For the reaction
`aA(s) + bB(g) rightarrow dD(s) + cC(g)`. Then

Options

A. `Delta H - Delta E = (b-d) RT`
B. `Delta H - Delta E = (c - b) RT`
C. `Delta H - Delta E = (a + b) - (c + d) RT`
D. `Delta H - Delta E = (a - d) RT`

Answer

To solve the problem, we need to analyze the given reaction and derive the relationship between the change in enthalpy (ΔH) and the change in internal energy (ΔE) using the number of moles of gaseous products and reactants.

### Step-by-Step Solution:

1. **Identify the Reaction Components**:
The reaction is given as:
\[ aA(s) + bB(g) \rightarrow dD(s) + cC(g) \]
Here, \(A\) and \(D\) are solids, while \(B\) and \(C\) are gases.

2. **Determine the Change in Moles of Gas (ΔN)**:
The change in the number of moles of gas (\(ΔN_g\)) is calculated by subtracting the total number of moles of gaseous reactants from the total number of moles of gaseous products:
\[ ΔN_g = \text{(moles of gaseous products)} - \text{(moles of gaseous reactants)} \]
In this case:
- Moles of gaseous products = \(c\) (from \(C(g)\))
- Moles of gaseous reactants = \(b\) (from \(B(g)\))

Therefore:
\[ ΔN_g = c - b \]

3. **Apply the Relationship Between ΔH and ΔE**:
The relationship between the change in enthalpy (ΔH) and the change in internal energy (ΔE) is given by:
\[ ΔH = ΔE + ΔN_g \cdot R \cdot T \]
Rearranging this equation gives:
\[ ΔH - ΔE = ΔN_g \cdot R \cdot T \]

4. **Substitute ΔN_g into the Equation**:
Now, substituting \(ΔN_g = c - b\) into the equation:
\[ ΔH - ΔE = (c - b) \cdot R \cdot T \]

5. **Final Result**:
Thus, the final expression we derive is:
\[ ΔH - ΔE = (c - b) \cdot R \cdot T \]

### Conclusion:
The correct answer to the question is:
\[ ΔH - ΔE = (c - b) \cdot R \cdot T \]