In which of the following conditions, the distance between the molecules of hydrogen gas would increase, filled in a container ?
(i) Some hydrogen gas leaking out the container.
(ii) Increasing the volume of container of hydrogen gas.
(iii) Increasing pressure on hydrogen gas contained in a closed container.
(iv) Adding more hydrogen gas to container without increasing the volume of the container.

Question

Accepted Answer

Option 3 is the correct answer, which includes conditions (i) and (ii). Let's explore why these conditions lead to an increase in the distance between the molecules of hydrogen gas and why the other options are incorrect.

1. **Explanation for Option 3:**

- **Condition (i): Some hydrogen gas leaking out of the container.**
     - When hydrogen gas leaks out of the container, the number of gas molecules inside the container decreases. Since the volume of the container remains the same, the remaining gas molecules have more space to move around. This results in an increase in the average distance between the molecules.

- **Condition (ii): Increasing the volume of the container of hydrogen gas.**
     - When the volume of the container is increased, the same number of hydrogen gas molecules now occupies a larger space. This expansion allows the molecules to spread out more, thereby increasing the distance between them.

2. **Why the other options are incorrect:**

- **Option 1: (ii) and (iii)**
     - Condition (iii) involves increasing the pressure on hydrogen gas contained in a closed container. Increasing pressure typically compresses the gas, reducing the volume it occupies and decreasing the distance between molecules. Therefore, condition (iii) does not lead to an increase in the distance between molecules, making this option incorrect.

- **Option 2: (ii) and (iv)**
     - Condition (iv) involves adding more hydrogen gas to the container without increasing the volume. This results in more molecules being packed into the same space, which decreases the distance between molecules. Thus, condition (iv) does not support an increase in the distance between molecules, making this option incorrect.

- **Option 4: (i) and (iii)**
     - As explained earlier, condition (iii) involves increasing pressure, which decreases the distance between molecules. Therefore, pairing condition (i) with condition (iii) does not support an increase in the distance between molecules, making this option incorrect.

In conclusion, Option 3 is correct because both conditions (i) and (ii) lead to an increase in the distance between the molecules of hydrogen gas. The other options include conditions that either do not affect or decrease the distance between the molecules, thus making them incorrect.