Most mixtures of hydrogen gas with oxygen gas are explosive. However, a mixture that contains less than 3.0 \(\% \mathrm{O}_{2}\) is not. If enough \(\mathrm{O}_{2}\) is added to a cylinder of \(\mathrm{H}_{2}\) at 33.2 atm to bring the total pressure to \(34.5 \mathrm{atm}\), is the mixture explosive?

When we mix different gases, such as oxygen and hydrogen, each contributing to the overall pressure in their container, we create a gas mixture. An important characteristic of gas mixtures to note is that the gases do not react chemically under normal conditions inside the mixture. They each maintain their chemical identities but share the total volume of the container.

Understanding gas mixtures is critical in many fields, including chemistry, environmental science, and industrial processes. For example, divers must be aware of the specific gas mixtures in their tanks to avoid decompression sickness, and engineers must mind the mix of gases when creating certain metal alloys.

When dealing with gas mixtures, it's also essential to understand the individual pressures that each gas exerts, which can be described by concepts like Dalton's Law of Partial Pressures. In the context of this exercise, analyzing the mixture of hydrogen and oxygen gases can determine whether an explosive compound is formed or not, which is a key safety consideration in many industries.

Explosive gas limits refer to the concentration range within which a gas mixture can ignite when exposed to a source of ignition, such as a spark. These limits are particularly important when working with combustible gases, as they delineate safe from hazardous conditions.

The lower explosive limit (LEL) is the lowest concentration of the gas in the air that can produce a flame upon ignition, and the upper explosive limit (UEL) is the highest concentration of the gas in the air that can produce a flame. These limits are usually expressed in percentages by volume. For instance, in the provided exercise, oxygen concentrations below 3.0% in a hydrogen-oxygen mixture are considered non-explosive.

Knowing these limits is vital in industries such as mining, chemical manufacturing, and any environment where gas leaks could occur. Preventative measures, such as monitoring gas concentrations and ensuring good ventilation, help maintain gas concentrations below explosive limits to prevent industrial accidents.

Dalton's Law of Partial Pressures is a principle in chemistry that reveals how in a mixture of non-reacting gases, each gas exerts pressure independently of others. The law states that the total pressure of a gas mixture is equal to the sum of the partial pressures of each component gas.

Mathematically, this is expressed as \( P_{total} = P_{gas1} + P_{gas2} + ... + P_{gasn} \), where \( P_{total} \) is the total pressure of the mixture, and each \( P_{gas} \) represents the partial pressure of a specific gas in the mixture.

In practical terms, this law allows us to calculate the amount of each gas in a mixture, which is what we do when solving the exercise. Utilizing Dalton's Law, we determined whether the added oxygen causes the gas mixture to exceed the explosive limit. Understanding this concept is pivotal in ensuring safety in situations where gas mixtures are present, whether in a laboratory setting or industrial processes.