For a reaction, `C_((s))+O_(2(g))rarrCO_(2(g))`
What is the relation between enthalpy of reaction `(DeltaH_(r)),` enthalpy of formation of `CO_(2)(DeltaH_(f))` and enthalpy of combustion of carbon `(DeltaH_("comb"))` ?

Options

A. `DeltaH_(r) gt DeltaH_(f) = DeltaH_("comb")`
B. `DeltaH_(r)=DeltaH_(f)=DeltaH_("comb")`
C. `DeltaH_(r)=DeltaH_(f)+DeltaH_("comb")`
D. `DeltaH_(r)=2xxDeltaH_(f)`

Explanation

To determine the relationship between the enthalpy of reaction (ΔH_r), the enthalpy of formation of CO₂ (ΔH_f), and the enthalpy of combustion of carbon (ΔH_comb), we can analyze the given reaction:

**Step 1: Write the reaction.**
The reaction is:
\[ C_{(s)} + O_{2(g)} \rightarrow CO_{2(g)} \]

**Step 2: Identify the processes involved.**
This reaction involves:
- The formation of carbon dioxide (CO₂) from carbon (C) and oxygen (O₂).
- The combustion of carbon, as carbon is reacting with oxygen to produce CO₂.

**Step 3: Understand the definitions.**
- **Enthalpy of Reaction (ΔH_r)**: This is the heat change associated with the reaction at constant pressure.
- **Enthalpy of Formation (ΔH_f)**: This is the heat change when one mole of a compound is formed from its elements in their standard states.
- **Enthalpy of Combustion (ΔH_comb)**: This is the heat change when one mole of a substance is completely burned in oxygen.

**Step 4: Relate the enthalpies.**
In this specific reaction:
- The enthalpy of formation of CO₂ (ΔH_f) is equal to the enthalpy change when carbon is burned in oxygen to form CO₂. Therefore, the enthalpy of reaction (ΔH_r) for the combustion of carbon to form CO₂ is equal to the enthalpy of formation of CO₂.

Thus, we can conclude:
\[ ΔH_r = ΔH_f = ΔH_{comb} \]

**Step 5: Final expression.**
The relationship can be expressed as:
\[ ΔH_r = ΔH_f = ΔH_{comb} \]