To determine the grams of NaOH required to prepare a 500 mL solution at a concentration of [tex]\( \frac{M}{10} \)[/tex] (which is 0.1 M), we follow these steps:
1. Convert the volume to liters:
Volume = 500 mL = 500 / 1000 L = 0.5 L
2. Identify the molarity:
Molarity (M) = [tex]\( \frac{M}{10} \)[/tex] = 0.1 M
3. Determine the molar mass of NaOH:
Molar mass of NaOH is calculated by summing the atomic masses of its components:
- Sodium (Na) = 22.99 g/mol
- Oxygen (O) = 16.00 g/mol
- Hydrogen (H) = 1.01 g/mol
Therefore, molar mass of NaOH = 22.99 + 16.00 + 1.01 = 40.00 g/mol
4. Calculate the mass of NaOH required using the formula:
The formula to find the mass is:
[tex]\[
\text{mass (g)} = \text{molarity (mol/L)} \times \text{volume (L)} \times \text{molar mass (g/mol)}
\][/tex]
Substituting the known values:
[tex]\[
\text{mass (g)} = 0.1 \, \text{mol/L} \times 0.5 \, \text{L} \times 40.00 \, \text{g/mol}
\][/tex]
Performing the multiplication:
[tex]\[
\text{mass (g)} = 0.1 \times 0.5 \times 40.00
\][/tex]
[tex]\[
\text{mass (g)} = 2.00 \, \text{g}
\][/tex]
Therefore, 2 grams of NaOH are required to prepare 500 mL of a [tex]\( \frac{M}{10} \)[/tex] NaOH solution.
