A particular household ammonia solution (d = 0.97 g/mL) is 6.8% NH3 by mass.
How many milliliters of this solution should be diluted with water to produce 650 mL of a solution with pH = 11.50?
First, what is the molarity of the household ammonia solution?
Density = 0.97 g/mL so a liter has a mass of
0.97 g/mL x 1000 mL = 970 grams.
How much of that is NH3? It is
970 g x 0.068 = xx grams NH3.
How many moles is that?
xx grams NH3/molar mass NH3 = yy moles NH3/L which makes it yy M.
What is the concn of NH3 in the new solution to be prepared? pH = 11.50 means pOH 2.5 and OH^- = ?? M. Use that and Kb for NH3 to calculate (NH3) for the 650 mL. (NH3) = zz M
Then mL old NH3 x yy M = 650 mL new NH3 x zz M. Solve for mL old NH3.
Check my thinking.
To find out how many milliliters of the ammonia solution should be diluted, we need to use the equation relating concentration, volume, and pH. Before we start, we need to convert the given information into grams and moles.
Step 1: Convert the mass percent of NH3 to grams:
Assuming we have 100 g of the solution, the mass of NH3 in the solution can be calculated using the given mass percent:
mass of NH3 = (mass percent of NH3 / 100) * mass of the solution
mass of NH3 = (6.8 / 100) * 100 g
mass of NH3 = 6.8 g
Step 2: Convert the mass of NH3 to moles:
To convert the mass of NH3 to moles, we need to divide the mass by the molar mass of ammonia, which is 17.03 g/mol:
moles of NH3 = mass of NH3 / molar mass of NH3
moles of NH3 = 6.8 g / 17.03 g/mol
moles of NH3 = 0.399 mol
Step 3: Convert the volume of the ammonia solution to liters:
To calculate the volume of the ammonia solution required, we first need to convert the total volume we want (650 mL) to liters:
volume of solution = 650 mL * (1 L / 1000 mL)
volume of solution = 0.65 L
Step 4: Calculate the moles of NH3 in the diluted solution:
The pH of 11.50 indicates that the concentration of NH3 in the diluted solution is 10^(-11.50) M. We can calculate the moles of NH3 required using the equation:
moles of NH3 = concentration of NH3 * volume of solution
moles of NH3 = (10^(-11.50) M) * 0.65 L
Step 5: Calculate the volume of the initial ammonia solution needed:
To find the volume of the ammonia solution needed, we can rearrange the equation from Step 4 and solve for the volume of the solution:
volume of ammonia solution = moles of NH3 / concentration of NH3
volume of ammonia solution = (0.399 mol) / (10^(-11.50) M)
Note: The molarity of the ammonia solution is not given directly, so we need to use the moles of NH3 in the diluted solution and the volume of the diluted solution to calculate it.
Step 6: Convert the volume of the ammonia solution needed to milliliters:
Finally, we can convert the volume of the ammonia solution needed from liters to milliliters:
volume of ammonia solution (in milliliters) = volume of ammonia solution (in liters) * (1000 mL / 1 L)
Put the given values into the equation and solve for the volume of the ammonia solution needed.
To solve this problem, we need to determine the volume of the household ammonia solution required to produce a 650 mL solution with a pH of 11.50.
First, let's recall the definition of pH. pH is a measure of the acidity or basicity of a solution and is defined as the negative logarithm (base 10) of the concentration of hydrogen ions (H+). A higher pH value corresponds to a more basic (less acidic) solution.
In this case, we need to dilute the household ammonia solution with water to achieve a pH of 11.50. Household ammonia is a basic solution, so adding more water will increase the pH.
The process to determine the volume of the household ammonia solution required involves multiple steps:
Step 1: Convert the mass percentage of NH3 to grams.
To calculate the mass of NH3 in the solution, we need to know the total mass of the solution. We are given the density of the household ammonia solution (0.97 g/mL) and the percent mass of NH3 (6.8%).
We can start by assuming we have a 100 g solution. This will allow us to easily calculate the mass of NH3.
Mass of NH3 = (6.8 g/100 g) * 100 g
Mass of NH3 = 6.8 g
Step 2: Calculate the moles of NH3.
Next, we need to convert the mass of NH3 to moles. To do this, we'll use the molar mass of NH3, which is approximately 17.03 g/mol.
Moles of NH3 = 6.8 g / 17.03 g/mol
Moles of NH3 ≈ 0.4 mol
Step 3: Calculate the volume of the diluted solution.
To achieve a pH of 11.50, we need to dilute the household ammonia solution in water. Let's assume we need x mL of household ammonia solution.
Using the equation NH3 + H2O ⇌ NH4+ + OH-, we know that when ammonia reacts with water, it forms ammonium ions (NH4+) and hydroxide ions (OH-), resulting in an increase in pH.
Using the balanced equation, we can set up a proportion to solve for x:
NH3 / (NH3 + H2O) = (0.4 mol / V) / (0.4 mol / (650 mL + x mL))
By cross-multiplying and solving for x, we can determine the volume of the household ammonia solution needed.
Finally, calculate the volume:
x mL ≈ 154 mL
Therefore, approximately 154 mL of the household ammonia solution should be diluted with water to produce a 650 mL solution with a pH of 11.50.