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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

Expert verified
The percent composition is 78.77% Sn and 21.23% O in SnOâ‚‚.

Step by step solution

01

Identify the Molar Mass of Each Element

First, determine the molar mass of each element in the compound. Tin (Sn) has a molar mass of 118.71 g/mol and Oxygen (O) has a molar mass of 16.00 g/mol.
02

Calculate the Total Molar Mass of SnO2

The formula \mathrm{SnO}_{2}\ consists of one tin atom and two oxygen atoms. Therefore, the molar mass of \mathrm{SnO}_{2}\ is calculated as: \[ m = 118.71 \, \mathrm{g/mol} \, (Sn) + 2 \times 16.00 \, \mathrm{g/mol} \, (O) = 150.71 \, \mathrm{g/mol} \] .
03

Calculate the Percent Composition of Sn

To find the percent composition of Sn in \mathrm{SnO}_{2}, calculate using the formula: \[ \text{Percent of Sn} = \left(\frac{118.71}{150.71}\right) \times 100\% = 78.77\% \] .
04

Calculate the Percent Composition of O

Similarly, calculate the percent composition of O in \mathrm{SnO}_{2}: \[ \text{Percent of O} = \left(\frac{2 \times 16.00}{150.71}\right) \times 100\% = 21.23\% \] .

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Molar Mass
Molar mass is an important concept in chemistry that helps us understand the quantities involved in chemical reactions. It is the mass of one mole of a substance, which is often measured in grams per mole (g/mol).
Molar mass provides a bridge between the atomic world and the world of measurable quantities.To calculate the molar mass of a compound, you simply sum the molar masses of all the atoms present in the compound. For example, in the compound tin dioxide \(\mathrm{SnO}_2\), we need to find the molar mass of tin (Sn) and oxygen (O). Tin has a molar mass of 118.71 g/mol, while oxygen has a molar mass of 16.00 g/mol. Since \(\mathrm{SnO}_2\) consists of one tin atom and two oxygen atoms, you calculate its total molar mass by using the formula:\[m = 118.71 \, \mathrm{g/mol} \, (Sn) + 2 \times 16.00 \, \mathrm{g/mol} \, (O) = 150.71 \, \mathrm{g/mol}\]Understanding molar mass is crucial as it forms the basis for calculating how much of each element is present in a compound and thus allows us to move forward with percent composition calculations.
Tin Dioxide
Tin dioxide, also known by its chemical formula \(\mathrm{SnO}_2\), is a compound comprising tin and oxygen. It is a commonly occurring mineral in Earth's crust and is often encountered in the context of extracting tin.Here are some critical properties of tin dioxide related to chemistry:
  • It consists of one tin atom and two oxygen atoms.
  • The molar mass of tin dioxide is 150.71 g/mol, calculated as shown above.
  • This compound is crucial for understanding the percent composition of elements because it combines different elements in a fixed ratio.
Moreover, knowing how to identify the chemical formula of a compound like tin dioxide enables chemists to determine the relative masses of its constituents, facilitating calculations like the percent composition by mass.
Percent Composition Calculation
Percent composition by mass is an essential calculation in chemistry. It helps us understand how much of each element is present in a compound relative to its total mass. The formula for calculating the percent composition of an element within a compound involves dividing the total mass of the element by the total molar mass of the compound, and then multiplying by 100.For \(\mathrm{SnO}_2\), the percent composition of each element can be calculated as follows:
  • For Tin (Sn): The mass of tin in the compound is 118.71 g/mol. Given the total molar mass of \(\mathrm{SnO}_2\) is 150.71 g/mol, the percent composition is:\[\text{Percent of Sn} = \left(\frac{118.71}{150.71}\right) \times 100\% = 78.77\%\]
  • For Oxygen (O): There are two oxygen atoms, each with a molar mass of 16.00 g/mol, leading to a total of 32.00 g/mol for oxygen. Therefore, the percent composition is:\[\text{Percent of O} = \left(\frac{2 \times 16.00}{150.71}\right) \times 100\% = 21.23\%\]
Understanding how to compute percent compositions helps in quantifying the proportions of elements in chemical compounds, which is essential for applications ranging from chemical analysis to synthesis.

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