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<title>Balancing chemical equations</title>
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<body>
<div class="exercise">
<p class="question">
Balance the following chemical equation:
</p>
<div class="problems">
<div id="h2-o2---h2o">
<div class="vars">
<var id="SOLUTION">[2, 1, 2]</var>
</div>
<div class="solution" data-type="multiple">
<code>\qquad</code>
<span class="sol coefficient" data-forms="integer, coefficient"><var>SOLUTION[0]</var></span><code>\text{H}_2 +</code>
<span class="sol coefficient" data-forms="integer, coefficient"><var>SOLUTION[1]</var></span><code>\text{O}_2 \rightarrow</code>
<span class="sol coefficient" data-forms="integer, coefficient"><var>SOLUTION[2]</var></span><code>\text{H}_2\text{O}</code>
</div>
<div class="hints">
<div>
<p>
There are <code>2 \text{ O}</code> on the left and only
<code>1</code> on the right, so multiply
<code>\text{H}_2\text{O}</code> by <code>\blue{2}</code>.
</p>
<p><code>\qquad
\text{H}_2 + \text{O}_2 \rightarrow \blue{2}\text{H}_2\text{O}
</code></p>
</div>
<div>
<p>
That gives us <code>4 \text{ H}</code> on the right and
only <code>2</code> on the left, so multiply
<code>\text{H}_2</code> by <code>\red{2}</code>.
</p>
<p><code>\qquad
\red{2}\text{H}_2 + \text{O}_2 \rightarrow 2\text{H}_2\text{O}
</code></p>
</div>
<div>
<p>The balanced equation is:</p>
<p><code>\qquad
2\text{H}_2 + \text{O}_2 \rightarrow 2\text{H}_2\text{O}
</code></p>
</div>
</div>
</div>
<div id="ch4-cl2---ccl4-hcl">
<div class="vars">
<var id="SOLUTION">[1, 4, 1, 4]</var>
</div>
<div class="solution" data-type="multiple">
<code>\qquad</code>
<span class="sol coefficient" data-forms="integer, coefficient"><var>SOLUTION[0]</var></span><code>\text{CH}_4 +</code>
<span class="sol coefficient" data-forms="integer, coefficient"><var>SOLUTION[1]</var></span><code>\text{Cl}_2 \rightarrow</code>
<span class="sol coefficient" data-forms="integer, coefficient"><var>SOLUTION[2]</var></span><code>\text{CCl}_4 +</code>
<span class="sol coefficient" data-forms="integer, coefficient"><var>SOLUTION[3]</var></span><code>\text{HCl}</code>
</div>
<div class="hints">
<p>
<code>\text{C}</code> is already balanced.
</p>
<div>
<p>
There are <code>4 \text{ H}</code> on the left and only
<code>1</code> on the right, so multiply
<code>\text{HCl}</code> by <code>\blue{4}</code>.
</p>
<p><code>\qquad
\text{CH}_4 + \text{Cl}_2 \rightarrow \text{CCl}_4 + \blue{4}\text{HCl}
</code></p>
</div>
<div>
<p>
That gives us <code>8 \text{ Cl}</code> on the right and
only <code>2</code> on the left, so multiply
<code>\text{Cl}_2</code> by <code>\red{4}</code>.
</p>
<p><code>\qquad
\text{CH}_4 + \red{4}\text{Cl}_2 \rightarrow \text{CCl}_4 + 4\text{HCl}
</code></p>
</div>
<div>
<p>The balanced equation is:</p>
<p><code>\qquad
\text{CH}_4 + 4\text{Cl}_2 \rightarrow \text{CCl}_4 + 4\text{HCl}
</code></p>
</div>
</div>
</div>
<div id="al-o2---al2o3">
<div class="vars">
<var id="SOLUTION">[4, 3, 2]</var>
</div>
<div class="solution" data-type="multiple">
<code>\qquad</code>
<span class="sol coefficient" data-forms="integer, coefficient"><var>SOLUTION[0]</var></span><code>\text{Al} +</code>
<span class="sol coefficient" data-forms="integer, coefficient"><var>SOLUTION[1]</var></span><code>\text{O}_2 \rightarrow</code>
<span class="sol coefficient" data-forms="integer, coefficient"><var>SOLUTION[2]</var></span><code>\text{Al}_2\text{O}_3</code>
</div>
<div class="hints">
<div>
<p>
There are <code>2 \text{ O}</code> on the left and
<code>3</code> on the right. The lowest common denominator
is <code>6</code>, so multiply
<code>\text{O}_2</code> by <code>\blue{3}</code> and
<code>\text{Al}_2\text{O}_3</code> by <code>\red{2}</code>.
