A gas in a closed container will exert much higher pressure due to gravity at the bottom than at the top.

Explanation

To solve the question regarding the pressure exerted by a gas in a closed container, we need to analyze the behavior of gas molecules and the effects of gravity.

### Step-by-Step Solution:

1. **Understanding the Concept of Pressure**:
Pressure is defined as the force exerted per unit area. In a gas, this pressure is due to the collisions of gas molecules with the walls of the container.

**Hint**: Remember that pressure is a measure of how much force is applied over a certain area.

2. **Behavior of Gas Molecules**:
Gas molecules are in constant random motion and collide with each other and the walls of the container. The forces between gas molecules are negligible compared to the forces acting on them due to their motion.

**Hint**: Consider how gas molecules behave in terms of motion and collisions rather than interactions with each other.

3. **Effect of Gravity on Gas**:
While gravity does act on gas molecules, the effect is minimal because the distance between gas molecules is large, and they are free to move. This means that the weight of the gas above does not significantly affect the pressure at the bottom compared to the pressure at the top.

**Hint**: Think about how the weight of a gas column affects pressure and how gases are less affected by gravity compared to liquids.

4. **Equal Pressure in All Directions**:
Due to the random motion of gas molecules and the negligible forces between them, the pressure exerted by the gas is uniform throughout the container. Therefore, the pressure at the bottom is not significantly higher than at the top.

**Hint**: Recall that in an ideal gas, pressure is uniform and does not vary with height in a closed container.

5. **Conclusion**:
The statement that a gas in a closed container will exert much higher pressure at the bottom than at the top is false. The pressure remains approximately equal throughout the container.

**Hint**: Summarize the key points: gas behavior, negligible intermolecular forces, and uniform pressure.

### Final Answer:
The statement is false; a gas in a closed container exerts equal pressure throughout, regardless of height.