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In the formula:

$$\text{Percentage}=\frac{\text{atomic mass of halogen}}{\text{molecular mass of Agx}}\frac{\text{mass of AgX}}{\text{mass of compound}}\cdot100$$

here mass of compound is the mass of the organic compound whose chemical composition is to be found.

What I don't understand is that: $\frac{\text{mass of AgX}}{\text{molecular mass of AgX}}\times\text{atomic mass of x}$ gives the mass of halogens in the product and to get percentage they are dividing the value with mass of compound and multiplying by 100. But we found the mass of halogen in the product then why are we diving it with mass of compound?

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Let's break it down.

We start with the mass of AgX.

$$\text{mass of AgX (g)}$$

Then, we divide by the molar mass of AgX to get the number of moles of AgX.

$$\text{moles of AgX(mol)}=\frac{\text{mass of AgX (g)}}{\text{molar mass of AgX (g/mol)}}$$

That's the same as the number of moles of halide (this is the crux of the problem).

What about the total mass of halide?

$$\text{mass of halide (g)} = \frac{\text{mass of AgX (g)}}{\text{molar mass of AgX (g/mol)}} \times \text{molar mass of halide (g/mol)}$$

So, if we divide this by the total mass of the compound, we should get the mass proportion of halide.

$$\text{proportion of halide} = \frac{\text{mass of AgX (g)}}{\text{molar mass of AgX (g/mol)}} \times \frac{\text{molar mass of halide (g/mol)}}{\text{mass of compound (g)}}$$

We just multiply this proportion by $100\%$ as a formality to get a percentage between 0-100 rather than 0-1.

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