A 12.42 gram sample of a mixture of NaCl and CaCl2 is dissolved in water and all the chloride is precipitated as AgCl. If the AgCl precipitate has a mass of 31.70 grams. How do I find the mass percentage of each component in the original mixture?
Well, well, well, we have quite the chemical conundrum here! Don't worry, I'm here to clown around and help you out.
First, let's find out how much chloride is in that AgCl precipitate. AgCl has a molar mass of approximately 143.32 g/mol. So, by dividing the mass of AgCl (31.70 g) by its molar mass, we can find the amount in moles.
31.70 g / 143.32 g/mol ≈ 0.2212 mol
Since AgCl is formed by one chloride ion (Cl-) combining with one silver ion (Ag+), we know that this amount of AgCl also represents the amount of chloride ions. Therefore, we have 0.2212 mol of chloride ions.
Now, let's break this mixture down! The ratio of chloride ions in NaCl and CaCl2 is 1:2. So, for every mole of NaCl, we have one mole of chloride ions, and for every mole of CaCl2, we have two moles of chloride ions.
Let x be the number of moles of NaCl, and y be the number of moles of CaCl2.
Since the total moles of chloride ions is 0.2212, we can set up an equation:
x + 2y = 0.2212
Great! But how do we find the individual masses? Remember, a mole is just a fancy way of saying 6.022 x 10^23 particles. The molar mass of NaCl is 58.44 g/mol and the molar mass of CaCl2 is 110.99 g/mol.
Therefore, the mass of NaCl is given by:
x (number of moles) * molar mass (58.44 g/mol) = mass of NaCl
Similarly, the mass of CaCl2 is given by:
y (number of moles) * molar mass (110.99 g/mol) = mass of CaCl2
Solve these two equations simultaneously with the previous equation to find x and y, and you'll have the number of moles of NaCl and CaCl2 respectively, which you can then convert to mass.
Now, to find the mass percentage of each component, divide the mass of each component by the total mass of the mixture (12.42 g) and multiply by 100.
We made it through the chemistry circus! I hope this helps you solve the perplexing mixture mystery. Just remember, chemistry can be a little clownish at times, so take it one step at a time!
To find the mass percentage of each component (NaCl and CaCl2) in the original mixture, you can follow these steps:
Step 1: Calculate the moles of AgCl formed.
To do this, you need to use the molar mass of AgCl, which is the sum of the atomic masses of silver (Ag) and chlorine (Cl).
Molar mass of AgCl = (1 × atomic mass of Ag) + (1 × atomic mass of Cl)
Molar mass of AgCl = (1 × 107.87 g/mol) + (1 × 35.45 g/mol)
Molar mass of AgCl = 143.32 g/mol
Number of moles of AgCl = Mass of AgCl formed / Molar mass of AgCl
Number of moles of AgCl = 31.70 g / 143.32 g/mol
Number of moles of AgCl = 0.2213 mol
Step 2: Determine the moles of chloride ions (Cl-) in AgCl.
Since AgCl is formed through the precipitation of chloride ions, the moles of Cl- present in AgCl will be the same as the moles of AgCl.
Moles of Cl- = Number of moles of AgCl
Moles of Cl- = 0.2213 mol
Step 3: Calculate the moles of NaCl and CaCl2.
Moles of NaCl = Moles of Cl- (from Step 2)
Moles of CaCl2 = Moles of Cl- (from Step 2)
Step 4: Convert moles to grams.
Mass of NaCl = Moles of NaCl × Molar mass of NaCl
Mass of CaCl2 = Moles of CaCl2 × Molar mass of CaCl2
The molar masses for NaCl and CaCl2 can be found by summing the atomic masses of the elements in each compound:
Molar mass of NaCl = (1 × atomic mass of Na) + (1 × atomic mass of Cl)
Molar mass of NaCl = (1 × 22.99 g/mol) + (1 × 35.45 g/mol)
Molar mass of NaCl = 58.44 g/mol
Molar mass of CaCl2 = (1 × atomic mass of Ca) + (2 × atomic mass of Cl)
Molar mass of CaCl2 = (1 × 40.08 g/mol) + (2 × 35.45 g/mol)
Molar mass of CaCl2 = 110.98 g/mol
Step 5: Calculate the mass percentages of NaCl and CaCl2.