</p>
<p><code>\qquad
\text{Al} + \blue{3}\text{O}_2 \rightarrow \red{2}\text{Al}_2\text{O}_3
</code></p>
</div>
<div>
<p>
That gives us <code>4 \text{ Al}</code> on the right and
only <code>1</code> on the left, so multiply
<code>\text{Al}</code> by <code>\pink{4}</code>.
</p>
<p><code>\qquad
\pink{4}\text{Al} + 3\text{O}_2 \rightarrow 2\text{Al}_2\text{O}_3
</code></p>
</div>
<div>
<p>The balanced equation is:</p>
<p><code>\qquad
4\text{Al} + 3\text{O}_2 \rightarrow 2\text{Al}_2\text{O}_3
</code></p>
</div>
</div>
</div>
<div id="ch4-o2---co2-h2o">
<div class="vars">
<var id="SOLUTION">[1, 2, 1, 2]</var>
</div>
<div class="solution" data-type="multiple">
<code>\qquad</code>
<span class="sol coefficient" data-forms="integer, coefficient"><var>SOLUTION[0]</var></span><code>\text{CH}_4 +</code>
<span class="sol coefficient" data-forms="integer, coefficient"><var>SOLUTION[1]</var></span><code>\text{O}_2 \rightarrow</code>
<span class="sol coefficient" data-forms="integer, coefficient"><var>SOLUTION[2]</var></span><code>\text{CO}_2 +</code>
<span class="sol coefficient" data-forms="integer, coefficient"><var>SOLUTION[3]</var></span><code>\text{H}_2\text{O}</code>
</div>
<div class="hints">
<p>
<code>\text{C}</code> is already balanced.
</p>
<div>
<p>
There are <code>4 \text{ H}</code> on the left and
<code>2</code> on the right, so multiply
<code>\text{H}_2\text{O}</code> by <code>\blue{2}</code>.
</p>
<p><code>\qquad
\text{CH}_4 + \text{O}_2 \rightarrow \text{CO}_2 + \blue{2}\text{H}_2\text{O}
</code></p>
</div>
<div>
<p>
That gives us <code>4 \text{ O}</code> on the right and
only <code>2</code> on the left, so multiply
<code>\text{O}_2</code> by <code>\red{2}</code>.
(Since oxygen is by itself on the left, it should be done
at the end because you can give it a coefficient without
affecting another element.)
</p>
<p><code>\qquad
\text{CH}_4 + \red{2}\text{O}_2 \rightarrow \text{CO}_2 + 2\text{H}_2\text{O}
</code></p>
</div>
<div>
<p>The balanced equation is:</p>
<p><code>\qquad
\text{CH}_4 + 2\text{O}_2 \rightarrow \text{CO}_2 + 2\text{H}_2\text{O}
</code></p>
</div>
</div>
</div>
<div id="nabr-cl2---nacl-br2">
<div class="vars">
<var id="SOLUTION">[2, 1, 2, 1]</var>
</div>
<div class="solution" data-type="multiple">
<code>\qquad</code>
<span class="sol coefficient" data-forms="integer, coefficient"><var>SOLUTION[0]</var></span><code>\text{NaBr} +</code>
<span class="sol coefficient" data-forms="integer, coefficient"><var>SOLUTION[1]</var></span><code>\text{Cl}_2 \rightarrow</code>
<span class="sol coefficient" data-forms="integer, coefficient"><var>SOLUTION[2]</var></span><code>\text{NaCl} +</code>
<span class="sol coefficient" data-forms="integer, coefficient"><var>SOLUTION[3]</var></span><code>\text{Br}_2</code>
</div>
<div class="hints">
<div>
<p>
There is <code>1 \text{ Br}</code> on the left and
<code>2</code> on the right, so multiply
<code>\text{NaBr}</code> by <code>\blue{2}</code>.
</p>
<p><code>\qquad
\blue{2}\text{NaBr} + \text{Cl}_2 \rightarrow \text{NaCl} + \text{Br}_2
</code></p>
</div>
<div>
<p>
There are <code>2 \text{ Cl}</code> on the left and
<code>1</code> on the right, so multiply
<code>\text{NaCl}</code> by <code>\red{2}</code>.
</p>
<p><code>\qquad
2\text{NaBr} + \text{Cl}_2 \rightarrow \red{2}\text{NaCl} + \text{Br}_2
</code></p>
</div>
<p>
Now <code>\text{Na}</code> is balanced again.
