Question #93ac1

The most important thing to look out for when dealing with a stoichiometry problem is if the chemical equation given to you is balanced. As it turns out, that is not the case here, i.e. your equation is unbalanced.

#"Na"_ 2"S"_ 2"O"_ (3(aq)) + "AgBr"_ ((s)) -> "NaBr"_ ((aq)) + "Na"_ 3["Ag"("S"_ 2"O"_ 3)_ 2] ""_ ((aq))#

In order to balance this equation out, you need #4# atoms of sodium, #"Na"#, on the reactants' side. You also need #2# thiosulfate ions, #"S"_2"O"_3^(2-)#, on the reactants' side. You can thus add a #color(red)(2)# coefficient in front of sodium thiosulfate, #"Na"_2"S"_2"O"_3#

#color(red)(2)"Na"_ 2"S"_ 2"O"_ (3(aq)) + "AgBr"_ ((s)) -> "NaBr"_ ((aq)) + "Na"_ 3["Ag"("S"_ 2"O"_ 3)_ 2] ""_ ((aq))#

Now, the balanced chemical equation tells you that every mole of silver bromide, #"AgBr"#, that takes part in the reaction consumes #color(red)(2)# moles of sodium thiosulfate and produces #1# mole of sodium bromide, #"NaBr"#.

The problem gives you grams of silver bromide, so right from the start you know that you must convert them to moles by using the compound's molar mass

#42.7 color(red)(cancel(color(black)("g"))) * "1 mole AgBr"/(187.77color(red)(cancel(color(black)("g")))) = "0.2274 moles AgBr"#

This many moles of silver bromide will consume

#0.2274 color(red)(cancel(color(black)("moles AgBr"))) * (color(red)(2)color(white)(a)"moles Na"_2"S"_2"O"_3)/(1color(red)(cancel(color(black)("mole AgBr")))) = "0.4548 moles Na"_2"S"_2"O"_3#

and produce

#0.2274color(red)(cancel(color(black)("moles AgBr"))) * "1 mole NaBr"/(1color(red)(cancel(color(black)("mole AgBr")))) = "0.2274 moles NaBr"#

Use the molar mass of sodium bromide to convert the number of moles to grams

#0.2274 color(red)(cancel(color(black)("moles NaBr"))) * "102.9 g"/(1color(red)(cancel(color(black)("mole NaBr")))) = color(green)(|bar(ul(color(white)(a/a)color(black)("23.4 g")color(white)(a/a)|)))#

You can thus say that the reaction of #"42.7 g"# of silver bromide produced #"23.4 g"# of aqueous sodium bromide and consumed

#"no. of moles of Na"_2"S"_2"O"_3 = color(green)(|bar(ul(color(white)(a/a)color(black)("0.455 moles")color(white)(a/a)|)))#

of sodium thiosulfate. Both answers are rounded to three sig figs, the number of sig figs you have for the mass of silver bromide.