Enthalpy of 1 mole monoatomic ideal gas is equals to :-

Options

A. `(3)/(2)RT`
B. `(5)/(2)RT`
C. RT
D. 2 RT

Explanation

To determine the enthalpy of 1 mole of a monoatomic ideal gas, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Formula for Enthalpy**:
The enthalpy change (ΔH) for a gas can be expressed as:
\[ \Delta H = n C_p \Delta T \]
where:
- \( n \) = number of moles of the gas,
- \( C_p \) = molar heat capacity at constant pressure,
- \( \Delta T \) = change in temperature.

2. **Identify the Molar Heat Capacity for Monoatomic Gas**:
For a monoatomic ideal gas, the molar heat capacity at constant pressure (\( C_p \)) is given by:
\[ C_p = \frac{5}{2} R \]
where \( R \) is the universal gas constant.

3. **Substitute the Values**:
Since we are considering 1 mole of the gas (\( n = 1 \)), we can substitute the values into the enthalpy change formula:
\[ \Delta H = 1 \cdot \frac{5}{2} R \Delta T \]
This simplifies to:
\[ \Delta H = \frac{5}{2} R \Delta T \]

4. **Integrate to Find Total Enthalpy**:
To find the total enthalpy (H), we can integrate with respect to temperature:
\[ H = \frac{5}{2} R T \]
Here, \( T \) is the absolute temperature of the gas.

5. **Conclusion**:
Therefore, the enthalpy of 1 mole of a monoatomic ideal gas is:
\[ H = \frac{5}{2} R T \]

### Final Answer:
The enthalpy of 1 mole of a monoatomic ideal gas is \( \frac{5}{2} R T \).