To calculate the percentage of the pesticide in the sample, we need to determine the amount of chloride that comes from the pesticide and then use that information to calculate the amount of pesticide in the sample.
Let's break down the problem step by step:
Step 1: Calculate the amount of Cl in the precipitated AgCl.
We know that the mass of AgCl is 0.0831 g. Since AgCl has a 1:1 ratio with Cl, the amount of Cl in AgCl is also 0.0831 g.
Step 2: Convert the amount of Cl to the amount of pesticide.
The Cl in AgCl comes from the pesticide. The molar mass of Cl is 35.45 g/mol. Since AgCl has a 1:1 ratio with Cl, the molar mass of AgCl is also 35.45 g/mol.
First, calculate the number of moles of Cl in AgCl:
moles of Cl = mass of Cl / molar mass of Cl
moles of Cl = 0.0831 g / 35.45 g/mol
Step 3: Calculate the amount of pesticide in the sample.
Now, we'll use the fact that there is 8.43% Cl by mass in the pesticide to calculate the mass of pesticide in the sample.
Let x be the mass of the pesticide in the 0.627 g sample. Since the pesticide is 8.43% Cl by mass, the mass of Cl from the pesticide is 0.0843 * x.
From Step 2, we know that the moles of Cl from AgCl is equal to the moles of Cl from the pesticide. Since moles = mass / molar mass, we can set up an equation:
moles of Cl from AgCl = moles of Cl from the pesticide
0.0831 g / 35.45 g/mol = (0.0843 * x) / 35.45 g/mol
Solving for x:
0.0831 g * 35.45 g/mol = 0.0843 * x
2.943 g/mol = 0.0843 * x
Now, solve for x:
x = (2.943 g/mol) / 0.0843
Step 4: Calculate the percentage of pesticide in the sample.
Now that we know the mass of the pesticide, x, we can calculate the percentage of pesticide in the sample.
percentage of pesticide = (mass of pesticide / mass of sample) * 100
percentage of pesticide = (x / 0.627 g) * 100
Substitute the value of x that we calculated:
percentage of pesticide = ((2.943 g/mol) / 0.0843) / 0.627 g * 100
Finally, calculate the percentage:
percentage of pesticide ≈ 54.89%
Therefore, the percentage of pesticide in the sample is approximately 54.89%.