What volume of a 15.0% by mass NaOH solution, which has a density of 1.116 g/mL, should be used to make 4.95 L of an NaOH solution with a pH of 10.4?
Express your answer to three significant figures and include the appropriate units.
To determine the volume of a 15.0% by mass NaOH solution needed to make 4.95 L of an NaOH solution with a pH of 10.4, we'll follow these steps:
Step 1: Calculate the mass of NaOH needed
Step 2: Convert the mass to volume using density
Step 1: Calculate the mass of NaOH needed
The equation for calculating mass from relative mass (percentage by mass) and total mass is:
mass of NaOH = (percentage by mass / 100) x total mass
Since we want to calculate the mass of NaOH needed, we can rearrange the equation:
percentage by mass = (mass of NaOH / total mass) x 100
Let's plug in the values:
percentage by mass = 15.0% = 0.150
total mass = volume of solution x density
We'll denote the mass of NaOH as m.
Therefore:
0.150 = (m / (4.95 L x 1.116 g/mL)) x 100
Step 2: Convert the mass to volume using density
We can rearrange the equation to solve for the mass of NaOH:
m = (0.150 x 4.95 L x 1.116 g/mL) / 100
Now we can calculate the mass of NaOH:
m = (0.150 x 4.95 x 1.116) g = 0.827 g
Finally, we can calculate the volume using the density:
volume = mass / density
volume = 0.827 g / 1.116 g/mL = 0.741 mL
Therefore, the volume of a 15.0% by mass NaOH solution needed to make 4.95 L of an NaOH solution with a pH of 10.4 is 0.741 mL.
To find the volume of the 15.0% NaOH solution needed, we need to use the equation:
\( \text{volume (mL)} = \frac{\text{mass (g)}}{\text{density (g/mL)}} \)
First, we need to calculate the mass of NaOH required in the final solution. To do this, we can use the equation:
\( \text{mass (g)} = \text{volume (L)} \times \text{concentration (g/L)} \)
Given that the final volume is 4.95 L and the pH is 10.4, we can assume that the solution is an aqueous solution of NaOH. This means that we can use the equation:
\( \text{[OH-]} = 10^{-pH} \)
To convert the concentration in moles per liter (M) to grams per liter (g/L), we can multiply the concentration by the molar mass of NaOH.
Now, let's calculate the mass of NaOH required:
\( \text{mass (g)} = 4.95 \, \text{L} \times \text{concentration (g/L)} \)
We are given the concentration of the NaOH solution as 15.0% by mass. This means that in 100 g of the solution, there are 15 g of NaOH. Therefore, the concentration of NaOH in g/L is:
\( \text{concentration (g/L)} = 15.0 \, \text{g} \times \frac{100}{100} \)
Next, let's calculate the volume of the 15.0% NaOH solution needed:
\( \text{volume (mL)} = \frac{\text{mass (g)}}{\text{density (g/mL)}} \)
We are given the density of the NaOH solution as 1.116 g/mL.
Finally, we can solve for the volume in liters by dividing the volume in milliliters by 1000 and express the answer to three significant figures.
First step: Determine the molarity of the 15.0% NaOH solution. It is
1.116 g/mL x 1000 mL x 0.15 x (1/40) = about 4 M but that's just an estimate. You calculate it and use your number, not mine.
Then mL1 x M1 = mL2 x M2
L1 = ?
M1 = 4 or whatever you obtained in your calculation.
L2 = 4.95 from the problem
M2 = Convert pH to pOH (pH + pOH = 14) and convert pOH to OH^- by pOH = -log(OH^-)
Post your work if you get stuck.