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## A question about gravimetric analysis

Hello, I have been studying undergraduate level chemistry courses for PhD proficiency exam, and I have very recently been started Analytical Chemistry.

I have a simple problem and I solved it in a different way, could you please show me how I can solve it by using the known "gravimetric factor"? Or I maybe have used it without noticing

The question is as follows:

 An organic sample, weighing 0.2795 grams and known to include $\displaystyle C_6H_6Cl_6~(290.83~g/mol)$ and $\displaystyle C_{14}H_9Cl_5~(354.49~g/mol)$, is ignited with oxygen gas in a quartz tube, and products obtained (CO2, H2, and HCl) are passed from a NaHCO3 solution. After acidification, the total chloride ions are found to precipitate 0.7161 grams of AgCl (143.22 g/mol). Calculate the halogen percentage of each chlorinated organic compounds.
Okay, my solution goes like this:

 290.83x+354.49y=0.2795 g 6*35.5x+5*35.5y=0.005*35.5 g (0.005 is the number of moles of AgCl) from there, rearrangement gives the following: 290.83x+354.49y=0.2795 g -425.388x-354.49y=-0.35448 g adding and dividing reveals that x=0.00055723 and from the second (or first) equation, y is found to be 0.0003313. The gram equivalents of these x and y are 0.1620592 grams and 0.11744254 grams, respectively. Their percentages are 57.98% and 42.02%, respectively. The textbook says that the correct answers are 57.80% and 42.20%, resp.
My questions:

1) What is the cause I am getting different answers? I am suspecting from using 35.5 grams/mol for chlorine atom; maybe I have to find more precise number from elsewhere; it is not given to me in this question.

2) Can you please show the solution of this problem by using gravimetric factor, along with its description? I have been unable to comprehend it so far.