Understanding the Problem
To find the atomic mass of an unknown metal, we use the law of conservation of mass and the concept of stoichiometry. We are given:
- Mass of metal ($M$) = $4\text{ g}$
- Mass of metal chloride ($MCl_2$) = $11.1\text{ g}$
- The metal is divalent, meaning its ion has a charge of $+2$. Thus, it forms a chloride with the formula $MCl_2$.
Step-by-Step Solution
1. Determine the mass of Chlorine used
According to the law of conservation of mass, the mass of reactants equals the mass of products. Since the reaction is $M + Cl_2 \rightarrow MCl_2$, we have: $\text{Mass of Chlorine} = \text{Mass of Metal Chloride} - \text{Mass of Metal}$ $\text{Mass of Chlorine} = 11.1\text{ g} - 4.0\text{ g} = 7.1\text{ g}$
2. Calculate the moles of Chlorine
The molar mass of Chlorine ($Cl$) is approximately $35.5\text{ g/mol}$. Since the chlorine gas used is $Cl_2$, its molar mass is $2 \times 35.5 = 71\text{ g/mol}$. $\text{Moles of } Cl_2 = \frac{\text{Mass}}{\text{Molar Mass}} = \frac{7.1\text{ g}}{71\text{ g/mol}} = 0.1\text{ moles}$
3. Determine the moles of Metal
From the balanced chemical equation $M + Cl_2 \rightarrow MCl_2$, we see that $1\text{ mole}$ of $M$ reacts with $1\text{ mole}$ of $Cl_2$. Therefore, the moles of metal used is also $0.1\text{ mol}$.
4. Calculate the atomic mass of the Metal
$\text{Molar Mass of Metal} (M) = \frac{\text{Mass of Metal}}{\text{Moles of Metal}}$ $M = \frac{4\text{ g}}{0.1\text{ mol}} = 40\text{ g/mol}$
The atomic mass of the metal is $40\text{ u}$ (likely Calcium).