The standard heat of combustion of a solid boron is equal to:

Options

A. `DeltaH_(f)^(@)(B_(2)O_(3))`
B. `1//2DeltaH_(f)^(@)(B_(2)O_(3))`
C. `2DeltaH_(f)^(@)(B_(2)O_(3))`
D. `1//2DeltaH_(f)^(@)(B_(2)O_(3))`

Explanation

To find the standard heat of combustion of solid boron, we can follow these steps:

### Step 1: Write the combustion reaction
The combustion of boron (B) can be represented by the following balanced chemical equation:
\[ 4B(s) + 3O_2(g) \rightarrow 2B_2O_3(s) \]

### Step 2: Understand the heat of combustion
The heat of combustion is the heat released when one mole of a substance is completely burned in oxygen. For boron, we need to find the heat released when 4 moles of solid boron combust.

### Step 3: Relate heat of combustion to heat of formation
The heat of combustion of boron can be related to the heat of formation of boron oxide (B2O3). The heat of combustion (ΔH_comb) of boron can be expressed as:
\[ \Delta H_{\text{comb}} = \Delta H_f(B_2O_3) \]
However, since the equation shows the formation of 2 moles of B2O3 from 4 moles of boron, we need to divide the heat of formation by 2 to find the heat of combustion per mole of boron:
\[ \Delta H_{\text{comb}}(B) = \frac{1}{2} \Delta H_f(B_2O_3) \]

### Step 4: Determine the sign of ΔH_comb
The heat of formation of B2O3 is typically a negative value because it is an exothermic reaction. Therefore, the heat of combustion of boron will also be negative:
\[ \Delta H_{\text{comb}}(B) < 0 \]

### Step 5: Choose the correct option
Given the options A, B, C, D, we can conclude that the heat of combustion of solid boron is negative, which means that option B is the correct answer.

### Final Answer:
The standard heat of combustion of solid boron is negative and corresponds to option B.

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