A particular household ammonia solution (D= 0.97g/ml) is 6.8% by mass.
How many milliliters of this solution should be diluted with water to produce 650 mL of a solution with pH= 11.65?
You need to know the molarity of the NH3 solution. That is
0.97 g/mL x 1000 mL, x 0.068 x (1/17) = ??M. I obtained abouat 4 M BUT you need to do it exactly. I rounded here and there.
Now move to the solution you wish to prepare. If pH = 11.65, then pOH = 2.35 and you can calculate the OH^- from this.
NH3 + H2O ==> NH4^+ + OH^-
Set up Kb expression, plug in NH4^+, OH^-, and Kb and solve for NH3 = ??
Then 4 M x mL = ??M x 650
Post your work if you get stuck. Check my work.
To solve this problem, we will need to use the concepts of mass percent, density, and pH.
Let's break down the problem into steps:
Step 1: Calculate the mass of ammonia in the original solution.
Given that the solution is 6.8% by mass, we can determine the mass of ammonia present in the solution. To do this, multiply the mass percent by the total mass of the solution.
Mass of ammonia = (6.8% / 100) * mass of solution
Step 2: Convert the mass of ammonia to volume using density.
Since the density of the solution is given as 0.97 g/mL, we can convert the mass of ammonia to volume by using the formula:
Volume of ammonia = Mass of ammonia / Density
Step 3: Calculate the volume of water needed.
We need to determine how much water should be added to the ammonia solution to reach a final volume of 650 mL. We can calculate the volume of water by subtracting the volume of the ammonia solution from the desired final volume.
Volume of water = Final volume - Volume of ammonia
Step 4: Calculate the pH of the final solution.
Given that the pH of the final solution is 11.65, we need to compare this with the pKa value of ammonia (NH3), which is approximately 9.25. We can use the Henderson-Hasselbalch equation:
pH = pKa + log(base/acid)
Since we want to create a basic solution, the ratio of base to acid should be greater than 1 (base/acid > 1) in order to achieve a pH higher than the pKa value.
Now, let's put all the steps together to solve the problem:
Step 1: Calculate the mass of ammonia in the original solution.
Given that the solution is 6.8% by mass and the desired final volume is 650 mL, we can calculate the mass of the solution:
Mass of solution = (6.8/100) * 0.97 * 650 g
Step 2: Convert the mass of ammonia to volume using density.
Given that the density of the solution is 0.97 g/mL, we can now calculate the volume of the ammonia solution:
Volume of ammonia = mass of ammonia / density
Step 3: Calculate the volume of water needed.
We need to determine the volume of water to be added to the ammonia solution to achieve a final volume of 650 mL. We can calculate this as:
Volume of water = 650 mL - Volume of ammonia
Step 4: Calculate the pH of the final solution.
Given that the desired pH is 11.65, and the pKa of ammonia is 9.25, we can determine the ratio of base to acid using the Henderson-Hasselbalch equation:
pH = pKa + log(base/acid)
Solving for base/acid:
base/acid = 10^(pH - pKa)
Now you can plug in the values and calculate the ratio of base to acid.
In summary, to determine how many milliliters of the ammonia solution should be diluted with water to produce a 650 mL solution with pH=11.65, you would follow the steps outlined above, calculating the mass of ammonia in the original solution, converting it to volume using density, and then calculating the volume of water needed. Finally, you would calculate the ratio of base to acid to determine the pH of the final solution.