Question

Calculate the number of \( \text{Ca}^{2+} \) ion in 222 g anhydrous calcium chloride? (At. Mass Ca = 40, Cl = 35.5)

• A. \( N_A \)
• B. \( 2N_A \)
• C. \( 3N_A \)
• D. \( 4N_A \)

Hint:

For ionic compounds, the number of ions in a given mass is calculated using Avogadro's number, which gives the number of formula units (ions) per mole.

Answer 1

The Correct Option is B

Step 1: Write the molecular formula for calcium chloride.
Calcium chloride is an ionic compound with the formula \( \text{CaCl}_2 \).

Step 2: Molar mass of calcium chloride.
To calculate the number of moles of \( \text{CaCl}_2 \), we first calculate its molar mass.
\[ \text{Molar mass of } \text{CaCl}_2 = \text{Molar mass of Ca} + 2 \times \text{Molar mass of Cl} = 40 + 2(35.5) = 111 \, \text{g/mol}. \]

Step 3: Number of moles of \( \text{CaCl}_2 \).
Now, calculate the number of moles in 222 g of \( \text{CaCl}_2 \):
\[ \text{Moles of } \text{CaCl}_2 = \frac{\text{Mass}}{\text{Molar mass}} = \frac{222}{111} = 2 \, \text{moles}. \]

Step 4: Number of \( \text{Ca}^{2+} \) ions.
In each mole of \( \text{CaCl}_2 \), there is one mole of \( \text{Ca}^{2+} \) ions. Therefore, 2 moles of \( \text{CaCl}_2 \) will contain \( 2 \times N_A \) \( \text{Ca}^{2+} \) ions, where \( N_A \) is Avogadro's number.

Step 5: Final Answer.
Thus, the number of \( \text{Ca}^{2+} \) ions in 222 g of calcium chloride is \( 2N_A \).