To determine how many moles of calcium chloride (CaCl₂) are needed to react completely with 6.2 moles of silver nitrate (AgNO₃), we start by examining the balanced chemical equation for the reaction:
[tex]\[
2 \, \text{AgNO}_3 + \text{CaCl}_2 \rightarrow 2 \, \text{AgCl} + \text{Ca(NO}_3\text{)}_2
\][/tex]
From this balanced equation, we observe the mole ratio between AgNO₃ and CaCl₂. Specifically, it states that 2 moles of AgNO₃ react with 1 mole of CaCl₂.
Given that we have 6.2 moles of AgNO₃, we need to determine how many moles of CaCl₂ are required to react with all of the AgNO₃.
We use the mole ratio to set up our calculation:
[tex]\[
\text{moles of CaCl}_2 = \text{moles of AgNO}_3 \times \frac{1 \text{ mole of CaCl}_2}{2 \text{ moles of AgNO}_3}
\][/tex]
Inserting the given quantity of AgNO₃ (6.2 moles):
[tex]\[
\text{moles of CaCl}_2 = 6.2 \text{ moles of AgNO}_3 \times \frac{1}{2}
\][/tex]
[tex]\[
\text{moles of CaCl}_2 = 6.2 \times 0.5
\][/tex]
[tex]\[
\text{moles of CaCl}_2 = 3.1
\][/tex]
Thus, to react completely with 6.2 moles of silver nitrate (AgNO₃), you need 3.1 moles of calcium chloride (CaCl₂).
Therefore, the correct answer is:
[tex]\[
3.1 \text{ mol CaCl}_2
\][/tex]