</p>
<div>
<p>The balanced equation is:</p>
<p><code>\qquad
2\text{NaBr} + \text{Cl}_2 \rightarrow 2\text{NaCl} + \text{Br}_2
</code></p>
</div>
</div>
</div>
<div id="mg-hcl---mgcl2-h2">
<div class="vars">
<var id="SOLUTION">[1, 2, 1, 1]</var>
</div>
<div class="solution" data-type="multiple">
<code>\qquad</code>
<span class="sol coefficient" data-forms="integer, coefficient"><var>SOLUTION[0]</var></span><code>\text{Mg} +</code>
<span class="sol coefficient" data-forms="integer, coefficient"><var>SOLUTION[1]</var></span><code>\text{HCl} \rightarrow</code>
<span class="sol coefficient" data-forms="integer, coefficient"><var>SOLUTION[2]</var></span><code>\text{MgCl}_2 +</code>
<span class="sol coefficient" data-forms="integer, coefficient"><var>SOLUTION[3]</var></span><code>\text{H}_2</code>
</div>
<div class="hints">
<div>
<p>
There are <code>2 \text{ Cl}</code> on the right and
only <code>1</code> on the left, so multiply
<code>\text{HCl}</code> by <code>\blue{2}</code>.
</p>
<p><code>\qquad
\text{Mg} + \blue{2}\text{HCl} \rightarrow \text{MgCl}_2 + \text{H}_2
</code></p>
</div>
<div>
<p>Now all atoms are balanced; the balanced equation is:</p>
<p><code>\qquad
\text{Mg} + 2\text{HCl} \rightarrow \text{MgCl}_2 + \text{H}_2
</code></p>
</div>
</div>
</div>
<div id="nh4no3---n2-o2-h2o">
<div class="vars">
<var id="SOLUTION">[2, 2, 1, 4]</var>
</div>
<div class="solution" data-type="multiple">
<code>\qquad</code>
<span class="sol coefficient" data-forms="integer, coefficient"><var>SOLUTION[0]</var></span><code>\text{NH}_4\text{NO}_3 \rightarrow</code>
<span class="sol coefficient" data-forms="integer, coefficient"><var>SOLUTION[1]</var></span><code>\text{N}_2 +</code>
<span class="sol coefficient" data-forms="integer, coefficient"><var>SOLUTION[2]</var></span><code>\text{O}_2 +</code>
<span class="sol coefficient" data-forms="integer, coefficient"><var>SOLUTION[3]</var></span><code>\text{H}_2\text{O}</code>
</div>
<div class="hints">
<p>
Start with the compound that has the most elements
<code>(\text{NH}_4\text{NO}_3)</code>.
</p>
<p>
There are <code>2 \text{N}</code> on the left and
<code>2 \text{N}</code> on the right, so <code>\text{N}</code>
is already balanced.
</p>
<div>
<p>
There are <code>4 \text{ H}</code> on the left and
<code>2</code> on the right, so multiply
<code>\text{H}_2\text{O}</code> by <code>\blue{2}</code>.
</p>
<p><code>\qquad
\text{NH}_4\text{NO}_3 \rightarrow \text{N}_2 + \text{O}_2 + \blue{2}\text{H}_2\text{O}
</code></p>
</div>
<div>
<p>
That gives us <code>3 \text{ O}</code> on the left and
<code>4</code> on the right. If we try giving
<code>\text{O}_2</code> a coefficient of <code>\red{\frac{1}{2}}</code>,
it gives us <code>3 \text{ O}</code> on both sides.
</p>
<p><code>\qquad
\text{NH}_4\text{NO}_3 \rightarrow \text{N}_2 + \red{\frac{1}{2}}\text{O}_2 + 2\text{H}_2\text{O}
</code></p>
</div>
<div>
<p>
Since fractions are not usually used as coefficients, multiply everything by <code>2</code> to get rid of the fraction.
</p>
<p><code>\qquad
2\text{NH}_4\text{NO}_3 \rightarrow 2\text{N}_2 + 1\text{O}_2 + 4\text{H}_2\text{O}
</code></p>
</div>
<div>
<p>The balanced equation is:</p>
<p><code>\qquad
2\text{NH}_4\text{NO}_3 \rightarrow 2\text{N}_2 + \text{O}_2 + 4\text{H}_2\text{O}
</code></p>
</div>
</div>
</div>
<div id="c2h6o-o2---co2-h2o">
<div class="vars">
<var id="SOLUTION">[1, 3, 2, 3]</var>
</div>
<div class="solution" data-type="multiple">
<code>\qquad</code>
<span class="sol coefficient" data-forms="integer, coefficient"><var>SOLUTION[0]</var></span><code>\text{C}_2\text{H}_6\text{O} +</code>
<span class="sol coefficient" data-forms="integer, coefficient"><var>SOLUTION[1]</var></span><code>\text{O}_2 \rightarrow</code>
<span class="sol coefficient" data-forms="integer, coefficient"><var>SOLUTION[2]</var></span><code>\text{CO}_2 +</code>
<span class="sol coefficient" data-forms="integer, coefficient"><var>SOLUTION[3]</var></span><code>\text{H}_2\text{O}</code>
</div>
<div class="hints">
<p>
For a combustion reaction, it is usually easiest to start
with <code>\text{C}</code>.
