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Heat of reaction is defined as the amoun...

Heat of reaction is defined as the amount of heat absorbed or evolved at a given temperaturewhen the reactants have combined to form the products is represented by a balanced chemcial equation. If the heat is denofed by q then the numerical value of q depends on the manner in which the reaction is performed for the two methods of conducting chemical reactions in calorimeters.
Constant volume W = 0 and `q_(v) = Delta E` Bomb calorimeter
Constant pressure W = - V `Delta`P, therefore `q_(P) = Delta E + P Delta V rar (V. Delta P)`
The heat capacity of a bomb calorimeter is 300 JK When 0.16 gm of methane was burnt in this calorimeter the temperature rose by `3^(@)`C. The value of `Delta`U per mole will be
a. 100 KJ
b. 90 KJ
c. 900 KJ
d. 48KJ

A

100 kJ

B

90 kJ

C

900 kJ

D

48 kJ

Text Solution

AI Generated Solution

The correct Answer is:
To find the value of ΔU (change in internal energy) per mole of methane when burned in a bomb calorimeter, we can follow these steps: ### Step-by-Step Solution: 1. **Identify the heat capacity of the calorimeter and the temperature change:** - Given: Heat capacity of the bomb calorimeter (C) = 300 J/K - Temperature change (ΔT) = 3°C = 3 K (since the change in temperature in Celsius is equivalent to Kelvin) 2. **Calculate the total heat absorbed by the calorimeter:** - The heat absorbed (q) can be calculated using the formula: \[ q = C \times \Delta T \] - Substituting the values: \[ q = 300 \, \text{J/K} \times 3 \, \text{K} = 900 \, \text{J} \] 3. **Convert the mass of methane to moles:** - The molar mass of methane (CH₄) is approximately 16 g/mol. - Given mass of methane = 0.16 g - Calculate the number of moles (n): \[ n = \frac{\text{mass}}{\text{molar mass}} = \frac{0.16 \, \text{g}}{16 \, \text{g/mol}} = 0.01 \, \text{mol} \] 4. **Calculate ΔU per mole:** - The heat released per mole of methane can be calculated by scaling the heat absorbed by the number of moles: \[ \Delta U = \frac{q}{n} = \frac{900 \, \text{J}}{0.01 \, \text{mol}} = 90000 \, \text{J/mol} = 90 \, \text{kJ/mol} \] 5. **Final Answer:** - The value of ΔU per mole of methane is 90 kJ. ### Conclusion: The correct answer is **b. 90 kJ**.
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