To find the molarity of the unknown HCl solution, we can use the concept of neutralization, which is based on the balanced equation for the reaction between hydrochloric acid (HCl) and sodium hydroxide (NaOH):

$\text{HCl (aq)} + \text{NaOH (aq)} \rightarrow \text{NaCl (aq)} + \text{H}_2\text{O (l)}$

From this equation, we see that HCl and NaOH react in a 1:1 molar ratio. This means the moles of HCl will be equal to the moles of NaOH used in the reaction.

Steps:

1. Calculate the moles of NaOH: We know the molarity (M) and the volume (V) of NaOH used. The formula to find the number of moles is: $\text{moles of NaOH} = M_{\text{NaOH}} \times V_{\text{NaOH}}$ where:

   • $M_{\text{NaOH}} = 0.75 \, \text{M}$
   • $V_{\text{NaOH}} = 20.0 \, \text{mL} = 0.0200 \, \text{L}$

   So, $\text{moles of NaOH} = 0.75 \, \text{M} \times 0.0200 \, \text{L} = 0.0150 \, \text{mol}$

2. Calculate the moles of HCl: Since the reaction is 1:1, the moles of HCl will be equal to the moles of NaOH. Therefore, moles of HCl = 0.0150 mol.

3. Calculate the molarity of the HCl solution: To find the molarity of HCl, we use the formula: $M_{\text{HCl}} = \frac{\text{moles of HCl}}{V_{\text{HCl}}}$ where:

   • moles of HCl = 0.0150 mol
   • $V_{\text{HCl}} = 10.0 \, \text{mL} = 0.0100 \, \text{L}$

   So, $M_{\text{HCl}} = \frac{0.0150 \, \text{mol}}{0.0100 \, \text{L}} = 1.50 \, \text{M}$

Final Answer:

The molarity of the unknown HCl solution is 1.50 M.

---

Would you like a more detailed explanation of any part of the process?

Here are 5 related questions:

1. How do you calculate molarity from the number of moles and volume of solution?
2. What is the significance of the 1:1 molar ratio in the neutralization reaction between HCl and NaOH?
3. How would you adjust the calculations if the concentration of NaOH was different?
4. What would happen if we used a different volume of NaOH or HCl in this titration?
5. How can we apply this method to determine the concentration of other unknown solutions?

Tip: Always ensure that the volume is in liters (L) when performing molarity calculations. If the volume is given in milliliters (mL), convert it to liters first.