Burning of coal is represented as `C(s)+O_(2)(g)rarr CO_(2)(g)`. The rate of this reaction is increased by

Options

A. Decrease in the concentration of oxygen
B. Powdering the jump of coal
C. Decreaisng the temperature of coal
D. Providing inert atmosphere

Explanation

To solve the question regarding the burning of coal represented by the reaction \( C(s) + O_2(g) \rightarrow CO_2(g) \), we need to analyze how the rate of this reaction can be increased.

### Step-by-Step Solution:

1. **Understanding the Reaction**:
- The reaction involves solid carbon (coal) reacting with gaseous oxygen to produce carbon dioxide. This is a heterogeneous reaction because it involves different phases (solid and gas).

2. **Analyzing the Options**:
- **Option A: Decrease in the concentration of oxygen**:
- Decreasing the concentration of a reactant (in this case, oxygen) would lead to a decrease in the rate of reaction. This is because fewer reactant molecules are available to collide and react. Hence, this option does not increase the rate of reaction.

- **Option B: Powdering the lump of coal**:
- Powdering the coal increases its surface area. In heterogeneous reactions, a larger surface area allows for more collisions between reactant molecules. This increases the rate of reaction significantly. Therefore, this option is likely to increase the rate of the reaction.

- **Option C: Decreasing the temperature of the coal**:
- Decreasing the temperature generally slows down the reaction rate because it reduces the kinetic energy of the molecules, leading to fewer effective collisions. Therefore, this option does not increase the rate of reaction.

- **Option D: Providing an inert atmosphere**:
- An inert atmosphere means that there is no oxygen present to react with the coal. Without oxygen, the burning cannot occur, which would decrease the rate of the reaction. Thus, this option does not increase the rate of reaction.

3. **Conclusion**:
- After analyzing all the options, we conclude that the only option that increases the rate of the reaction is **Option B: Powdering the lump of coal**.

### Final Answer:
The rate of the reaction is increased by **powdering the lump of coal** (Option B).