Which of the following quantities is the same for all ideal gases at the same temperature?

Options

A. (a)the kinetic energy of 1 mole
B. (b)The kinetic energy of 1 g
C. (c)The number of molecules in 1mole
D. (d)The number of molecules in 1g.

Answer

To solve the question "Which of the following quantities is the same for all ideal gases at the same temperature?" we need to analyze the options provided and understand the principles of the kinetic theory of gases.

### Step-by-Step Solution:

1. **Understanding the Question**: The question asks which quantity remains constant for all ideal gases when they are at the same temperature. We need to evaluate each option carefully.

2. **Option 1: Kinetic Energy of 1 Mole**:
- The kinetic energy (KE) of one mole of an ideal gas can be calculated using the formula:
\[ KE = \frac{3}{2} RT \]
where \( R \) is the universal gas constant and \( T \) is the temperature in Kelvin. Since \( R \) and \( T \) are constants for a given temperature, the kinetic energy of one mole of any ideal gas is the same at the same temperature.
- **Conclusion**: This option is correct.

3. **Option 2: Kinetic Energy of 1 Gram**:
- The kinetic energy of 1 gram of gas depends on the number of molecules in that gram, which varies with the molar mass of the gas. Different gases have different molar masses, leading to different numbers of molecules in 1 gram, and thus different kinetic energies.
- **Conclusion**: This option is incorrect.

4. **Option 3: Number of Molecules in 1 Mole**:
- The number of molecules in one mole of any substance is defined by Avogadro's number, which is approximately \( 6.022 \times 10^{23} \). This is a constant for all substances, including all ideal gases.
- **Conclusion**: This option is correct.

5. **Option 4: Number of Molecules in 1 Gram**:
- The number of molecules in 1 gram of a gas varies depending on the molar mass of the gas. Since different gases have different molar masses, the number of molecules in 1 gram will differ from one gas to another.
- **Conclusion**: This option is incorrect.

### Final Answer:
The quantities that are the same for all ideal gases at the same temperature are:
- **Option 1: Kinetic Energy of 1 Mole**
- **Option 3: Number of Molecules in 1 Mole**