</p>
<div>
<p>
There are <code>2 \text{ C}</code> on the left and
<code>1</code> on the right, so multiply
<code>\text{CO}_2</code> by <code>\blue{2}</code>.
</p>
<p><code>\qquad
\text{C}_2\text{H}_6\text{O} + \text{O}_2 \rightarrow \blue{2}\text{CO}_2 + \text{H}_2\text{O}
</code></p>
</div>
<div>
<p>
There are <code>6 \text{ H}</code> on the left and
<code>2</code> on the right, so multiply
<code>\text{H}_2\text{O}</code> by <code>\red{3}</code>.
</p>
<p><code>\qquad
\text{C}_2\text{H}_6\text{O} + \text{O}_2 \rightarrow 2\text{CO}_2 + \red{3}\text{H}_2\text{O}
</code></p>
</div>
<div>
<p>
That gives us <code>7 \text{ O}</code> on the right and
<code>3</code> on the left, so multiply
<code>\text{O}_2</code> by <code>\pink{3}</code>.
</p>
<p><code>\qquad
\text{C}_2\text{H}_6\text{O} + \pink{3}\text{O}_2 \rightarrow 2\text{CO}_2 + 3\text{H}_2\text{O}
</code></p>
</div>
<div>
<p>The balanced equation is:</p>
<p><code>\qquad
\text{C}_2\text{H}_6\text{O} + 3\text{O}_2 \rightarrow 2\text{CO}_2 + 3\text{H}_2\text{O}
</code></p>
</div>
</div>
</div>
<div id="mg-o2---mgo">
<div class="vars">
<var id="SOLUTION">[2, 1, 2]</var>
</div>
<div class="solution" data-type="multiple">
<code>\qquad</code>
<span class="sol coefficient" data-forms="integer, coefficient"><var>SOLUTION[0]</var></span><code>\text{Mg} +</code>
<span class="sol coefficient" data-forms="integer, coefficient"><var>SOLUTION[1]</var></span><code>\text{O}_2 \rightarrow</code>
<span class="sol coefficient" data-forms="integer, coefficient"><var>SOLUTION[2]</var></span><code>\text{MgO}</code>
</div>
<div class="hints">
<div>
<p>
There are <code>2 \text{ O}</code> on the left and only
<code>1</code> on the right, so multiply
<code>\text{MgO}</code> by <code>\blue{2}</code>.
</p>
<p><code>\qquad
\text{Mg} + \text{O}_2 \rightarrow \blue{2}\text{MgO}
</code></p>
</div>
<div>
<p>
That gives us <code>2 \text{ Mg}</code> on the right and
only <code>1</code> on the left, so multiply
<code>\text{Mg}</code> by <code>\red{2}</code>.
</p>
<p><code>\qquad
\red{2}\text{Mg} + \text{O}_2 \rightarrow 2\text{MgO}
</code></p>
</div>
<div>
<p>The balanced equation is:</p>
<p><code>\qquad
2\text{Mg} + \text{O}_2 \rightarrow 2\text{MgO}
</code></p>
</div>
</div>
</div>
<div id="al-hcl---alcl3-h2">
<div class="vars">
<var id="SOLUTION">[2, 6, 2, 3]</var>
</div>
<div class="solution" data-type="multiple">
<code>\qquad</code>
<span class="sol coefficient" data-forms="integer, coefficient"><var>SOLUTION[0]</var></span><code>\text{Al} +</code>
<span class="sol coefficient" data-forms="integer, coefficient"><var>SOLUTION[1]</var></span><code>\text{HCl} \rightarrow</code>
<span class="sol coefficient" data-forms="integer, coefficient"><var>SOLUTION[2]</var></span><code>\text{AlCl}_3 +</code>
<span class="sol coefficient" data-forms="integer, coefficient"><var>SOLUTION[3]</var></span><code>\text{H}_2</code>
</div>
<div class="hints">
<div>
<p>
There is <code>1 \text{ H}</code> and <code>1 \text{ Cl}</code> on the left and
<code>3 \text{ Cl}</code> and <code>2 \text{ H}</code> on the right.
