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?
I have worked this problem earlier. Scroll down to the answer to Kyle who posted at 6:48 pm today and my response is there.
thank you!
To solve this problem, we need to follow a few steps:
Step 1: Calculate the mass of ammonia in the original solution.
Step 2: Determine the volume of the original solution required to obtain the desired pH.
Step 3: Calculate the volume of water needed to dilute the solution.
Let's go through these steps one by one:
Step 1: Calculate the mass of ammonia in the original solution.
The solution is 6.8% ammonia by mass, which means that for every 100 g of the solution, there are 6.8 g of ammonia.
To find the mass of ammonia in the solution, we need to multiply the mass percent by the total mass of the solution.
The total mass of the solution can be calculated by multiplying the density (D) by the volume (V): mass = density x volume.
Given the density (D) of the solution is 0.97 g/ml and let's assume the mass is 100 g (for ease of calculation).
So, the volume of the solution can be obtained by dividing the mass by the density: volume = mass / density = 100 g / 0.97 g/ml ≈ 103 ml.
Therefore, in 100 g of the solution, there are 6.8 g of ammonia.
Step 2: Determine the volume of the original solution required to obtain the desired pH.
To determine the volume of the original solution required to obtain the desired pH, we need some additional information, such as the concentration of ammonia in the original solution and the pKa value for ammonia in water.
Given that the pH of the desired solution is 11.65, we can assume that the concentration of ammonia (NH3) and its conjugate base (NH4OH) will be approximately equal.
Using the pKa value for ammonia because pKa = 9.25, we can use the Henderson-Hasselbalch equation to relate pH to the ratio of base to acid in the solution:
pH = pKa + log([A-]/[HA]),
where [A-] is the concentration of the base and [HA] is the concentration of the acid.
Since we are assuming [A-] ≈ [HA], we can simplify the equation to:
pH = pKa + log(1) = pKa.
Therefore, we can say that the initial concentration of ammonia in the solution should have a pH equal to the pKa value.
Now, using the volume of the solution we calculated earlier (103 ml), and assuming that the final volume required is 650 ml, we can set up the equation:
(103 ml) / (650 ml + 103 ml) = (pKa of ammonia) / 11.65.
Simplifying this equation, we can solve for the volume of the original solution:
103 ml = (650 ml + 103 ml) x (pKa of ammonia) / 11.65.
By rearranging the equation, we can solve for the volume of the original solution:
(650 ml + 103 ml) x (pKa of ammonia) = 103 ml x 11.65.
Now, substitute the given values:
(650 ml + 103 ml) x (9.25) = 103 ml x 11.65.
Solving this equation will give you the volume of the original solution required to obtain the desired pH.
Step 3: Calculate the volume of water needed to dilute the solution.
To calculate the volume of water needed to dilute the solution, subtract the volume of the original solution from the desired final volume:
Volume of water = (Desired final volume) - (Volume of original solution).
Once you have the volume of water, you can mix it with the calculated volume of the original solution to obtain the desired solution with a pH of 11.65.