In basic thermodynamics, which of the following substances will have the highest entropy under normal conditions among the options given?

Introduction / Context:
This question tests your conceptual understanding of entropy, a central idea in thermodynamics. Entropy is often described as a measure of disorder, randomness or the number of possible microscopic arrangements of a system. In simple exam questions, you are usually asked to compare entropy for solids, liquids and gases qualitatively. Recognising that gases generally have higher entropy than liquids and solids at similar temperatures helps you quickly identify the correct option without performing detailed calculations.

Given Data / Assumptions:

• We compare hydrogen gas, diamond (a solid), liquid nitrogen and liquid mercury.
• All substances are considered under normal laboratory conditions, not at extreme temperatures or pressures.
• Entropy is being compared qualitatively, not numerically.
• We assume standard physical states: hydrogen as a gas, nitrogen as a cryogenic liquid, diamond as a solid and mercury as a liquid metal.

Concept / Approach:
For a given substance or for similar conditions, the general rule is that gases have the highest entropy, liquids have intermediate entropy and solids have the lowest entropy. This is because gas molecules are free to move in a large volume and can occupy many more microscopic configurations than molecules locked in a solid lattice or constrained in a liquid. Among the options, hydrogen is a light diatomic gas at room temperature, whereas diamond is a rigid crystalline solid, and both nitrogen and mercury are liquids. Therefore, based on state alone, hydrogen gas must have the highest entropy.

Step-by-Step Solution:
Step 1: Classify each substance by physical state: hydrogen is a gas, diamond is a solid, liquid nitrogen is a cryogenic liquid and mercury is a liquid metal. Step 2: Recall the qualitative entropy order: solid < liquid < gas, where gas has the largest entropy for comparable conditions. Step 3: Compare hydrogen with the other options. As a gas, hydrogen molecules can move freely and occupy a much larger volume, giving many more possible microstates. Step 4: Recognise that diamond has a very ordered crystal structure, which corresponds to low entropy. Step 5: Understand that both liquid nitrogen and liquid mercury have higher entropy than solids but still less than gases because the molecules are more constrained than in a gas. Step 6: Conclude that hydrogen gas has the highest entropy among the given options.

Verification / Alternative check:
If you think in terms of molecular motion, hydrogen molecules move rapidly in all directions and can be present in a large volume, making the system highly disordered. In contrast, atoms in diamond vibrate around fixed positions in a rigid lattice, giving very few configurations. Liquid nitrogen and liquid mercury allow some flow but still maintain short range order. Standard thermodynamic tables also show that molar entropies of gases at standard conditions are significantly larger than those of liquids and solids, which confirms the qualitative reasoning.

Why Other Options Are Wrong:
Diamond has a very ordered crystalline structure, giving it one of the lowest entropies among the listed substances. Liquid nitrogen does have more entropy than many solids, but as a liquid it still has less entropy than a gas such as hydrogen at similar conditions. Mercury is a liquid metal with mobile atoms but still has fewer accessible microstates than a gas, so its entropy is lower than that of hydrogen gas.

Common Pitfalls:
Some learners mistakenly think that heavier substances always have higher entropy because they seem more complex. Others may confuse energy content with entropy. The key is to focus on the state of matter and the degree of freedom of the particles. Gases always win in terms of randomness and number of microstates. Remembering the simple ordering solid < liquid < gas is usually enough to answer qualitative entropy questions correctly in competitive exams.

Final Answer:
Among the given substances, the one with the highest entropy is Hydrogen gas.