Question

The explosion of a mixture consisting of one volume of a gas being studied and one volume of \(\mathrm{H}_{2}\) yielded one volume water vapour and one volume of \(\mathrm{N}_{2}\). The formula of gas being studied, is (a) \(\mathrm{NO}\) (b) \(\mathrm{NO}_{2}\) (c) \(\mathrm{N}_{2} \mathrm{O}\) (d) \(\mathrm{N}_{2} \mathrm{O}_{3}\)

Short answer

\( \mathrm{NO} \) is the formula of the gas being studied because the reaction yields one volume of water vapor and one volume of nitrogen gas, indicating a 1:1:1:1 ratio for the reactants and products.

Step-by-step solution

Understand the chemical reaction

Recognize that the chemical reaction involves a mixture of the unknown gas and hydrogen, which upon explosion yields water vapor and nitrogen gas. The volumes of reactants and products follow the law of combining volumes. Since each reactant and product occupies one volume unit, their molar ratio is 1:1.

Derive the stoichiometry

From the information given, construct a general chemical equation for the reaction: \( \text{Unknown gas} + \mathrm{H}_{2} \rightarrow \mathrm{H}_{2}O + \mathrm{N}_{2} \). Assume the unknown gas has a general formula of \( \mathrm{N}_{x}\mathrm{O}_{y} \). The volume ratio indicates a 1:1 stoichiometry between the reactants and products.

Conserve elements

According to the law of conservation of mass, elements must be balanced in the reaction. Since there are two atoms of hydrogen on the left side of the equation, two atoms of hydrogen must be present in the water vapor. The unknown gas must therefore not contain hydrogen.

Determine the composition of the unknown gas

Nitrogen and oxygen from the unknown gas must combine to form water and nitrogen gas. As all components are in a 1:1 volume ratio and using Avogadro's law (equal volumes of gases at the same temperature and pressure contain an equal number of molecules), there's likely one nitrogen in the unknown gas since it yields one volume of nitrogen gas. Also, since the total volume doesn't change after the explosion, the unknown gas probably contains only one oxygen atom to form one volume of water vapor with the hydrogen. The empirical formula for the gas being studied is likely \( \mathrm{NO} \).

Verify with the given options

Analyze the given options to see which one matches the empirical formula derived from the given reaction information. The only option that has one nitrogen and one oxygen atom is \( \mathrm{NO} \).

Key concepts

Law of Combining Volumes

The Law of Combining Volumes is a classic principle in the world of chemistry, especially when dealing with gases. It states that when gases react together at a constant temperature and pressure, the volumes of the reactant and product gases (if they are gaseous) are in simple whole number ratios to each other. This is a direct consequence of Avogadro's Law, which we will explore in a further section.

For example, in the given exercise, we see that one volume of an unknown gas reacts with one volume of hydrogen gas to produce one volume of water vapor and one volume of nitrogen gas. This 1:1:1:1 volume ratio perfectly illustrates the Law of Combining Volumes.

Understanding this law allows us to deduce the stoichiometry of a reaction without knowing the exact quantities of the reacting substances, as long as we know their volume ratios. So, when you come across a chemical reaction involving gases, think about the volumes and remember the simplicity the law implies!

Chemical Equation Balancing

Balancing a Chemical Equation is crucial in the study of chemistry. It's the process of ensuring that the number of atoms for each element is the same on both sides of the equation, to satisfy the Law of Conservation of Mass. This means whatever matter you start with in a reaction, you must end up with—nothing is created or destroyed, it simply changes form.

Take the reaction in our exercise: we begin with an unknown nitrogen-oxygen compound and hydrogen. After the reaction, the products formed are water and nitrogen gas. To balance this equation, we focus on making sure that the number of nitrogen and oxygen atoms before and after the reaction are equal. The steps provided in the solution apply this principle to lead us to the correct empirical formula of the unknown gas, showing the practical application of balancing equations in identifying unknowns in chemical reactions.
Subheading: Why Balancing Equations Matters

• It ensures that the reaction abides by the Law of Conservation of Mass.
• It allows for accurate calculation of reactants and products (stoichiometry).
• It provides insight into the ratio of molecules involved in the reaction.

Avogadro's Law

Another pillar in the world of chemistry is Avogadro's Law, which tells us that equal volumes of gases, at the same temperature and pressure, will contain an equal number of molecules. This is incredibly handy when dealing with gas reactions—it means we can use volume in place of counting individual molecules, which would be impractically huge numbers to work with.

For our exercise, this law helps us conclude that the unknown gas, which occupies the same volume as the hydrogen gas under the same conditions, must contain the same number of molecules. When we consider the 1:1:1:1 relationship in the volumes of reactants and products, The Avogadro's Law and the Law of Combining Volumes help us to confidently say that the unknown gas is composed of one nitrogen and one oxygen atom, leading to the formula NO. Remember, Avogadro's Law is fundamental to understanding molar relationships in gaseous reactions and materials, making it invaluable in determining molecular formulas.