Assertion (A) : If `30 mL` of `H_(2)` and `20 mL` of `O_(2)` react to form water, `5 mL` of `H_(2)` is left at the end of the reaction.
Reason (R ): `H_(2)` is the limiting reagent.

Options

A. If both (A) and (R ) are correct and (R ) is the correct explantion for (A)
B. If both (A) and (R ) are correct but (R ) is not the correct explantion for (A)
C. If (A) is correct but (R ) is incorrect.
D. If (A) and (R ) are incorrect.

Explanation

To solve the question step by step, we will analyze the assertion and reason provided in the question.

### Step 1: Write the balanced chemical equation for the reaction.
The reaction between hydrogen and oxygen to form water can be represented as:
\[ 2H_2 + O_2 \rightarrow 2H_2O \]

### Step 2: Determine the stoichiometric ratios.
From the balanced equation, we see that:
- 2 volumes of \(H_2\) react with 1 volume of \(O_2\).
- Therefore, 1 volume of \(H_2\) requires \(0.5\) volumes of \(O_2\).

### Step 3: Calculate the amount of \(O_2\) required for the given \(H_2\).
Given that we have \(30 \, mL\) of \(H_2\):
- The amount of \(O_2\) required can be calculated as:
\[ \text{Required } O_2 = \frac{30 \, mL \, H_2}{2} = 15 \, mL \, O_2 \]

### Step 4: Compare the available \(O_2\) with the required \(O_2\).
We have \(20 \, mL\) of \(O_2\) available, which is more than the \(15 \, mL\) required. Therefore, \(O_2\) is in excess.

### Step 5: Determine the limiting reagent.
Since \(H_2\) is required in a higher ratio compared to \(O_2\) and we have more than enough \(O_2\), \(H_2\) is the limiting reagent.

### Step 6: Calculate the remaining \(H_2\) after the reaction.
Since \(30 \, mL\) of \(H_2\) is available and \(15 \, mL\) of \(O_2\) is consumed:
- The amount of \(H_2\) that reacts with \(15 \, mL\) of \(O_2\) is:
\[ \text{Reacted } H_2 = 30 \, mL - 15 \, mL = 15 \, mL \]
- Therefore, the remaining \(H_2\) after the reaction is:
\[ \text{Remaining } H_2 = 30 \, mL - 15 \, mL = 15 \, mL \]

### Step 7: Analyze the assertion and reason.
- The assertion states that \(5 \, mL\) of \(H_2\) is left at the end of the reaction, which is incorrect as we calculated \(15 \, mL\) remaining.
- The reason states that \(H_2\) is the limiting reagent, which is correct.

### Conclusion:
- Assertion (A) is incorrect.
- Reason (R) is correct.

### Final Answer:
Assertion is incorrect, but the reason is correct.

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