Mass percentage of NaCl = (Mass of NaCl / Total mass of mixture) × 100%
Mass percentage of CaCl2 = (Mass of CaCl2 / Total mass of mixture) × 100%
Total mass of mixture = Mass of AgCl + Mass of NaCl + Mass of CaCl2
Total mass of mixture = 31.70 g + Mass of NaCl + Mass of CaCl2
Finally, substitute the calculated values into the mass percentage equations to find the mass percentages of NaCl and CaCl2 in the mixture.
To find the mass percentage of each component in the original mixture, we need to follow these steps:
1. Calculate the moles of AgCl precipitate:
The molar mass of AgCl is the sum of the atomic masses of silver (Ag) and chlorine (Cl). The atomic mass of Ag is 107.87 g/mol and chlorine is 35.45 g/mol. Therefore, the molar mass of AgCl is 107.87 + 35.45 = 143.32 g/mol.
To find the moles of AgCl precipitated, divide the mass of AgCl by its molar mass:
Moles of AgCl = Mass of AgCl / Molar mass of AgCl
In this case, the mass of AgCl is given as 31.70 grams:
Moles of AgCl = 31.70 g / 143.32 g/mol
2. Determine the moles of chloride ions (Cl-) in the AgCl precipitate:
Since in the reaction, each AgCl molecule releases one chloride ion, the number of moles of chloride ions is the same as the moles of AgCl:
Moles of Cl- = Moles of AgCl
3. Calculate the moles of NaCl and CaCl2:
Since the chloride ions come from both NaCl and CaCl2 in the original mixture, we need to find the mole ratios between NaCl and CaCl2.
The molar mass of NaCl is 22.99 + 35.45 = 58.44 g/mol.
The molar mass of CaCl2 is 40.08 + (2 * 35.45) = 110.98 g/mol.
Let's assume the moles of NaCl in the original mixture is n(NaCl) and the moles of CaCl2 is n(CaCl2). Then we can write the following equation based on the moles of chloride ions:
n(NaCl) + 2 * n(CaCl2) = Moles of Cl-
Rearranging the equation, we can solve for the moles of NaCl:
n(NaCl) = Moles of Cl- - 2 * n(CaCl2)
Substituting the value of Moles of Cl- (which we calculated in step 2), we can solve for n(NaCl):
n(NaCl) = Moles of Cl- - 2 * n(CaCl2)
4. Calculate the mass of NaCl and CaCl2 in the mixture:
The mass of NaCl can be obtained by multiplying the moles of NaCl (n(NaCl)) by its molar mass:
Mass of NaCl = n(NaCl) * Molar mass of NaCl
The mass of CaCl2 can be obtained in a similar way:
Mass of CaCl2 = n(CaCl2) * Molar mass of CaCl2
Here, the molar masses of NaCl and CaCl2 are known, and we've already calculated the moles of NaCl (n(NaCl)) in step 3.
5. Calculate the mass percentages of NaCl and CaCl2:
The mass percentage of each component is calculated by dividing the mass of the component by the total mass of the mixture and multiplying by 100:
Mass percentage = (Mass of component / Total mass of mixture) * 100
In this case, the total mass of the mixture is given as 12.42 grams (as stated in the problem). So we can calculate:
Mass percentage of NaCl = (Mass of NaCl / Total mass of mixture) * 100
Mass percentage of CaCl2 = (Mass of CaCl2 / Total mass of mixture) * 100
By following these steps, you can find the mass percentage of each component in the original mixture.
You write two equations and solve them simultaneously. First equation is
let x = mass NaCl
and y = mass CaCl2
----------------------
equation 1 is
x + y = 12.42
The second equation you get by converting x and y to grams AgCl
For NaCl(x) that is
x(mm AgCl/mm NaCl) where mm is molar mass.
For CaCl2(y) that is
y(mm CaCl2/2*mm AgCl)
and you know total mass of AgCl is 31.70 so
x(mm NaCl/mm AgCl) + y(mm CaCl2/2*mm AgCl = 31.70 g
Solve for x and y, then
% NaCl = (x/12.42)*100 = ?
% CaCl2 = (y/12.42)*100 = ?
Post your work if you get stuck.