A sample of 5.61 grams of NaOH is dissolved
into 627 mL of aqueous 0.250 M NaOH (assume
no volume change). This solution is
then poured into 2.16 gallons of water. (You
may assume that the two volumes can be
added.) What is the concentration of NaOH
in the final solution?
Answer in units of M.
How many mols NaOH in 5.61? That's mols = grams/molar mass = ?
How many molos in the solution. That is mols = M x L = ?
Total mols NaOH = sum of the two above = ?
M = mols/L solution. You know mols. Convert 2.16 gallons to L and add to the 627 for total volume.
To find the concentration of NaOH in the final solution, we can use the concept of moles and molarity.
Step 1: Convert the volume of water from gallons to liters.
Since 1 gallon is approximately equal to 3.78541 liters, we have:
2.16 gallons × 3.78541 L/gallon = 8.1819 L
Step 2: Calculate the amount of NaOH in moles in the original solution.
To do this, we need to use the formula:
moles = mass / molar mass
The molar mass of NaOH (sodium hydroxide) is:
Na = 22.99 g/mol
O = 16.00 g/mol
H = 1.01 g/mol
So, the molar mass of NaOH = 22.99 + 16.00 + 1.01 = 40.00 g/mol
Given a sample of 5.61 grams of NaOH, we can calculate the moles of NaOH:
moles = mass / molar mass = 5.61 g / 40.00 g/mol = 0.14025 mol
Step 3: Calculate the initial volume of the NaOH solution in liters.
To do this, we need to convert milliliters to liters:
627 mL × 1 L/1000 mL = 0.627 L
Step 4: Calculate the initial moles of NaOH in the solution.
The molarity (M) of the solution is defined as moles of solute per liter of solution. In this case, the molarity is given as 0.250 M NaOH. Therefore, the initial moles of NaOH in the solution can be found using the equation:
moles = Molarity × Volume
moles = 0.250 mol/L × 0.627 L = 0.15675 mol
Step 5: Find the total moles of NaOH after mixing.
The total moles of NaOH in the final solution can be obtained by adding the initial moles from the sample and the initial moles from the solution:
Total moles = moles from sample + moles from solution
Total moles = 0.14025 mol + 0.15675 mol = 0.297 mol
Step 6: Calculate the final volume of the solution.
The final volume of the solution can be obtained by adding the volume of the original solution to the volume of water:
Final volume = volume of original solution + volume of water
Final volume = 0.627 L + 8.1819 L = 8.8089 L
Step 7: Calculate the concentration of NaOH in the final solution.
The concentration (molarity) of the final solution can be found using the equation:
Molarity = moles / volume
Molarity = 0.297 mol / 8.8089 L ≈ 0.0337 M
Therefore, the concentration of NaOH in the final solution is approximately 0.0337 M.