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The question involves a dilution of a sodium nitrate (\( \text{NaNO}_3 \)) solution. The dilution formula, often used in such cases, is:

\[
M_1 V_1 = M_2 V_2
\]

Where:
- \( M_1 \) is the initial concentration,
- \( V_1 \) is the initial volume,
- \( M_2 \) is the final concentration, and
- \( V_2 \) is the final volume.

### Given dataThe question involves a dilution of a sodium nitrate (\( \text{NaNO}_3 \)) solution. The dilution formula, often used in such cases, is:

\[
M_1 V_1 = M_2 V_2
\]

Where:
- \( M_1 \) is the initial concentration,
- \( V_1 \) is the initial volume,
- \( M_2 \) is the final concentration, and
- \( V_2 \) is the final volume.

### Given 
- \( M_1 = 8.75 \, \text{M} \) (initial concentration),
- \( V_1 = 50.6 \, \text{mL} \) (initial volume),
- \( M_2 = 1.00 \, \text{M} \) (final concentration),
- \( V_2 = ? \, \text{L} \) (final volume, to be determined).

We are asked to find \( V_2 \), the final volume, in liters.

### Step-by-Step Solution:
1. Use the dilution formula:

\[
M_1 V_1 = M_2 V_2
\]

Substitute the known values:

\[
(8.75 \, \text{M}) (50.6 \, \text{mL}) = (1.00 \, \text{M}) (V_2)
\]

2. Solve for \( V_2 \):

\[
V_2 = \frac{(8.75)(50.6)}{1.00}
\]

\[
V_2 = 442.75 \, \text{mL}
\]

3. Convert the result from mL to liters (since \( 1 \, \text{L} = 1000 \, \text{mL} \)):

\[
V_2 = \frac{442.75 \, \text{mL}}{1000} = 0.44275 \, \text{L}
\]

4. Round to the appropriate number of significant figures (3 significant figures based on the given data):

\[
V_2 = 0.443 \, \text{L}
\]

### Final Answer:
The final volume is \( 0.443 \, \text{L} \).

Would you like further clarification or additional details on any part of the process?

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Here are 5 related questions you might explore:
1. How would the final volume change if the initial concentration were halved?
2. What is the purpose of dilution in chemical processes?
3. How would the formula change if multiple solutes were involved?
4. What are the common applications of sodium nitrate in chemistry?
5. How do you calculate moles from molarity and volume?

**Tip:** Always ensure to match the number of significant figures in your final answer with the least precise value given in the problem!

A chemist must dilute 50.6 mL of 8.75 M aqueous sodium nitrate (NaNO3) solution until the concentration falls to 1.00 M. Calculate the final volume in liters.

Learn how to calculate the final volume when diluting a sodium nitrate (NaNO3) solution from 8.75 M to 1.00 M. This step-by-step solution demonstrates the use of the dilution formula M1V1 = M2V2, with given initial and final concentrations. Suitable for high school chemistry students.

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