When chemical reactions are added any products of the first reaction that are reactants in the second reaction must be balanced between the two reactions. In the first step of this synthesis 2 moles of KAl(OH)4 are generated, but in the second step only 1 mole of KAl(OH)4 is consumed. We rectify this imbalance by multiplying the entire second equation by 2 before adding the two equations together to get the overall balanced chemical equation for the synthesis.
Original balanced chemical equations:
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2 Al (s) + 2 KOH (aq) + 6 H2O (l) → 2 KAl(OH)4 (aq) + 3 H2 (g)
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KAl(OH)4 (aq) + 2 H2SO4 (aq) + 8 H2O (l) → KAl(SO4)2 +12 H2O (s)
Multiplying the second equation by 2 gives:
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2 Al (s) + 2 KOH (aq) + 6 H2O (l) → 2 KAl(OH)4 (aq) + 3 H2 (g)
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2 KAl(OH)4 (aq) + 4 H2SO4 (aq) + 16 H2O (l) → 2 KAl(SO4)2 +12 H2O (s)
Adding the two equations together, canceling moles of species that appear on opposite sides of the equation (2 moles of KAl(OH)4 on opposite sides of the arrow cancel) and combining species that appear on the same side of the equation (6 H2O + 16 H2O = 22 H2O) gives :
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2 Al (s) + 2 KOH (aq) + 4 H2SO4 (aq) + 22 H2O (l) → 3 H2 (g) + 2 KAl(SO4)2 + 12 H2O (s)