1.5g `CdCl_(2)` was formed to contain 0.9g Cd. Calculate the atmic weight of Cd.

Options

A. 118
B. 112
C. 106.5
D. 53.25

Answer

To calculate the atomic weight of cadmium (Cd) based on the information given, we can follow these steps:

### Step 1: Determine the mass of chlorine in cadmium chloride (CdCl₂)
Given that 1.5 g of cadmium chloride contains 0.9 g of cadmium, we can find the mass of chlorine by subtracting the mass of cadmium from the total mass of cadmium chloride.

\[ \text{Mass of Cl} = \text{Mass of CdCl}_2 - \text{Mass of Cd} = 1.5 \, \text{g} - 0.9 \, \text{g} = 0.6 \, \text{g} \]

### Step 2: Calculate the molar mass of chlorine in CdCl₂
Chlorine has an atomic mass of approximately 35.5 g/mol. Since there are 2 chlorine atoms in cadmium chloride (CdCl₂), we can calculate the total molar mass of chlorine in the compound.

\[ \text{Molar mass of Cl in CdCl}_2 = 2 \times 35.5 \, \text{g/mol} = 71 \, \text{g/mol} \]

### Step 3: Set up the ratio of masses to find the atomic weight of cadmium
We know that the mass of chlorine that combines with cadmium is 0.6 g, and the mass of cadmium is 0.9 g. We can set up a ratio based on the molar masses:

\[ \frac{\text{Molar mass of Cl}}{\text{Mass of Cl}} = \frac{\text{Molar mass of Cd}}{\text{Mass of Cd}} \]

Substituting the known values:

\[ \frac{71 \, \text{g/mol}}{0.6 \, \text{g}} = \frac{\text{Molar mass of Cd}}{0.9 \, \text{g}} \]

### Step 4: Solve for the molar mass of cadmium
Cross-multiplying gives us:

\[ 71 \, \text{g/mol} \times 0.9 \, \text{g} = \text{Molar mass of Cd} \times 0.6 \, \text{g} \]

Calculating the left side:

\[ 63.9 = \text{Molar mass of Cd} \times 0.6 \]

Now, divide both sides by 0.6 to find the molar mass of cadmium:

\[ \text{Molar mass of Cd} = \frac{63.9}{0.6} = 106.5 \, \text{g/mol} \]

### Conclusion
The atomic weight of cadmium (Cd) is approximately **106.5 g/mol**.

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