The lowest common denominator for the right is <code>6</code>, so multiply
<code>\text{AlCl}_3</code> by <code>\blue{2}</code> and
<code>\text{H}_2</code> by <code>\red{3}</code>.
</p>
<p><code>\qquad
\text{Al} + \text{HCl} \rightarrow \blue{2}\text{AlCl}_3 + \red{3}\text{H}_2
</code></p>
</div>
<div>
<p>
That gives us <code>6 \text{ H}</code> and <code>6 \text{ Cl}</code>
on the right, so multiply
<code>\text{HCl}</code> by <code>\pink{6}</code>.
</p>
<p><code>\qquad
\text{Al} + \pink{6}\text{HCl} \rightarrow 2\text{AlCl}_3 + 3\text{H}_2
</code></p>
</div>
<div>
<p>
That gives us <code>2 \text{ Al}</code> on the right and
only <code>1</code> on the left, so multiply
<code>\text{Al}</code> by <code>\green{2}</code>.
</p>
<p><code>\qquad
\green{2}\text{Al} + 6\text{HCl} \rightarrow 2\text{AlCl}_3 + 3\text{H}_2
</code></p>
</div>
<div>
<p>The balanced equation is:</p>
<p><code>\qquad
2\text{Al} + 6\text{HCl} \rightarrow 2\text{AlCl}_3 + 3\text{H}_2
</code></p>
</div>
</div>
</div>
<div id="cacl2-na2po4---ca3po42-nacl">
<div class="vars">
<var id="SOLUTION">[3, 2, 1, 6]</var>
</div>
<div class="solution" data-type="multiple">
<code>\qquad</code>
<span class="sol coefficient" data-forms="integer, coefficient"><var>SOLUTION[0]</var></span><code>\text{CaCl}_2 +</code>
<span class="sol coefficient" data-forms="integer, coefficient"><var>SOLUTION[1]</var></span><code>\text{Na}_3\text{PO}_4 \rightarrow</code>
<span class="sol coefficient" data-forms="integer, coefficient"><var>SOLUTION[2]</var></span><code>\text{Ca}_3\text{(PO}_4\text{)}_2 +</code>
<span class="sol coefficient" data-forms="integer, coefficient"><var>SOLUTION[3]</var></span><code>\text{NaCl}</code>
</div>
<div class="hints">
<div>
<p>
We can treat the phosphate polyatomic ion <code>\text{(PO}_4\text{)}</code> as an atom, symbolized by <code>\green{X}</code>:
</p>
<p><code>\qquad
\text{CaCl}_2 + \text{Na}_3\green{\text{PO}_4} \rightarrow \text{Ca}_3(\green{\text{PO}_4\text{}})_2 + \text{NaCl}
</code></p>
<p><code>\qquad
\text{CaCl}_2 + \text{Na}_3\green{X} \rightarrow \text{Ca}_3\green{X}_2 + \text{NaCl}
</code></p>
</div>
<div>
<p>
There is <code>1 \space X</code> on the left and <code>2 \space X</code>
on the right, so multiply
<code>\text{Na}_3X</code> by <code>\blue{2}</code>.
</p>
<p><code>\qquad
\text{CaCl}_2 + \blue{2}\text{Na}_3X \rightarrow \text{Ca}_3X_2 + \text{NaCl}
</code></p>
</div>
<div>
<p>
There are <code>6 \text{ Na}</code> on the left and only
<code>1</code> on the right, so multiply
<code>\text{NaCl}</code> by <code>\red{6}</code>.
</p>
<p><code>\qquad
\text{CaCl}_2 + 2\text{Na}_3X \rightarrow \text{Ca}_3X_2 + \red{6}\text{NaCl}
</code></p>
</div>
<div>
<p>
That gives us <code>6 \text{ Cl}</code> on the right and
only <code>2</code> on the left, so multiply
<code>\text{CaCl}_2</code> by <code>\pink{3}</code>.
</p>
<p><code>\qquad
\pink{3}\text{CaCl}_2 + 2\text{Na}_3X \rightarrow \text{Ca}_3X_2 + 6\text{NaCl}
</code></p>
</div>
<p>
Now <code>\text{Ca}</code> is balanced too.
