To calculate the mass of sodium hydroxide (NaOH) needed to create a solution with a specific molar concentration, you can use the formula:
\[ \text{mass (g)} = \text{molarity (mol/L)} \times \text{volume (L)} \times \text{molar mass (g/mol)} \]
First, you need to convert the volume from milliliters to liters:
\[ 200 , \text{ml} = 0.200 , \text{L} \]
Next, identify the molar mass of sodium hydroxide (NaOH). The molar mass can be calculated as follows:
- Sodium (Na): Approximately 23.0 g/mol
- Oxygen (O): Approximately 16.0 g/mol
- Hydrogen (H): Approximately 1.0 g/mol
\[ \text{Molar mass of NaOH} = 23.0 + 16.0 + 1.0 = 40.0 , \text{g/mol} \]
Now, substitute the values into the formula:
- Molarity (M) = 6.4 mol/dm³ = 6.4 mol/L
- Volume (L) = 0.200 L
- Molar mass (g/mol) = 40.0 g/mol
\[ \text{mass (g)} = 6.4 , \text{mol/L} \times 0.200 , \text{L} \times 40.0 , \text{g/mol} \]
Calculating this gives:
\[ \text{mass (g)} = 6.4 \times 0.200 \times 40.0 = 51.2 , \text{g} \]
Therefore, you need to dissolve 51.2 grams of NaOH in 200 mL of solution to achieve a concentration of 6.4 mol/dm³.