To calculate the grams of solute (NaOH) needed to prepare 3.50 liters of a 4.50 M solution, follow these steps:
### Step 1: Understand the given values
- Volume of the solution ([tex]\(V\)[/tex]) = 3.50 liters (L)
- Molarity of the solution ([tex]\(M\)[/tex]) = 4.50 mol/L
- Molar mass of NaOH ([tex]\(M_m\)[/tex]) = 40.00 g/mol
### Step 2: Calculate the moles of NaOH required
The molarity ([tex]\(M\)[/tex]) of a solution is defined as the number of moles of solute per liter of solution:
[tex]\[ M = \frac{\text{moles of solute}}{\text{liters of solution}} \][/tex]
Rearranging this formula to solve for the moles of solute (which in this case is NaOH):
[tex]\[ \text{moles of NaOH} = M \times V \][/tex]
Substitute the given values:
[tex]\[ \text{moles of NaOH} = 4.50 \, \text{mol/L} \times 3.50 \, \text{L} \][/tex]
[tex]\[ \text{moles of NaOH} = 15.75 \, \text{mol} \][/tex]
### Step 3: Convert moles of NaOH to grams
To find the mass in grams, we use the molar mass of NaOH. The molar mass ([tex]\(M_m\)[/tex]) is given as 40.00 g/mol.
[tex]\[ \text{mass of NaOH} = \text{moles of NaOH} \times M_m \][/tex]
Substitute the values:
[tex]\[ \text{mass of NaOH} = 15.75 \, \text{mol} \times 40.00 \, \text{g/mol} \][/tex]
[tex]\[ \text{mass of NaOH} = 630.0 \, \text{g} \][/tex]
### Final Answer
The mass of NaOH needed to prepare 3.50 liters of a 4.50 M NaOH solution is:
[tex]\[ \boxed{630.0 \, \text{g}} \][/tex]
