 10^(-14) at 35°C, we can follow these steps:

### Step 1: Understand the relationship between temperature and Kw
The ionic product of water (Kw) varies with temperature. As temperature increases, Kw increases, and as temperature decreases, Kw decreases.

### Step 2: Identify the given values
- Kw at 35°C = 1.96 x 10^(-14)
- We need to find Kw at 10°C.

### Step 3: Analyze the trend
Since 10°C is lower than 35°C, we expect Kw at 10°C to be less than 1.96 x 10^(-14).

### Step 4: Evaluate the options
We need to look at the provided options and determine which one is less than 1.96 x 10^(-14):
1. 2.95 x 10^(-14) (greater than 1.96 x 10^(-14))
2. 10^(-7) (greater than 1.96 x 10^(-14))
3. 2.95 x 10^(-14) (greater than 1.96 x 10^(-14))
4. 10^(-12) (less than 1.96 x 10^(-14))

### Step 5: Select the correct option
From the analysis, the only value that is less than 1.96 x 10^(-14) is 10^(-12). Therefore, the ionic product of water at 10°C is:

**Kw at 10°C = 10^(-12)**

### Final Answer:
Kw at 10°C = 10^(-12)

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