Question

What is the Mass of \(0.5\) moles of \(\mathrm{O}_{3}\) molecules? (a) \(16 \mathrm{~g}\) (b) \(20 \mathrm{~g}\) (c) \(48 \mathrm{~g}\) (d) \(24 \mathrm{~g}\)

Short answer

The mass of \(0.5\) moles of \(\mathrm{O}_3\) is \(24 \mathrm{~g}\).

Step-by-step solution

Understand the Problem

We need to find the mass of \(0.5\) moles of \(\mathrm{O}_3\) molecules. The answer choices are given as mass in grams.

Identify the Molar Mass of Ozone \(\mathrm{O}_3\)

To solve the problem, we first need to know the molar mass of ozone \(\mathrm{O}_3\). Ozone is made up of three oxygen atoms. The atomic mass of oxygen is approximately \(16\text{ u (unified atomic mass units)}\). Consequently, the molar mass of ozone is calculated as follows:\[\text{Molar mass of } \mathrm{O}_3 = 3 \times 16 = 48 \text{ g/mol}\]

Calculate the Mass of 0.5 Moles of \(\mathrm{O}_3\)

Now that we know the molar mass of \(\mathrm{O}_3\) is \(48 \text{ g/mol}\), we can calculate the mass of \(0.5\) moles by using the following formula:\[\text{Mass} = \text{Number of moles} \times \text{Molar mass}\]Substitute in the values for this problem:\[\text{Mass} = 0.5 \times 48 = 24 \text{ g}\]

Check the Answer Choices

Finally, let's verify which answer choice corresponds to our calculated mass. Among the available options, \(24 \mathrm{~g}\) matches our calculated value.

Key concepts

Ozone Chemistry

Ozone plays a crucial role in our atmosphere. It consists of three oxygen atoms, giving it the molecular formula \(\mathrm{O}_3\). Unlike diatomic oxygen (\(\mathrm{O}_2\)), which we breathe, ozone acts as a powerful protective barrier against harmful ultraviolet radiation. Every oxygen atom in ozone contributes to its unique characteristics, both chemically and functionally in our environment. By understanding ozone chemistry, we can appreciate the delicate balance it maintains in our atmosphere. Additionally, the reactivity of ozone makes it essential in industrial applications like water purification and air treatment. Keeping track of the ozone levels is vital for environmental scientists to monitor effects such as pollution and climate change. When dealing with exercises involving ozone, knowledge of its molecular structure and properties is the starting point. Knowing that it comprises three oxygen atoms helps in determining its molar mass, fundamental in calculations involving the substance.

Mole Concept

The mole is a fundamental concept in chemistry for quantifying substances. It represents a quantity — in this case, the number of atoms, molecules, or particles. One mole contains approximately \(6.022 \times 10^{23}\) entities (Avogadro's number). This concept allows chemists to work at the macroscopic scale while knowing they have exact atomic and molecular amounts. Understanding the mole concept is crucial in solving problems related to stoichiometry, where conversions between moles, mass, and entities are needed. For example, when calculating the mass of \(0.5\) moles of ozone, knowing the molar mass is vital. In this case, \(0.5\) moles corresponds directly to half the molar mass, demonstrating the mole's role as a bridge between microscopic particles and measurable amounts.

Mass Calculation

Calculating the mass of a substance when given its moles is a straightforward process, yet it's essential to comprehension in chemistry. It allows us to measure substances accurately and use them as intended in experiments and reactions.To perform a mass calculation, you first determine the molar mass of the chemical compound. For ozone \(\mathrm{O}_3\), this is the sum of the atomic masses of its constituent atoms. With each oxygen atom having a mass of approximately \(16\text{ u}\), the molar mass of ozone totals \(48 \text{ g/mol}\).Once the molar mass is known, simply apply the formula \[\text{Mass} = \text{Number of Moles} \times \text{Molar Mass}\]. For \(0.5\) moles of ozone, multiply \(0.5\) by \(48\), resulting in \(24 \mathrm{~g}\). These calculations are foundational in chemistry, enabling conversion between theoretical moles and practical mass. The ease of converting moles to mass allows for accurate predictions and reproducibility in scientific work.