Question

Two flasks \(\mathrm{A}\) and \(\mathrm{B}\) of \(\mathrm{I} 1\) capacity each contains \(\mathrm{SO}_{2}\) and \(\mathrm{Br}_{2}\) gases, respectively, maintained at \(340 \mathrm{~K}\) and pressure of \(1.5\) atm. If number of \(\mathrm{Br}_{2}\) molecules in flask \(\mathrm{B}\) is \(N\), the total number of atoms in flask A will be (a) \(\underline{N}\) (b) \(2 N\) (c) \(N / 2\) (d) \(3 N\)

Short answer

The total number of atoms in flask A will be (d) 3N.

Step-by-step solution

State the Given Information

We are given two flasks A and B, each with 1 liter capacity. Flask A contains sulfur dioxide (SO2) gas, and flask B contains bromine (Br2) gas. Both are at 340 K temperature and 1.5 atm pressure. It's also given that the number of Br2 molecules in flask B is N.

Apply Avogadro's Law

Avogadro's Law states that equal volumes of gases, at the same temperature and pressure, contain an equal number of molecules. Since both flasks are of the same volume, and the conditions of temperature and pressure are the same, flasks A and B contain the same number of molecules. Therefore, the number of SO2 molecules in flask A is also N.

Calculate the Total Number of Atoms in Flask A

Each molecule of SO2 consists of one sulfur (S) atom and two oxygen (O) atoms, totaling three atoms per molecule. Therefore, for N molecules of SO2, the total number of atoms is 3 times N or 3N.

Key concepts

Gas Laws

Understanding the behavior of gases is critical in various scientific and industrial processes. The Gas Laws are a series of fundamental principles that describe the relationships between the pressure, volume, temperature, and the number of particles in a gas. One of the most well-known gas laws is Avogadro's Law, which tells us that given the same conditions of temperature and pressure, equal volumes of different gases contain an equal number of molecules. This can be expressed in the formula \[\begin{equation} V \text{∝} n \text{(at constant temperature and pressure)}\end{equation}\] where V represents volume and n is the number of moles of the gas. This is a cornerstone in solving many stoichiometry problems involving gaseous reactants or products.

When working with gas law problems, it's essential to assure that all the considered gases are indeed ideal or close to ideal, as real gases can deviate from these laws under high pressure or low temperature. In the exercise provided, the use of Avogadro's law is valid as the gases are contained under conditions where they can be assumed to behave ideally.

Stoichiometry

Stoichiometry is a section of chemistry that involves calculating the quantities of reactants and products in chemical reactions. It is derived from the Greek words \'stoicheion\' (element) and \'metron\' (measure). In stoichiometry, the relationship between the amounts of reactants and products is based on the balanced chemical equation for the reaction, and it allows for predictions about the amount of product that will form during a reaction under specific conditions.

One can perform calculations that take into account the mole ratios between reactants and products, the mass of substances involved, or, as in the case with gases, the volumes of gaseous reactants and products. In the exercise, we use stoichiometric principles to relate the number of molecules of one substance to the number of atoms in another. This involves understanding the molecular composition of the substances involved. Since sulfur dioxide (\[\begin{equation}SO_{2}\end{equation}\] ) contains three atoms in one molecule, we reason stoichiometrically to determine the total number of atoms present in the flask.

Molecular and Atomic Counting

Molecular and atomic counting is a foundational concept for understanding the composition of substances at the molecular level. The process is relatively straightforward for elements since each atom represents one count. However, for compounds, one must take note of the specific number of each type of atom within a molecule to correctly determine total atomic counts. For instance, the counting of atoms within a molecule of sulfur dioxide (SO₂) involves identifying that there is one sulfur atom and two oxygen atoms, bringing the total to three atoms per molecule.

The concept of Avogadro's constant, \[\begin{equation}6.022 \times 10^{23}\end{equation}\] molecules per mole, becomes crucial when we need to relate molecular counts to measurable quantities. In the original exercise, knowing that the number of bromine molecules (\[\begin{equation}Br_{2}\end{equation}\] ) in flask B is N, and understanding that each SO₂ molecule contains three atoms, allows us to calculate that the total number of atoms in flask A is three times N, thus 3N.