Answered

You can use mole ratios and molar mass to determine the masses of substances involved in a chemical reaction. Using the periodic table, calculate the molar mass of iron (III) oxide $\left( Fe _2 O _3\right)$. Type in your answer using two decimal places.



Note: Molar mass should always be reported to two decimal places because the periodic table uses two. Significant figures do not apply to molar masses.



Molar mass of $Fe _2 O _3=\square\text{ g/mol}$

Verified Answer :

  • Identify the number of atoms for each element in \(Fe_2O_3\) (2 iron, 3 oxygen).
  • Use the standard atomic weights: \(Fe = 55.85 \text{ g/mol}\) and \(O = 16.00 \text{ g/mol}\).
  • Calculate the total molar mass: \(M = (2 \times 55.85) + (3 \times 16.00) = 159.70 \text{ g/mol}\).
  • The final result is \(\boxed{159.70 \text{ g/mol}}\).

Explanation

  1. Analyzing the Composition of Iron(III) Oxide

To determine the molar mass of iron(III) oxide (\(Fe_2O_3\)), we identify its constituent elements and their respective atomic masses from the periodic table. Iron(III) oxide is composed of 2 iron (Fe) atoms and 3 oxygen (O) atoms. The molar mass of a compound is calculated by summing the products of the number of atoms of each element and their respective atomic molar masses. We use the standard atomic masses: \(M_{Fe} = 55.85 \text{ g/mol}\) and \(M_{O} = 16.00 \text{ g/mol}\).

  1. Calculating the Molar Mass

We use the formula for the total molar mass of \(Fe_2O_3\):
\[M_{Fe_2O_3} = (2 \times M_{Fe}) + (3 \times M_{O})\]
Substituting the known atomic masses into the expression:
\[M_{Fe_2O_3} = (2 \times 55.85 \text{ g/mol}) + (3 \times 16.00 \text{ g/mol})\]
Performing the multiplication for each component:
\[2 \times 55.85 = 111.70 \text{ g/mol}\]
\[3 \times 16.00 = 48.00 \text{ g/mol}\]
Summing these values:
\[111.70 \text{ g/mol} + 48.00 \text{ g/mol} = 159.70 \text{ g/mol}\]
Therefore, the molar mass of iron(III) oxide is \(159.70 \text{ g/mol}\).

Examples

In real-life chemistry and engineering, calculating molar mass is fundamental for preparing solutions of specific concentrations, determining the stoichiometry of chemical reactions, and manufacturing materials. For instance, in the production of rust-resistant coatings or in metallurgical processes involving iron ore, chemists rely on accurate molar mass calculations to determine the exact amounts of reactants needed, ensuring efficiency and safety in industrial applications. Understanding how to calculate molar mass is the first step toward predicting the outcomes of these chemical processes.

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