To solve the problem, we need to determine the standard enthalpy of formation for ethane (\( \text{C}_2\text{H}_6 \)) using the given combustion reaction.
1. Given Reaction:
The balanced chemical equation for the combustion of ethane is:
$$ 2\text{C}_2\text{H}_6(g) + 7\text{O}_2(g) \rightarrow 4\text{CO}_2(g) + 6\text{H}_2\text{O}(l); \quad \Delta H = -4100 \, \text{kJ} $$
2. Enthalpy Calculation Setup:
Let \( \Delta H_f^\circ(\text{C}_2\text{H}_6) = x \). The enthalpy change can be expressed as:
$$ \Delta H = \Delta H_f^\circ(\text{products}) - \Delta H_f^\circ(\text{reactants}) $$
3. Substituting Values:
Using known enthalpy values (\( \Delta H_f^\circ(\text{CO}_2) = -410 \, \text{kJ/mol} \) and \( \Delta H_f^\circ(\text{H}_2\text{O}) = -285 \, \text{kJ/mol} \)):
$$ -4100 = [4(-410) + 6(-285)] - [2x + 0] $$
4. Final Calculation:
Solving the equation gives:
$$ x = -375 \, \text{kJ} $$
Final Answer:
The standard enthalpy of formation for ethane is \( \boxed{-375 \, \text{kJ}} \).
To determine the heat of formation of C2H6(g), we'll analyze the given combustion reaction and apply thermodynamic principles.
1. Balanced Combustion Reaction:
The combustion equation for ethane is:
C2H6(g) + (7/2)O2(g) → 2CO2(g) + 3H2O(l)
2. Using Hess's Law:
The enthalpy change can be calculated as:
ΔH°combustion = Σ(n × ΔH°f products) - Σ(n × ΔH°f reactants)
3. Substituting Known Values:
Given data:
- ΔH°combustion = -4100 kJ for 2 moles → -2050 kJ/mol
- ΔH°f(CO2) = -410 kJ/mol
- ΔH°f(H2O) = -285 kJ/mol
- ΔH°f(O2) = 0 kJ/mol
Let ΔH°f(C2H6) = x
4. Setting Up the Equation:
-2050 = [2(-410) + 3(-285)] - [x + (7/2)(0)]
-2050 = [-820 - 855] - x
-2050 = -1675 - x
5. Solving for x:
x = -1675 + 2050
x = 375 kJ
Thus, ΔH°f(C2H6) = -375 kJ (heat of formation is exothermic)
Final Answer:
The heat of formation of C2H6(g) is -375 kJ.
Match List-I with List-II: List-I List-II
In the given cycle ABCDA, the heat required for an ideal monoatomic gas will be:
A solid cylinder of mass 2 kg and radius 0.2 m is rotating about its own axis without friction with angular velocity 5 rad/s. A particle of mass 1 kg moving with a velocity of 5 m/s strikes the cylinder and sticks to it as shown in figure.
The angular velocity of the system after the particle sticks to it will be: