Ensure the number of atoms and charge is the same on both the left and right side of the equation. Since you start with Br2, I'd expect 2 Br atoms or ions on the right hand side. Br?
+ S2O3^2- + H2O -> 2Br^- + SO4^2- + H+ (not balanced) Now look at the sulfur atoms and you'll see these need work as well. Br? + S2O3^2- + H2O -> 2Br^- + 2SO4^2- + H+ (not balanced) Next look at the oxygen atoms Br?
+ S2O3^2- + 5H2O -> 2Br^- + 2SO4^2- + H+ (not balanced) Next look at the hydrogen atoms Br? + S2O3^2- + 5H2O -> 2Br^- + 2SO4^2- + 10H+ (not balanced) Lastly balance the amount of bromine to ensure charges match. Bromine is the obvious candidate to adjust, since it doesn't effect the ionic compound SO4^2- in the product.
4Br? + S2O3^2- + 5H2O -> 8Br^- + 2SO4^2- + 10H+ (balanced).
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