A' on heating at `700^(@)C` in air gives a white infusible amorphous powder (B) which is decomposed when heated in the currect of steam to give white powder 'C' and a gas 'D'.'D' turns red litmus blue and in aqueous solution , gives reddish brown ppt with `K_(2)HgI_(4)`. compound 'C on strong heating gives 'E.
'C' is

Options

A. `B_(2)O_(3)`
B. `H_(3)BO_(3)`
C. `P_(2)O_(5)`
D. `SiO_(2)`

Explanation

To solve the problem step by step, we will analyze the information provided and deduce the compounds involved.

### Step 1: Identify Compound A
The problem states that compound A, when heated at 700°C in air, produces a white infusible amorphous powder B. Since the reaction occurs in air, which consists mainly of nitrogen and oxygen, we can deduce that compound A is likely a boron compound, specifically boron nitride (BN).

**Hint:** Consider common compounds that can react with air at high temperatures to form stable oxides or nitrides.

### Step 2: Identify Compound B
When boron nitride (BN) is heated in air, it forms boron oxide (B2O3) as compound B. B2O3 is a white, amorphous powder that is infusible.

**Hint:** Look for the products of boron compounds when they react with oxygen at high temperatures.

### Step 3: Heating Compound B with Steam
Next, compound B (B2O3) is heated in the presence of steam (H2O). This reaction leads to the formation of compound C and gas D. The reaction of boron oxide with water typically produces boric acid (H3BO3) and hydrogen gas (H2).

**Hint:** Consider the reactions of metal oxides with water and how they can form acids or bases.

### Step 4: Identify Compound C
From the previous step, we deduce that compound C is boric acid (H3BO3).

**Hint:** Think about the products formed when oxides of non-metals react with water.

### Step 5: Identify Gas D
Gas D is produced alongside compound C. The problem states that gas D turns red litmus blue, indicating it is basic in nature. Since hydrogen gas (H2) does not turn litmus blue, we can conclude that gas D is ammonia (NH3), which is produced when boric acid reacts with a base.

**Hint:** Look for gases that are basic and can affect litmus paper.

### Step 6: Reaction of Compound C to Form Compound E
When boric acid (H3BO3) is heated strongly, it can dehydrate to form boron trioxide (B2O3), which is compound E.

**Hint:** Consider the thermal decomposition of acids and how they can yield oxides.

### Final Answer
Thus, compound C is **H3BO3 (boric acid)**.