An endothermic reaction has a positive internal energy change `triangleU.` In such a case, what is the minimum value that activation energy can have ?

Options

A. `triangleU`
B. `triangle=triangleH+trianglenRT`
C. `triangleU=triangleH-trianglenRT`
D. `triangleU=triangleE_(a)+RT`

Answer

To determine the minimum value that activation energy (Ea) can have for an endothermic reaction with a positive internal energy change (ΔU), we can follow these steps:

### Step 1: Understand the Concepts
In an endothermic reaction, the change in enthalpy (ΔH) is positive. This means that the system absorbs heat from the surroundings. The relationship between internal energy change (ΔU) and enthalpy change (ΔH) can be expressed as:
\[ \Delta H = \Delta U + \Delta nRT \]
where Δn is the change in the number of moles of gas, R is the gas constant, and T is the temperature in Kelvin.

### Step 2: Rearranging the Equation
From the equation above, we can rearrange it to express ΔU in terms of ΔH:
\[ \Delta U = \Delta H - \Delta nRT \]

### Step 3: Analyze the Activation Energy
The activation energy (Ea) is the minimum energy required for a reaction to occur. For an endothermic reaction, the activation energy must be greater than the change in internal energy (ΔU) because the reactants need to overcome this energy barrier to reach the transition state.

### Step 4: Determine the Minimum Value of Activation Energy
Since ΔU is positive for an endothermic reaction, the minimum value of Ea must also be positive. Therefore, the minimum value of activation energy can be expressed as:
\[ E_a \geq \Delta U \]

### Conclusion
Thus, the minimum value that activation energy can have for an endothermic reaction with a positive internal energy change (ΔU) is at least equal to ΔU, which is a positive value.

### Final Answer
The minimum value that activation energy (Ea) can have is:
\[ E_a \geq \Delta U \]

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