A solution of sodium hydroxide has a density of 1.14 g/mL and contains 32.8% sodium hydroxide by mass. If 40.0 mL of this solution is diluted with 30.0 mL of water, what is the concentration of the dilute sodium hydroxide?
The Correct Answer and Explanation is :
To determine the concentration of the diluted sodium hydroxide (NaOH) solution, follow these steps:
Step 1: Determine the mass of NaOH in the original solution
- Density of NaOH solution = 1.14 g/mL
- Volume of original solution = 40.0 mL
- Mass of solution = Density × Volume
[
1.14 \, \text{g/mL} \times 40.0 \, \text{mL} = 45.6 \, \text{g}
] - The solution contains 32.8% NaOH by mass, so:
[
\frac{32.8}{100} \times 45.6 = 14.9568 \approx 14.96 \, \text{g NaOH}
]
Step 2: Determine the final volume after dilution
- Original volume = 40.0 mL
- Added water = 30.0 mL
- Final volume = 40.0 + 30.0 = 70.0 mL
Step 3: Calculate the molarity of NaOH in the diluted solution
- Molar mass of NaOH = 40.0 g/mol
- Moles of NaOH in solution:
[
\frac{14.96 \, \text{g}}{40.0 \, \text{g/mol}} = 0.374 \, \text{moles}
] - Molarity (( M )) is moles per liter of solution:
[
M = \frac{\text{moles of NaOH}}{\text{volume in liters}} = \frac{0.374}{0.070}
]
[
M = 5.34 \, M
]
Final Answer:
The concentration of NaOH in the diluted solution is 5.34 M.
Explanation (300 words)
The problem involves diluting a concentrated sodium hydroxide solution and determining the molarity of the new solution. We start by calculating the mass of NaOH in the original 40.0 mL solution. Given that the solution has a density of 1.14 g/mL, its total mass is found by multiplying by the volume, yielding 45.6 g. Since 32.8% of this mass is NaOH, we calculate the NaOH mass as 14.96 g.
Next, we consider the dilution. Adding 30.0 mL of water to the 40.0 mL solution results in a total final volume of 70.0 mL. Since dilution only changes volume and not the amount of solute, the number of moles of NaOH remains the same. To determine the number of moles, we divide the 14.96 g of NaOH by its molar mass (40.0 g/mol), obtaining 0.374 moles.
Finally, molarity (( M )) is defined as moles of solute per liter of solution. Converting 70.0 mL to 0.070 L, we calculate:
[
M = \frac{0.374}{0.070} = 5.34 \, M
]
This result indicates that after dilution, the concentration of the NaOH solution is 5.34 M, meaning there are 5.34 moles of NaOH per liter of solution.
Now, I’ll generate an image illustrating this dilution process.
I’ve generated an image illustrating the dilution process of sodium hydroxide (NaOH) solution. It visually represents the initial concentrated solution, the addition of water, and the final diluted solution with its new concentration. Let me know if you need any modifications!
