What volume of a 15.0% by mass NaOH solution, which has a density of 1.116 g/mL, should be used to make 4.40 L of an NaOH solution with a pH of 10.5?
too confusing
14-pH=pOH=14-10.5=3.5
pOH=-log[OH-]=3.5
10^-(pOH)=10^-(3.5)=OH concentration in M
4.40L*(OH concentration in M)= moles of OH
moles of OH*(39.997 g/mol)= mass of NaOH needed
mass of NaOH needed
Since 15% is 0.15g of NaOH/g of solution, solving for g of solution
mass of NaOH needed/(0.15g of NaOH/g of solution)= g of solution needed.
g of solution needed/1.116 g/mL= volume in mL
Report your answer with 3 sig figs.
To find the volume of the 15.0% by mass NaOH solution needed to make the desired solution, we need to consider the mass of NaOH in the solution.
First, we'll calculate the mass of the desired NaOH solution using its density and volume:
Mass = Density x Volume
Given that the density of the solution is 1.116 g/mL and the desired volume is 4.40 L, we can calculate the mass as follows:
Mass = 1.116 g/mL x 4.40 L x 1000 mL/L
Now, we need to find the mass of NaOH in the solution. The 15.0% by mass NaOH solution means that 15.0 grams of NaOH are present in 100 grams of the solution. We can set up a proportion to find the mass of NaOH in the desired solution:
15.0 g NaOH / 100 g solution = x g NaOH / Mass of desired solution
Simplifying the proportion:
(15.0 g NaOH) x (Mass of desired solution) = (100 g solution) x (x g NaOH)
Now, we can solve for x (mass of NaOH in the desired solution):
x g NaOH = (15.0 g NaOH) x (Mass of desired solution) / (100 g solution)
Next, we need to convert the mass of NaOH to volume using its molar mass and the equation:
Moles = Mass / Molar mass
The molar mass of NaOH is approximately 40.0 g/mol. So, we can calculate the moles of NaOH:
moles of NaOH = x g NaOH / 40.0 g/mol
Now, we can convert the moles of NaOH to volume using the relationship:
Volume = Moles / Molarity
The molarity of a solution is defined as moles of solute per liter of solution. Since we want a pH value of 10.5, which is a basic solution, we know that the concentration of hydroxide ions (OH-) will be equal to the concentration of NaOH in the solution.
In a basic solution, the concentration of hydroxide ions is given by pOH = -log[OH-]
Since we have a pH value of 10.5, we can calculate the pOH:
pOH = 14 - pH
pOH = 14 - 10.5
Now, we can calculate the concentration of hydroxide ions:
[OH-] = 10^(-pOH)
Finally, we can calculate the volume of the 15.0% NaOH solution needed to make the desired solution:
Volume = moles of NaOH / [OH-] concentration
By plugging in the values we have calculated, the final answer will give us the volume of the 15.0% NaOH solution needed to make the desired solution with a pH of 10.5.