Carbon and oxygen react in ratio 3 : 8 by mass to form `CO_(2)` . What weight of carbon should be used to react completely with 32 g of oxygen ?

Options

A. 10 g
B. 15 g
C. 12 g
D. 7g

Answer

To solve the problem, we need to find out how much carbon is required to react completely with 32 grams of oxygen, given that carbon and oxygen react in a mass ratio of 3:8.

### Step-by-Step Solution:

1. **Understand the Mass Ratio**:
The mass ratio of carbon to oxygen is given as 3:8. This means for every 3 grams of carbon, 8 grams of oxygen are required.

2. **Set Up the Equation**:
Let the mass of carbon be represented as \(3x\) and the mass of oxygen as \(8x\). According to the problem, we know the mass of oxygen is 32 grams.

3. **Relate Oxygen Mass to the Ratio**:
From the mass of oxygen, we can set up the equation:
\[ 8x = 32 \]

4. **Solve for \(x\)**:
To find \(x\), divide both sides of the equation by 8:
\[ x = \frac{32}{8} = 4 \]

5. **Calculate the Mass of Carbon**:
Now that we have \(x\), we can find the mass of carbon:
\[ \text{Mass of Carbon} = 3x = 3 \times 4 = 12 \text{ grams} \]

6. **Conclusion**:
Therefore, the weight of carbon that should be used to react completely with 32 grams of oxygen is **12 grams**.

### Final Answer:
The weight of carbon required is **12 grams**.

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