Question

a hand warmer packet contains iron powder (fe) that reacts with oxygen in the air to produce heat. the reaction forms iron(iii) oxide, fe₂o₃. calculate the molar mass of fe₂o₃. compare the molar mass of fe₂o₃ to the molar mass of o₂. which one is heavier? explain.

Explanation:

Part 1: Calculate the molar mass of $\ce{Fe_{2}O_{3}}$

Step 1: Find atomic masses

The atomic mass of Fe (iron) is approximately $55.85\ \text{g/mol}$, and the atomic mass of O (oxygen) is approximately $16.00\ \text{g/mol}$.

Step 2: Calculate mass of Fe in $\ce{Fe_{2}O_{3}}$

There are 2 Fe atoms. So, mass of Fe = $2\times55.85\ \text{g/mol} = 111.7\ \text{g/mol}$.

Step 3: Calculate mass of O in $\ce{Fe_{2}O_{3}}$

There are 3 O atoms. So, mass of O = $3\times16.00\ \text{g/mol} = 48.00\ \text{g/mol}$.

Step 4: Sum the masses

Molar mass of $\ce{Fe_{2}O_{3}}$ = mass of Fe + mass of O = $111.7\ \text{g/mol} + 48.00\ \text{g/mol} = 159.7\ \text{g/mol}$.

Part 2: Compare molar mass of $\ce{Fe_{2}O_{3}}$ and $\ce{O_{2}}$

Step 1: Calculate molar mass of $\ce{O_{2}}$

Molar mass of $\ce{O_{2}}$ = $2\times16.00\ \text{g/mol} = 32.00\ \text{g/mol}$.

Step 2: Compare the two molar masses

The molar mass of $\ce{Fe_{2}O_{3}}$ is $159.7\ \text{g/mol}$ and that of $\ce{O_{2}}$ is $32.00\ \text{g/mol}$. Since $159.7 > 32.00$, $\ce{Fe_{2}O_{3}}$ has a greater molar mass, meaning it is heavier on a per - mole basis. This is because the sum of the atomic masses of the atoms in $\ce{Fe_{2}O_{3}}$ (2 Fe and 3 O) is greater than the sum of the atomic masses of the two O atoms in $\ce{O_{2}}$.

Answer:

• Molar mass of $\ce{Fe_{2}O_{3}}$: $\boldsymbol{159.7\ \text{g/mol}}$ (or approximately $160\ \text{g/mol}$)
• $\ce{Fe_{2}O_{3}}$ is heavier. The molar mass of $\ce{Fe_{2}O_{3}}$ ($159.7\ \text{g/mol}$) is greater than the molar mass of $\ce{O_{2}}$ ($32.00\ \text{g/mol}$) because the sum of the atomic masses of the atoms in one mole of $\ce{Fe_{2}O_{3}}$ (2 Fe and 3 O) is larger than the sum of the atomic masses of the two O atoms in one mole of $\ce{O_{2}}$.