Which of the following is incorrect ?

Options

A. When `NO_2` is dissolved in cold water , a mixture of nitrous and nitric acid is formed
B. When `NO_2` is dissolved in hot water , the same reaction occurs as that in cold water
C. `N_2O_5` is made by the reaction of `P_4O_(10)` with nitric acid vapours
D. `NO_2` is very corrosive gas and reacts directly with a number of metals

Answer

To solve the question "Which of the following is incorrect?", we will analyze each option provided and determine their correctness based on chemical principles.

### Step-by-Step Solution:

1. **Option A: When NO2 is dissolved in cold water, a mixture of nitrous and nitric acid is formed.**
- When nitrogen dioxide (NO2) is dissolved in cold water, it reacts to form a mixture of nitrous acid (HNO2) and nitric acid (HNO3). The reaction can be represented as:
\[ 2 NO_2 + H_2O \rightarrow HNO_2 + HNO_3 \]
- This statement is **true**.

2. **Option B: When NO2 is dissolved in hot water, the same reaction occurs as in cold water.**
- In hot water, the reaction is different. NO2 can dimerize to form N2O4, which then reacts with water to produce HNO2 and HNO3, but additionally, the heat can lead to the decomposition of HNO2 into nitrogen oxides (NO and NO2):
\[ N_2O_4 + H_2O \rightarrow HNO_2 + HNO_3 \]
\[ HNO_2 \xrightarrow{heat} NO + NO_2 + H_2O \]
- Therefore, the products differ from those formed in cold water. This statement is **incorrect**.

3. **Option C: N2O5 is made by the reaction of P4O10 with nitric acid.**
- The reaction of phosphorus pentoxide (P4O10) with nitric acid (HNO3) indeed produces dinitrogen pentoxide (N2O5):
\[ P_4O_{10} + 4 HNO_3 \rightarrow 2 N_2O_5 + 4 H_2O \]
- This statement is **true**.

4. **Option D: NO2 is a very corrosive gas and reacts directly with a number of metals.**
- Nitrogen dioxide (NO2) is known to be a corrosive gas and can react with metals to form metal nitrates. It is also a paramagnetic substance due to the presence of an unpaired electron, which contributes to its reactivity.
- This statement is **true**.

### Conclusion:
The only incorrect statement among the options provided is **Option B**.