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 \(\mathrm{SnO}_{2}\).

Short answer

Sn is 78.75% and O is 21.25% by mass in SnO2.

Step-by-step solution

Find the Molar Mass of SnO2

First, we need to calculate the molar mass of SnO2 by adding the molar masses of tin (Sn) and oxygen (O). The atomic mass of Sn is approximately 118.71 g/mol, and the atomic mass of O is about 16.00 g/mol. Since there are two oxygen atoms in SnO2, we have: Molar mass of SnO2 = 118.71 g/mol (Sn) + 2 × 16.00 g/mol (O) = 118.71 g/mol + 32.00 g/mol = 150.71 g/mol

Calculate the Mass Percent of Sn

To find the percent composition of Sn, we use the formula:\[\text{Percent by mass of Sn} = \left( \frac{\text{mass of Sn in } \mathrm{SnO}_2}{\text{molar mass of } \mathrm{SnO}_2} \right) \times 100\%\]Substitute the values:\[\text{Percent by mass of Sn} = \left( \frac{118.71}{150.71} \right) \times 100\% = 78.75\%\]

Calculate the Mass Percent of O

Next, to find the percent composition of O, we use the formula:\[\text{Percent by mass of O} = \left( \frac{\text{mass of O in } \mathrm{SnO}_2}{\text{molar mass of } \mathrm{SnO}_2} \right) \times 100\%\]Substitute the values:\[\text{Percent by mass of O} = \left( \frac{32.00}{150.71} \right) \times 100\% = 21.25\%\]

Key concepts

Molar Mass

The concept of molar mass is crucial when dealing with chemical calculations. Simply put, the molar mass is the mass of one mole of a substance, typically expressed in grams per mole (g/mol). It's essential for converting between atomic mass units measured in kilograms and grams on a macroscopic scale, allowing us to connect with quantities we can physically measure.

To compute the molar mass of a compound, add the atomic masses of each element present, multiplied by their respective number of atoms in the molecule. For \(\text{SnO}_2\), this involves adding the mass of one tin (Sn) atom to the masses of two oxygen (O) atoms. Calculate like this:
- Tin (Sn) atomic mass = 118.71 g/mol
- Oxygen (O) atomic mass = 16.00 g/mol

Since there are two oxygen atoms in \(\text{SnO}_2\), multiply their atomic mass by two. Thus, \( ext{molar mass of SnO}_2 = 118.71 \, g/mol + 2 \times 16.00 \, g/mol = 150.71 \, g/mol\). This molar mass is the starting point for further calculations like those involving percent composition.

Chemical Composition

In chemistry, understanding the chemical composition of a compound gives insight into the specific elements and their proportions present within it. This is fundamentally described by the chemical formula. For example, in \(\text{SnO}_2\), the chemical formula indicates one tin (Sn) atom and two oxygen (O) atoms as part of the compound.

- The subscript following an element symbol in a formula tells how many atoms of that element there are in the compound.
- The absence of a subscript indicates only one atom of that element.

Through chemical composition, you can determine both qualitative (what elements are present) and quantitative (how many atoms of each) aspects. Once the basic composition is known, it becomes possible to perform more advanced calculations, like determining mass percentages. This knowledge helps understand the properties of the compound and predict its behavior in reactions.

Mass Percent Calculation

Mass percent is a way to express how much of a particular element is present in a compound relative to the total compound mass. It is practical for expressing concentrations in mixtures or solutions. To calculate it, use the formula:
- \(\text{Percent by mass} = \left( \frac{\text{mass of the element}}{\text{molar mass of the compound}} \right) \times 100\%\)

Here's how you can apply it to \(\text{SnO}_2\):
- The calculated molar mass is 150.71 g/mol.
- Mass of tin (Sn) in \(\text{SnO}_2\) is 118.71 g/mol. This makes its percent mass:
\(\text{Percent by mass of Sn} = \left( \frac{118.71}{150.71} \right) \times 100\% = 78.75\%\).
- Likewise, the mass of oxygen (O) present is 32.00 g/mol. Its percent mass is:
\(\text{Percent by mass of O} = \left( \frac{32.00}{150.71} \right) \times 100\% = 21.25\%.\)

These percentages add up to 100%, giving a complete picture of how each element contributes to the compound's overall mass. Mass percent calculations are fundamental in chemistry for determining the composition and purity of compounds, essential for both practical lab work and theoretical studies.