10 litres of `O_(2)` gas is reacted with 30 litres of CO at S.T.P. The volumes of each gas present at the end of the reaction are

Options

A. `CO=10` litres, `CO_(2)=20` litres
B. `O_(2)=10` litres, `CO=30` litres
C. `CO=20` litres, `CO_(2) = 10` lites
D. `O_(2) = 10` litres, `CO_(2)=20` litres

Explanation

To solve the problem of how much gas remains after the reaction of 10 liters of \( O_2 \) with 30 liters of \( CO \) at STP, we need to follow these steps:

### Step 1: Write the balanced chemical equation
The reaction between carbon monoxide (\( CO \)) and oxygen (\( O_2 \)) produces carbon dioxide (\( CO_2 \)). The balanced equation for this reaction is:

\[ 2 CO + O_2 \rightarrow 2 CO_2 \]

### Step 2: Determine the stoichiometry of the reaction
From the balanced equation, we can see that:
- 2 volumes of \( CO \) react with 1 volume of \( O_2 \).
- This means that for every 1 liter of \( O_2 \), 2 liters of \( CO \) are required.

### Step 3: Calculate the amount of \( CO \) needed for the available \( O_2 \)
We have 10 liters of \( O_2 \). According to the stoichiometry:
- To react with 10 liters of \( O_2 \), we need:
\[ 10 \, \text{liters of } O_2 \times 2 = 20 \, \text{liters of } CO \]

### Step 4: Compare the required \( CO \) with the available \( CO \)
We have 30 liters of \( CO \) available, but only 20 liters are needed to react with the 10 liters of \( O_2 \). Therefore, \( O_2 \) will be the limiting reactant.

### Step 5: Calculate the remaining volumes of gases after the reaction
- **Consumption of \( O_2 \)**: All 10 liters of \( O_2 \) will be consumed.
- **Consumption of \( CO \)**: 20 liters of \( CO \) will react with the 10 liters of \( O_2 \).

Thus, the remaining \( CO \) will be:
\[ 30 \, \text{liters (initial)} - 20 \, \text{liters (reacted)} = 10 \, \text{liters of } CO \]

### Step 6: Calculate the amount of \( CO_2 \) produced
According to the balanced equation, 2 volumes of \( CO \) produce 2 volumes of \( CO_2 \). Therefore, the 20 liters of \( CO \) that reacted will produce:
\[ 20 \, \text{liters of } CO_2 \]

### Final Result
At the end of the reaction, the volumes of each gas present are:
- \( CO \): 10 liters
- \( CO_2 \): 20 liters

### Summary
- The final volumes of gases after the reaction are:
- \( CO \): 10 liters
- \( CO_2 \): 20 liters

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