A 0.774 g
mixture containing only sodium chloride and potassium chloride was dissolved in water. It required 29.6 mL
of 0.416 M AgNO3
to completely precipitate all of the chloride present. What is percent composition by mass of sodium chloride and potassium chloride in the mixture?
This requires two equations and they are solved simultaneously.
Let X = mass NaCl and
Let Y = mass KCl
equn 1 is X + Y = 0.774 g
To save typing mm = molar mass then
equn 2 comes from
mols AgCl due to NaCl + mols AgCl due to KCl = total mols AgCl formed
[X(mm AgCl/mm NaCl)] +[Y(mm AgCl/mm KCl)] = MAgNO3*LAgNO3
Solve those two equations simultaneously to obtain X = grams NaCl and Y = grams KCl.
Then %NaCl = (X/mass sample)*100 = ?
%KCL = (Y/mass sample)*100 = ?
Post your work if you get stuck.
To find the percent composition by mass of sodium chloride (NaCl) and potassium chloride (KCl) in the mixture, we need to use the information given about the precipitation reaction.
Let's begin by determining the moles of chloride ions (Cl-) present in the mixture:
Molarity of AgNO3 solution = 0.416 M
Volume of AgNO3 solution used = 29.6 mL = 0.0296 L
Moles of Cl- ions = Molarity * Volume
Moles of Cl- ions = 0.416 M * 0.0296 L = 0.0123 mol
Since each chloride ion comes from either NaCl or KCl, we can assume that the moles of Cl- ions are equal to the sum of moles of chloride ions from NaCl and KCl:
Moles of Cl- ions = Moles of Cl- from NaCl + Moles of Cl- from KCl
Let's assume the mass of NaCl in the mixture is x grams and the mass of KCl is y grams.
Molar mass of NaCl = 22.99 g/mol (sodium) + 35.45 g/mol (chlorine) = 58.44 g/mol
Molar mass of KCl = 39.10 g/mol (potassium) + 35.45 g/mol (chlorine) = 74.55 g/mol
Using the assumption above, we can calculate the moles of Cl- ions from NaCl and KCl:
Moles of Cl- from NaCl = (x / 58.44) mol
Moles of Cl- from KCl = (y / 74.55) mol
Substituting these values into the equation for the moles of Cl- ions:
0.0123 mol = (x / 58.44) mol + (y / 74.55) mol
Next, we need to consider the mass of the mixture itself. The total mass of the mixture is given as 0.774 g, which is equal to the sum of the masses of NaCl and KCl:
Total mass of mixture = mass of NaCl + mass of KCl
0.774 g = x g + y g
We now have a system of two equations. Solving this system of equations will give us the values of x (mass of NaCl) and y (mass of KCl), allowing us to determine the percent composition by mass.
Let's solve the system of equations using substitution or elimination method.
To find the percent composition by mass of sodium chloride (NaCl) and potassium chloride (KCl) in the mixture, we can follow these steps:
Step 1: Calculate the number of moles of AgNO3 used.
Given that the volume of the AgNO3 solution is 29.6 mL and the concentration is 0.416 M, we can use the formula:
moles of AgNO3 = concentration x volume (in L)
First, convert the volume to liters:
29.6 mL = 29.6/1000 L = 0.0296 L
Now calculate the moles of AgNO3:
moles of AgNO3 = 0.416 M x 0.0296 L = 0.01226 moles
Step 2: Determine the moles of chloride ions (Cl-) present in the mixture.
Since AgNO3 reacts with chloride ions to form a white precipitate of AgCl, the moles of AgNO3 used will be equal to the moles of chloride ions present.
moles of Cl- = moles of AgNO3 = 0.01226 moles
Step 3: Calculate the mass of the chloride ions (Cl-) present in the mixture.
The molar mass of Cl- is 35.45 g/mol.
mass of Cl- = moles of Cl- x molar mass of Cl-
= 0.01226 moles x 35.45 g/mol
= 0.4347487 g
Step 4: Calculate the percent composition of each component (NaCl and KCl).
Let's assume the mass of NaCl in the mixture is x grams.
Therefore, the mass of KCl will be (0.774 g - x) grams.
The molar mass of NaCl is 58.44 g/mol, and the molar mass of KCl is 74.55 g/mol.
We can create the following equation based on the masses of chloride ions present in each salt:
x moles of NaCl x 35.45 g/mol + (0.774 g - x) moles of KCl x 35.45 g/mol = 0.4347487 g
Now solve this equation for x to find the mass of NaCl:
35.45x + 35.45(0.774 - x) = 0.4347487
Simplifying the equation:
35.45x + 27.4593 - 35.45x = 0.4347487
27.4593 = 0.4347487
x = 0.012505 g
Step 5: Calculate the percent composition by mass of NaCl and KCl in the mixture.
Percent composition of NaCl = (mass of NaCl / total mass of mixture) x 100%
= (0.012505 g / 0.774 g) x 100%
≈ 1.61%
Percent composition of KCl = (mass of KCl / total mass of mixture) x 100%
= ((0.774 g - 0.012505 g) / 0.774 g) x 100%
≈ 98.39%
Therefore, the percent composition by mass of sodium chloride (NaCl) and potassium chloride (KCl) in the mixture is approximately 1.61% and 98.39% respectively.