Heat of combustion of A(s) is -10" kcal mol"^(-1) and that of B is-"15 kcal mol"^(-1). On combustion of 3 mol of A and x mol of B , the heat released "105 kcal ". What is the value of x ?

Answer

To solve the problem, we need to determine the value of \( x \) (the number of moles of B) given the heat of combustion for substances A and B and the total heat released during their combustion.

### Step-by-Step Solution:

1. **Identify the heat of combustion for A and B:**
- Heat of combustion of A (per mole) = -10 kcal/mol
- Heat of combustion of B (per mole) = -15 kcal/mol

2. **Calculate the total heat released from the combustion of A:**
- Since 3 moles of A are combusted, the total heat released from A is:
\[ \text{Heat from A} = 3 \, \text{moles} \times (-10 \, \text{kcal/mol}) = -30 \, \text{kcal} \]

3. **Set up the equation for total heat released:**
- The total heat released from the combustion of 3 moles of A and \( x \) moles of B is given as -105 kcal (since heat released is a negative value).
- The heat released from B can be expressed as:
\[ \text{Heat from B} = x \, \text{moles} \times (-15 \, \text{kcal/mol}) = -15x \, \text{kcal} \]

4. **Combine the heats:**
- The total heat released can be expressed as:
\[ \text{Total Heat} = \text{Heat from A} + \text{Heat from B} \]
- Substituting the known values:
\[ -105 \, \text{kcal} = -30 \, \text{kcal} + (-15x \, \text{kcal}) \]

5. **Rearranging the equation:**
- Simplifying the equation:
\[ -105 = -30 - 15x \]
- Adding 30 to both sides:
\[ -105 + 30 = -15x \]
\[ -75 = -15x \]

6. **Solving for \( x \):**
- Divide both sides by -15:
\[ x = \frac{-75}{-15} = 5 \]

### Conclusion:
The value of \( x \) is 5. Therefore, 5 moles of B are combusted.