What is meant by the term lower in energy? Which is lower in energy, a mixture of hydrogen and oxygen gases or liquid water? How do you know? Which of the two is more stable? How do you know?

The term "lower in energy" refers to a state of a system where its overall potential energy is lower compared to another state. In chemistry, compounds or mixtures with lower energy states are generally more stable, as they release energy in the form of heat or light during the process of achieving that state.

Here, we have two systems: (1) a mixture of hydrogen and oxygen gases, and (2) liquid water. In the first system, hydrogen and oxygen exist as individual gas molecules. In the second system, hydrogen and oxygen have combined to form water molecules. To compare the energy states of these two systems, we can investigate their relative energy release when they form the other system.

When hydrogen and oxygen gases react to form water, the following chemical reaction takes place: \[2H_2(g) + O_2(g) \rightarrow 2H_2O(l)\] This reaction is exothermic, meaning it releases energy (in the form of heat) during the process. The negative standard enthalpy change (ΔH) for this reaction indicates that the system is losing energy: \[\Delta _rH^{\circ} = -285.8\:kJ/mol\] The fact that energy is released during this reaction means that liquid water has a lower energy state than a mixture of hydrogen and oxygen gases.

In general, systems in a lower energy state are considered more stable because they tend to be less reactive and require an input of energy to undergo changes. Since liquid water has a lower energy state than a mixture of hydrogen and oxygen gases, it is considered more stable. This stability can be observed in daily life, as liquid water is far less prone to spontaneous combustion or explosion than a mixture of hydrogen and oxygen gases. In summary, liquid water is lower in energy and more stable than a mixture of hydrogen and oxygen gases. This conclusion is based on the energy released during the reaction between hydrogen and oxygen gases to form water molecules and the general concept that lower energy states correlate with increased stability.