Understanding the Concept
In chemistry, the mole concept allows us to relate the mass of a substance to the number of atoms or molecules it contains. When a problem asks to compare the number of atoms in two different compounds, the key is to determine the total number of specific atoms (in this case, oxygen) and use that as a bridge to calculate the unknown mass.
The Problem Statement
Calculate the mass of carbon monoxide (CO) having the same number of oxygen atoms as are present in 88 g of carbon dioxide ($CO_2$).
Step-by-Step Solution
Step 1: Find the number of moles of $CO_2$
First, calculate the molar mass of $CO_2$:
- Carbon (C) = 12 g/mol
- Oxygen (O) = 16 g/mol
- Molar Mass of $CO_2 = 12 + (2 \times 16) = 44 \text{ g/mol}$
Now, calculate the moles of $CO_2$ in 88 g: $\text{Moles of } CO_2 = \frac{\text{Given Mass}}{\text{Molar Mass}} = \frac{88 \text{ g}}{44 \text{ g/mol}} = 2 \text{ moles}$
Step 2: Determine the number of oxygen atoms
Each molecule of $CO_2$ contains 2 oxygen atoms. Therefore, 1 mole of $CO_2$ contains 2 moles of oxygen atoms.
- In 2 moles of $CO_2$, the moles of O atoms = $2 \times 2 = 4 \text{ moles of O atoms}$.
Step 3: Relate this to Carbon Monoxide (CO)
We need an amount of CO that also contains 4 moles of oxygen atoms. Each molecule of CO contains only 1 oxygen atom.
- To have 4 moles of oxygen atoms, we must have 4 moles of CO molecules.
Step 4: Calculate the mass of CO
Now, find the molar mass of CO:
- Molar Mass of CO = $12 + 16 = 28 \text{ g/mol}$
Finally, calculate the mass: $\text{Mass of CO} = \text{Moles} \times \text{Molar Mass}$ $\text{Mass of CO} = 4 \text{ moles} \times 28 \text{ g/mol} = 112 \text{ g}$
Summary
By breaking the problem down into molar relationships, we determined that 88 g of $CO_2$ contains 4 moles of oxygen atoms. Since one molecule of CO contains one oxygen atom, we require 4 moles of CO to match that count, resulting in a total mass of 112 g.