A sample of 5.52 grams of NaOH is dissolved
into 659 mL of aqueous 0.250 M NaOH (assume
no volume change). This solution is
then poured into 1.52 gallons of water. (You
may assume that the two volumes can be
added.) What is the concentration of NaOH
in the final solution?
To find the concentration of NaOH in the final solution, we can use the concept of molarity (M). Molarity is defined as the number of moles of solute (in this case, NaOH) per liter of solution.
First, let's convert the volume of the NaOH solution from milliliters (mL) to liters (L). We have 659 mL, so we divide by 1000 to get:
659 mL ÷ 1000 = 0.659 L
Next, let's calculate the number of moles of NaOH in the initial solution. We can use the formula:
moles = mass / molar mass
The molar mass of NaOH is the sum of the atomic masses of sodium (Na), oxygen (O), and hydrogen (H):
Na: 22.99 g/mol
O: 16.00 g/mol
H: 1.01 g/mol
Molar mass of NaOH = (22.99) + (16.00) + (1.01) = 39.00 g/mol
Now, we can calculate the number of moles of NaOH in the initial solution:
moles = 5.52 g / 39.00 g/mol = 0.1415 mol
Since we know the number of moles and volume of the initial solution, we can calculate the initial molarity:
Molarity (initial) = moles / volume (in liters) = 0.1415 mol / 0.659 L = 0.2148 M
Now let's determine the final volume of the solution. We have 1.52 gallons, and we need to convert this to liters. Since 1 gallon is approximately 3.785 L:
1.52 gallons x 3.785 L/gallon = 5.7572 L
Now we can calculate the concentration of NaOH in the final solution, using the principle of solution dilution. The number of moles of NaOH remains constant throughout the dilution process:
moles (initial) = moles (final)
So, we have:
moles (initial) = moles (final)
0.1415 mol = moles (final)
Now, let's calculate the final volume of the solution by adding the volume of the initial NaOH solution and the volume of water:
volume (final) = volume (initial NaOH solution) + volume (water)
volume (final) = 0.659 L + 5.7572 L
volume (final) = 6.4162 L
Finally, we can calculate the concentration of NaOH in the final solution:
Molarity (final) = moles (final) / volume (final)
Molarity (final) = 0.1415 mol / 6.4162 L = 0.0220 M
Therefore, the concentration of NaOH in the final solution is 0.0220 M.
mols NaOH in 5.52 grams is mols = grams/molar mass = ?
mols NaOH in the solution of NaOH is mols = M x L = ?
Total mols NaOH = mols in the 5.52g + mols in the solution = ?
Convert 1.52 gallons to L. 1 gallon = 3.785 L.
total volume is L in 1.52 gallons + 659 mL(convert to L first).
Then M of the final NaOH solution is M = total mols NaOH/total volume solution.