</p>
<div>
<p>Replacing <code>\text{PO}_4</code> for <code>X</code>, the balanced equation is:</p>
<p><code>\qquad
3\text{CaCl}_2 + 2\text{Na}_3\text{PO}_4 \rightarrow \text{Ca}_3\text{(PO}_4\text{)}_2 + 6\text{NaCl}
</code></p>
</div>
</div>
</div>
<div id="n2h4-o2---no2-h2o">
<div class="vars">
<var id="SOLUTION">[1, 3, 2, 2]</var>
</div>
<div class="solution" data-type="multiple">
<code>\qquad</code>
<span class="sol coefficient" data-forms="integer, coefficient"><var>SOLUTION[0]</var></span><code>\text{N}_2\text{H}_4 +</code>
<span class="sol coefficient" data-forms="integer, coefficient"><var>SOLUTION[1]</var></span><code>\text{O}_2 \rightarrow</code>
<span class="sol coefficient" data-forms="integer, coefficient"><var>SOLUTION[2]</var></span><code>\text{NO}_2 +</code>
<span class="sol coefficient" data-forms="integer, coefficient"><var>SOLUTION[3]</var></span><code>\text{H}_2\text{O}</code>
</div>
<div class="hints">
<div>
<p>
There are <code>2 \text{ N}</code> on the left and
only <code>1</code> on the right, so multiply
<code>\text{NO}_2</code> by <code>\blue{2}</code>.
</p>
<p><code>\qquad
\text{N}_2\text{H}_4 + \text{O}_2 \rightarrow \blue{2}\text{NO}_2 + \text{H}_2\text{O}
</code></p>
</div>
<div>
<p>
There are <code>4 \text{ H}</code> on the left and
only <code>2</code> on the right, so multiply
<code>\text{H}_2\text{O}</code> by <code>\red{2}</code>.
</p>
<p><code>\qquad
\text{N}_2\text{H}_4 + \text{O}_2 \rightarrow 2\text{NO}_2 + \red{2}\text{H}_2\text{O}
</code></p>
</div>
<div>
<p>
That gives us <code>6 \text{ O}</code> on the right and
only <code>2</code> on the left, so multiply
<code>\text{O}_2</code> by <code>\pink{3}</code>.
(Since oxygen is by itself on the left, it should be done
at the end because you can give it a coefficient without
affecting another element.)
</p>
<p><code>\qquad
\text{N}_2\text{H}_4 + \pink{3}\text{O}_2 \rightarrow 2\text{NO}_2 + 2\text{H}_2\text{O}
</code></p>
</div>
<div>
<p>The balanced equation is:</p>
<p><code>\qquad
\text{N}_2\text{H}_4 + 3\text{O}_2 \rightarrow 2\text{NO}_2 + 2\text{H}_2\text{O}
</code></p>
</div>
</div>
</div>
<div id="fe-h2o---fe3o4-h2">
<div class="vars">
<var id="SOLUTION">[3, 4, 1, 4]</var>
</div>
<div class="solution" data-type="multiple">
<code>\qquad</code>
<span class="sol coefficient" data-forms="integer, coefficient"><var>SOLUTION[0]</var></span><code>\text{Fe} +</code>
<span class="sol coefficient" data-forms="integer, coefficient"><var>SOLUTION[1]</var></span><code>\text{H}_2\text{O} \rightarrow</code>
<span class="sol coefficient" data-forms="integer, coefficient"><var>SOLUTION[2]</var></span><code>\text{Fe}_3\text{O}_4 +</code>
<span class="sol coefficient" data-forms="integer, coefficient"><var>SOLUTION[3]</var></span><code>\text{H}_2</code>
</div>
<div class="hints">
<div>
<p>
There are <code>3 \text{ Fe}</code> on the right and
only <code>1</code> on the left, so multiply
<code>\text{Fe}</code> by <code>\blue{3}</code>.
</p>
<p><code>\qquad
\blue{3}\text{Fe} + \text{H}_2\text{O} \rightarrow \text{Fe}_3\text{O}_4 + \text{H}_2
</code></p>
</div>
<div>
<p>
There are <code>4 \text{ O}</code> on the right and
only <code>1</code> on the left, so multiply
<code>\text{H}_2\text{O}</code> by <code>\red{4}</code>.
</p>
<p><code>\qquad
3\text{Fe} + \red{4}\text{H}_2\text{O} \rightarrow \text{Fe}_3\text{O}_4 + \text{H}_2
</code></p>
</div>
<div>
<p>
That gives us <code>8 \text{ H}</code> on the left and
only <code>2</code> on the right, so multiply
<code>\text{H}_2</code> by <code>\pink{4}</code>.
(Since hydrogen is by itself on the right, it should be done
at the end because you can give it a coefficient without
affecting another element.)
</p>
<p><code>\qquad
3\text{Fe} + 4\text{H}_2\text{O} \rightarrow \text{Fe}_3\text{O}_4 + \pink{4}\text{H}_2
</code></p>
</div>
<div>
<p>The balanced equation is:</p>
<p><code>\qquad
3\text{Fe} + 4\text{H}_2\text{O} \rightarrow \text{Fe}_3\text{O}_4 + 4\text{H}_2
</code></p>
</div>
</div>
</div>
<div id="nh4no3---n2o-h2o">
<div class="vars">
<var id="SOLUTION">[1, 1, 2]</var>
</div>
<div class="solution" data-type="multiple">
<code>\qquad</code>
<span class="sol coefficient" data-forms="integer, coefficient"><var>SOLUTION[0]</var></span><code>\text{NH}_4\text{NO}_3 \rightarrow</code>
<span class="sol coefficient" data-forms="integer, coefficient"><var>SOLUTION[1]</var></span><code>\text{N}_2\text{O} +</code>
<span class="sol coefficient" data-forms="integer, coefficient"><var>SOLUTION[2]</var></span><code>\text{H}_2\text{O}</code>
</div>
<div class="hints">
<p>
There are <code>2 \text{ N}</code> on the right and
<code>2</code> on the left, so <code>\text{N}</code>
is already balanced.
</p>
<div>
<p>
There are <code>4 \text{ H}</code> on the left and
only <code>2</code> on the right, so multiply
<code>\text{H}_2\text{O}</code> by <code>\blue{2}</code>.
</p>
<p><code>\qquad
\text{NH}_4\text{NO}_3 \rightarrow \text{N}_2\text{O} + \blue{2}\text{H}_2\text{O}
</code></p>
</div>
<p>
There are <code>3 \text{ O}</code> on the right and
<code>3</code> on the left, so <code>\text{O}</code>
is already balanced.
</p>
<div>
<p>The balanced equation is:</p>
<p><code>\qquad
\text{NH}_4\text{NO}_3 \rightarrow \text{N}_2\text{O} + 2\text{H}_2\text{O}
</code></p>
</div>
</div>
</div>
<div id="hgo---hg-o2">
<div class="vars">
<var id="SOLUTION">[2, 2, 1]</var>
</div>
<div class="solution" data-type="multiple">
<code>\qquad</code>
<span class="sol coefficient" data-forms="integer, coefficient"><var>SOLUTION[0]</var></span><code>\text{HgO} \rightarrow</code>
<span class="sol coefficient" data-forms="integer, coefficient"><var>SOLUTION[1]</var></span><code>\text{Hg} +</code>
<span class="sol coefficient" data-forms="integer, coefficient"><var>SOLUTION[2]</var></span><code>\text{O}_2</code>
</div>
<div class="hints">
<div>
<p>
There are <code>2 \text{ O}</code> on the right and
only <code>1</code> on the left, so multiply
<code>\text{HgO}</code> by <code>\blue{2}</code>.
</p>
<p><code>\qquad
\blue{2}\text{HgO} \rightarrow \text{Hg} + \text{O}_2
</code></p>
</div>
<div>
<p>
Now there are <code>2 \text{ Hg}</code> on the left and
only <code>1</code> on the right, so multiply
<code>\text{Hg}</code> by <code>\red{2}</code>.
</p>
<p><code>\qquad
2\text{HgO} \rightarrow \red{2}\text{Hg} + \text{O}_2
</code></p>
</div>
<div>
<p>The balanced equation is:</p>
<p><code>\qquad
2\text{HgO} \rightarrow 2\text{Hg} + \text{O}_2
</code></p>
</div>
</div>
</div>
<div id="sio2-hf---sif4-h2o">
<div class="vars">
<var id="SOLUTION">[1, 4, 1, 2]</var>
</div>
<div class="solution" data-type="multiple">
<code>\qquad</code>
<span class="sol coefficient" data-forms="integer, coefficient"><var>SOLUTION[0]</var></span><code>\text{SiO}_2 +</code>
<span class="sol coefficient" data-forms="integer, coefficient"><var>SOLUTION[1]</var></span><code>\text{HF} \rightarrow</code>
<span class="sol coefficient" data-forms="integer, coefficient"><var>SOLUTION[2]</var></span><code>\text{SiF}_4 +</code>
<span class="sol coefficient" data-forms="integer, coefficient"><var>SOLUTION[3]</var></span><code>\text{H}_2\text{O}</code>
</div>
<div class="hints">
<p>
There is <code>1 \text{ Si}</code> on the right and
<code>1</code> on the left, so <code>\text{Si}</code>
is already balanced.
</p>
<div>
<p>
There are <code>2 \text{ O}</code> on the left and
only <code>1</code> on the right, so multiply
<code>\text{H}_2\text{O}</code> by <code>\blue{2}</code>.
