Problem 37 - Chemistry

Question

Tin (Sn) exists in Earth's crust as \(\mathrm{SnO}_{2}\). Calculate the percent composition by mass of \(\mathrm{Sn}\) and \(\mathrm{O}\) in \(\mathrm{SnO}_{2}\)

Step-by-Step Solution

Answer

The percent composition by mass of Tin (Sn) in \(\mathrm{SnO}_{2}\) is 78.77% and for Oxygen (O) is 21.23%.

Step 1: Calculate the Molar Masses

First, you need to determine the molar mass of each of the elements and the compound. Using the atomic weights from the periodic table, the atomic weight of Tin (Sn) is approximately 118.71 g/mol and for Oxygen (O) is approximately 16.00 g/mol. For \(\mathrm{SnO}_{2}\), multiply the atomic weight of Oxygen by 2 and then add the atomic weight of Tin: \(118.71 + 2(16.00) = 150.71 g/mol\).

Step 2: Calculate the Percent Composition

Then, calculate the percent composition of Tin (Sn) and Oxygen (O) in \(\mathrm{SnO}_{2}\). The formula is \((\text{mass of element} / \text{molar mass of compound}) \times 100\% \). For Tin (Sn), it's \( (118.71 g/mol / 150.71 g/mol) \times 100\%= 78.77\%\). For Oxygen (O), it's \((2(16.00 g/mol) / 150.71 g/mol) \times 100\% = 21.23\%\).

Key Concepts

Molar Mass

The concept of molar mass is fundamental in chemistry, providing a bridge between the atomic and macroscopic worlds. Molar mass represents the mass of one mole of a given substance, usually expressed in grams per mole (g/mol). The "mole" is one of the seven base SI units and is defined as containing exactly 6.022 x 10²³ particles, whether they're atoms, molecules, or ions.
For calculating the molar mass of a compound, you sum the molar masses of its constituent elements, each multiplied by the number of atoms of that element in the compound. Take tin oxide (SnO₂), for instance. It consists of 1 atom of tin (Sn) and 2 atoms of oxygen (O).

• Tin (Sn): Approximately 118.71 g/mol
• Oxygen (O) (2 atoms): 2 x 16.00 g/mol = 32.00 g/mol

Thus, the molar mass of SnO₂ is the sum of these two amounts: 118.71 g/mol + 32.00 g/mol = 150.71 g/mol.

Tin Oxide

Tin oxide, specifically stannic oxide, is a significant compound in various industrial applications. Its chemical formula is denoted as SnO₂, meaning that one molecule consists of one tin atom and two oxygen atoms. As such, tin oxide is a type of binary compound, where binary refers to its two-element composition.
Understanding the structure and properties of tin oxide is key to determining and calculating its percent composition by mass.

• Tin (Sn) forms the major part of the compound, contributing most of the weight due to its larger atomic mass compared to oxygen.
• Oxygen (O), while lighter, contributes to the compound's stability and reactivity.

Applications of tin oxide include things like use in ceramics, glass coatings, and as an opacifying agent. Knowing its composition is crucial for those in material science fields.

Atomic Weight

Atomic weight, often interchangeable with relative atomic mass in chemistry, is a dimensionless quantity that provides a weighted average of the atomic masses of an element's isotopes, measured relative to one-twelfth of the mass of carbon-12.
For practical applications such as chemical reactions, the atomic weight allows for conversion between mass and amount of substance (moles).
Here’s how it applies to our example:

• Tin (Sn) has an atomic weight of approximately 118.71 g/mol, highlighting its contribution to the compound's overall mass.
• Oxygen (O), despite its relatively small atomic weight of 16.00 g/mol, plays a crucial role when its multiplicity (as in 2 atoms) is considered.

These atomic weights are taken from periodic tables and are used to calculate molar masses and ultimately, percent compositions of compounds.

Chemical Formula

A chemical formula is an essential tool in chemistry that succinctly represents the elements in a compound and their corresponding quantities. It serves as a shorthand method for chemists to convey detailed information about compounds without using long descriptive text.
Let’s take tin oxide as an example, which is represented by the formula SnO₂. This denotes:

• "Sn" for tin, indicating the presence of one atom of tin.
• "O₂" for oxygen, indicating the presence of two atoms of oxygen.

Such formulas are critical for helping you determine the stoichiometry of a compound, which describes how these elements combine and react with each other. Understanding the chemical formula is vital when calculating percent compositions, as this formula lets you know the exact ratio of elements in the compound.