To find the molarity of the [tex]\( HCl \)[/tex] solution, we can follow these steps:
1. Write the balanced chemical equation:
[tex]\[
2 HCl + Ca(OH)_2 \rightarrow CaCl_2 + 2 H_2O
\][/tex]
According to the equation, 2 moles of [tex]\( HCl \)[/tex] react with 1 mole of [tex]\( Ca(OH)_2 \)[/tex].
2. Determine the moles of [tex]\( Ca(OH)_2 \)[/tex]:
We are given that the volume of [tex]\( Ca(OH)_2 \)[/tex] is 2.00 [tex]\( L \)[/tex] and its molarity is 1.50 [tex]\( M \)[/tex]. We can calculate the moles of [tex]\( Ca(OH)_2 \)[/tex] using:
[tex]\[
\text{Moles of } Ca(OH)_2 = \text{Molarity} \times \text{Volume} = 1.50 \, M \times 2.00 \, L = 3.00 \text{ moles }
\][/tex]
3. Calculate the moles of [tex]\( HCl \)[/tex] needed:
From the balanced equation, we see that 2 moles of [tex]\( HCl \)[/tex] react with 1 mole of [tex]\( Ca(OH)_2 \)[/tex]. Therefore, the moles of [tex]\( HCl \)[/tex] needed are:
[tex]\[
\text{Moles of }HCl = 2 \times \text{Moles of } Ca(OH)_2 = 2 \times 3.00 \text{ moles} = 6.00 \text{ moles}
\][/tex]
4. Calculate the molarity of the [tex]\( HCl \)[/tex] solution:
We are given that the volume of the [tex]\( HCl \)[/tex] solution is 1.00 [tex]\( L \)[/tex]. Molarity is defined as the number of moles of solute per liter of solution. Therefore, the molarity of [tex]\( HCl \)[/tex] is:
[tex]\[
\text{Molarity of } HCl = \frac{\text{Moles of } HCl}{\text{Volume in liters}} = \frac{6.00 \text{ moles}}{1.00 \text{ L}} = 6.00 \, M
\][/tex]
So, the molarity of the [tex]\( HCl \)[/tex] solution is [tex]\( 6.00 \, M \)[/tex].
Answer:
The correct answer is [tex]\( 6.00 \, M \)[/tex].
