Questions: Balance the given chemical reaction. Al2(SO4)3(aq) + KOH(aq) -> Al(OH)3( s) + K2 SO4(aq) balanced equation:

Balance the given chemical reaction. Al2(SO4)3(aq) + KOH(aq) -> Al(OH)3( s) + K2 SO4(aq) balanced equation:
Transcript text: Balance the given chemical reaction. \[ \mathrm{Al}_{2}\left(\mathrm{SO}_{4}\right)_{3}(\mathrm{aq})+\mathrm{KOH}(\mathrm{aq}) \rightarrow \mathrm{Al}(\mathrm{OH})_{3}(\mathrm{~s})+\mathrm{K}_{2} \mathrm{SO}_{4}(\mathrm{aq}) \] balanced equation: $\square$
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Solution

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Solution Steps

Step 1: Identify the Compounds and Their Formulas

The given chemical reaction involves the following compounds:

  • Aluminum sulfate: \(\mathrm{Al}_{2}\left(\mathrm{SO}_{4}\right)_{3}\)
  • Potassium hydroxide: \(\mathrm{KOH}\)
  • Aluminum hydroxide: \(\mathrm{Al}(\mathrm{OH})_{3}\)
  • Potassium sulfate: \(\mathrm{K}_{2}\mathrm{SO}_{4}\)
Step 2: Write the Unbalanced Equation

The unbalanced chemical equation is: \[ \mathrm{Al}_{2}\left(\mathrm{SO}_{4}\right)_{3}(\mathrm{aq}) + \mathrm{KOH}(\mathrm{aq}) \rightarrow \mathrm{Al}(\mathrm{OH})_{3}(\mathrm{s}) + \mathrm{K}_{2}\mathrm{SO}_{4}(\mathrm{aq}) \]

Step 3: Balance the Aluminum Atoms

There are 2 aluminum atoms in \(\mathrm{Al}_{2}\left(\mathrm{SO}_{4}\right)_{3}\) and 1 aluminum atom in \(\mathrm{Al}(\mathrm{OH})_{3}\). To balance the aluminum atoms, place a coefficient of 2 in front of \(\mathrm{Al}(\mathrm{OH})_{3}\): \[ \mathrm{Al}_{2}\left(\mathrm{SO}_{4}\right)_{3} + \mathrm{KOH} \rightarrow 2\mathrm{Al}(\mathrm{OH})_{3} + \mathrm{K}_{2}\mathrm{SO}_{4} \]

Step 4: Balance the Sulfate Ions

There are 3 sulfate ions in \(\mathrm{Al}_{2}\left(\mathrm{SO}_{4}\right)_{3}\) and 1 sulfate ion in \(\mathrm{K}_{2}\mathrm{SO}_{4}\). To balance the sulfate ions, place a coefficient of 3 in front of \(\mathrm{K}_{2}\mathrm{SO}_{4}\): \[ \mathrm{Al}_{2}\left(\mathrm{SO}_{4}\right)_{3} + \mathrm{KOH} \rightarrow 2\mathrm{Al}(\mathrm{OH})_{3} + 3\mathrm{K}_{2}\mathrm{SO}_{4} \]

Step 5: Balance the Potassium Atoms

There are 6 potassium atoms needed on the right side (from 3 \(\mathrm{K}_{2}\mathrm{SO}_{4}\)), so place a coefficient of 6 in front of \(\mathrm{KOH}\): \[ \mathrm{Al}_{2}\left(\mathrm{SO}_{4}\right)_{3} + 6\mathrm{KOH} \rightarrow 2\mathrm{Al}(\mathrm{OH})_{3} + 3\mathrm{K}_{2}\mathrm{SO}_{4} \]

Step 6: Balance the Oxygen and Hydrogen Atoms

Check the balance of oxygen and hydrogen atoms:

  • Oxygen: 12 from \(\mathrm{Al}_{2}\left(\mathrm{SO}_{4}\right)_{3}\) and 6 from \(\mathrm{KOH}\) on the left; 6 from \(\mathrm{Al}(\mathrm{OH})_{3}\) and 12 from \(\mathrm{K}_{2}\mathrm{SO}_{4}\) on the right.
  • Hydrogen: 6 from \(\mathrm{KOH}\) on the left; 6 from \(\mathrm{Al}(\mathrm{OH})_{3}\) on the right.

The equation is now balanced.

Final Answer

The balanced chemical equation is: \[ \boxed{\mathrm{Al}_{2}\left(\mathrm{SO}_{4}\right)_{3}(\mathrm{aq}) + 6\mathrm{KOH}(\mathrm{aq}) \rightarrow 2\mathrm{Al}(\mathrm{OH})_{3}(\mathrm{s}) + 3\mathrm{K}_{2}\mathrm{SO}_{4}(\mathrm{aq})} \]

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