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Let's solve these two problems step by step:

### 14. **Potassium Nitrate Solution Molarity**

You need to make **10.0 L** of **1.2 M** KNO₃. What molarity must the potassium nitrate solution be if you are to use only **2.5 L** of it?

This is a dilution problem, and the formula to use is:

\[
M_1 \times V_1 = M_2 \times V_2
\]

Where:
- \( M_1 \) is the molarity of the more concentrated solution (which we are solving for),
- \( V_1 \) is the volume of the more concentrated solution (2.5 L),
- \( M_2 \) is the molarity of the diluted solution (1.2 M),
- \( V_2 \) is the volume of the diluted solution (10.0 L).

Rearranging the formula to solve for \( M_1 \):

\[
M_1 = \frac{M_2 \times V_2}{V_1}
\]

Substituting the values:

\[
M_1 = \frac{1.2 \, \text{M} \times 10.0 \, \text{L}}{2.5 \, \text{L}} = \frac{12}{2.5} = 4.8 \, \text{M}
\]

So, the molarity of the potassium nitrate solution must be **4.8 M**.

---

### 15. **New Concentration of Lithium Chloride Solution**

You dilute **175 mL** of a **1.6 M** solution of LiCl to **1.0 L**. What is the new concentration of the solution?

Again, using the dilution formula:

\[
M_1 \times V_1 = M_2 \times V_2
\]

Where:
- \( M_1 = 1.6 \, \text{M} \) (initial molarity),
- \( V_1 = 175 \, \text{mL} = 0.175 \, \text{L} \) (initial volume),
- \( V_2 = 1.0 \, \text{L} \) (final volume),
- \( M_2 \) is the final molarity (which we are solving for).

Rearranging the formula to solve for \( M_2 \):

\[
M_2 = \frac{M_1 \times V_1}{V_2}
\]

Substituting the values:

\[
M_2 = \frac{1.6 \, \text{M} \times 0.175 \, \text{L}}{1.0 \, \text{L}} = \frac{0.28}{1.0} = 0.28 \, \text{M}
\]

The new concentration of the solution is **0.28 M**.

---

Would you like further details on these solutions or any additional explanations?

### Related Questions:
1. What is the formula for molarity, and how is it derived?
2. How would the calculations change if the final volume in problem 15 were different?
3. How is dilution used in real-world applications such as chemistry labs?
4. What would happen if you used a smaller initial volume of LiCl in problem 15?
5. How can you experimentally verify the molarity of a solution?

**Tip:** When diluting solutions, always remember that the product of the initial concentration and volume must equal the product of the final concentration and volume.

14. You need to make 10.0 L of 1.2 M KNO₃. What molarity must the potassium nitrate solution be if you are to use only 2.5 L of it? 15. If you dilute 175 mL of a 1.6 M solution of LiCl to 1.0 L, what is the new concentration of the solution?

Learn how to calculate the molarity of potassium nitrate and lithium chloride solutions using dilution concepts. This guide covers step-by-step problem-solving using the dilution formula M1 * V1 = M2 * V2 and applies it to practical examples of preparing KNO₃ and LiCl solutions.

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