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QUESTION

# Calculate the %Br in a 1.0234g mixture of AgCl and AgBr if the mixture contains 0.6635g of Ag?

"% Br" = 24.91%

The trick here is to realize that the number of moles of chloride anions, "Cl"^(-), and bromide anions, "Br"^(-), will be equal to the number of moles of silver(I) cations, "Ag"^(+), present in the sample.

Notice that one mole of silver chloride contains one mole of silver(I) cations and one mole of chloride anions

"AgCl" -> "Ag"^(+) + "Cl"^(-)

Likewise, one mole of silver bromide contains one mole of silver(I) cations and one mole of bromide anions

"AgBr" -> "Ag"^(+) + "Br"^(-)

color(red)(!)color(white)(a)From this point on, I will refer to the silver(I) cations as silver, and o the chloride and bromide anions as chlorine and bromine, respectively.

If you take n_x to be the number of moles of silver chloride and n_y to be the number of moles of silver bromide present in the mixture, you can say that the mixture will contain

n_(Ag) = n_x + n_y -> the total number of moles of silver

n_(Br) = n_y -> the number of moles of bromine

n_(Cl) = n_x -> the number of moles of chlorine

Now, use silver's molar mass to determine how many moles you get in that sample

0.6635color(red)(cancel(color(black)("g"))) * "1 mole Ag"/(107.868color(red)(cancel(color(black)("g")))) = "0.006151 moles Ag"

This means that you have

n_(Ag) = n_y + n_x = "0.006151 moles"" " " "color(orange)("(*)")

Use the total mass of the sample to find the combined mass of bromine and chlorine present in the mixture

m_"mixture" = m_(Ag) + m_(Br) + m_(Cl)

m_(Cl) + m_(Br) = "1.0234 g" - "0.6635 g"

m_(Cl) + m_(Br) = "0.3599 g" " " " "color(orange)("(* *)")

As you know, the molar mass of a element tells you the mass of one mole of said element. This means that you can write the number of moles of an element in terms of the mass and the molar mass

color(purple)(|bar(ul(color(white)(a/a)color(black)(M_M = m/n implies n = m/M_M)color(white)(a/a)|)))

This means that the number of moles of chlorine present in the sample will be

n_(x) = (m_(Cl)color(red)(cancel(color(black)("g"))))/("35.453"color(red)(cancel(color(black)("g"))) "mol"^(-1)) = m_(Cl)/35.453color(white)(a)"moles Cl"

Likewise, the number of moles of bromine present in the sample will be

n_y = (m_(Br)color(red)(cancel(color(black)("g"))))/(79.904color(red)(cancel(color(black)("g")))"mol"^(-1)) = m_(Br)/79.904color(white)(a)"moles Br"

This means that equation color(orange)("(*)") becomes

m_(Cl)/35.453 + m_(Br)/79.904 = 0.006151

Use equation color(orange)("(* *)") to find the mass of elemental chlorine

m_(Cl) = 0.3599 - m_(Br)

Plug this into the above equation to find the mass of elemental bromine present in the sample

(0.3599 - m_(Br))/35.453 + m_(Br)/79.904 = 0.006151

This will be equivalent to

0.01015 - 0.01569 * m_(Br) = 0.006151

m_(Br) = (0.01015 - 0.006151)/0.01569 = 0.2549

The mixture contains

m_(Br) = "0.2549 g Br"

This means that the of bromine in the sample will be

"% Br" = (0.2549 color(red)(cancel(color(black)("g"))))/(1.0234color(red)(cancel(color(black)("g")))) xx 100 = color(green)(|bar(ul(color(white)(a/a)"24.91%"color(white)(a/a)|)))

The answer is rounded to four , the number of sig figs you have for the mass of silver present in the sample.