</p>
<p><code>\qquad
\text{SiO}_2 + \text{HF} \rightarrow \text{SiF}_4 + \blue{2}\text{H}_2\text{O}
</code></p>
</div>
<div>
<p>
Now there are <code>4 \text{ H}</code> on the right and
only <code>1</code> on the left, so multiply
<code>\text{HF}</code> by <code>\red{4}</code>.
</p>
<p><code>\qquad
\text{SiO}_2 + \red{4}\text{HF} \rightarrow \text{SiF}_4 + 2\text{H}_2\text{O}
</code></p>
</div>
<p>
Now <code>\text{F}</code> is balanced too.
</p>
<div>
<p>The balanced equation is:</p>
<p><code>\qquad
\text{SiO}_2 + 4\text{HF} \rightarrow \text{SiF}_4 + 2\text{H}_2\text{O}
</code></p>
</div>
</div>
</div>
<div id="mgoh2-hcl---mgcl2-h2o">
<div class="vars">
<var id="SOLUTION">[1, 2, 1, 2]</var>
</div>
<div class="solution" data-type="multiple">
<code>\qquad</code>
<span class="sol coefficient" data-forms="integer, coefficient"><var>SOLUTION[0]</var></span><code>\text{Mg(OH)}_2 +</code>
<span class="sol coefficient" data-forms="integer, coefficient"><var>SOLUTION[1]</var></span><code>\text{HCl} \rightarrow</code>
<span class="sol coefficient" data-forms="integer, coefficient"><var>SOLUTION[2]</var></span><code>\text{MgCl}_2 +</code>
<span class="sol coefficient" data-forms="integer, coefficient"><var>SOLUTION[3]</var></span><code>\text{H}_2\text{O}</code>
</div>
<div class="hints">
<p>
There is <code>1 \text{ Mg}</code> on the right and
<code>1</code> on the left, so <code>\text{Mg}</code>
is already balanced.
</p>
<div>
<p>
There are <code>2 \text{ Cl}</code> on the right and
only <code>1</code> on the left, so multiply
<code>\text{HCl}</code> by <code>\blue{2}</code>.
</p>
<p><code>\qquad
\text{Mg(OH)}_2 + \blue{2}\text{HCl} \rightarrow \text{MgCl}_2 + \text{H}_2\text{O}
</code></p>
</div>
<div>
<p>
Now there are <code>4 \text{ H}</code> on the left and
only <code>2</code> on the right, so multiply
<code>\text{H}_2\text{O}</code> by <code>\red{2}</code>.
</p>
<p><code>\qquad
\text{Mg(OH)}_2 + 2\text{HCl} \rightarrow \text{MgCl}_2 + \red{2}\text{H}_2\text{O}
</code></p>
</div>
<p>
Now <code>\text{O}</code> is balanced too.
</p>
<div>
<p>The balanced equation is:</p>
<p><code>\qquad
\text{Mg(OH)}_2 + 2\text{HCl} \rightarrow \text{MgCl}_2 + 2\text{H}_2\text{O}
</code></p>
</div>
</div>
</div>
<div id="h2so4-pboh4---pbso42-h2o">
<div class="vars">
<var id="SOLUTION">[2, 1, 1, 4]</var>
</div>
<div class="solution" data-type="multiple">
<code>\qquad</code>
<span class="sol coefficient" data-forms="integer, coefficient"><var>SOLUTION[0]</var></span><code>\text{H}_2\text{SO}_4 +</code>
<span class="sol coefficient" data-forms="integer, coefficient"><var>SOLUTION[1]</var></span><code>\text{Pb(OH)}_4 \rightarrow</code>
<span class="sol coefficient" data-forms="integer, coefficient"><var>SOLUTION[2]</var></span><code>\text{Pb(SO}_4\text{)}_2 +</code>
<span class="sol coefficient" data-forms="integer, coefficient"><var>SOLUTION[3]</var></span><code>\text{H}_2\text{O}</code>
</div>
<div class="hints">
<div>
<p>
We can treat the sulfate polyatomic ion <code>\text{(SO}_4\text{)}</code> as an atom, symbolized by <code>\green{X}</code>:
</p>
<p><code>\qquad
\text{H}_2\green{\text{SO}_4} + \text{Pb(OH)}_4 \rightarrow \text{Pb(}\green{\text{SO}_4}\text{)}_2 + \text{H}_2\text{O}
</code></p>
<p><code>\qquad
\text{H}_2\green{X} + \text{Pb(OH)}_4 \rightarrow \text{Pb}\green{X}_2 + \text{H}_2\text{O}
</code></p>
</div>
<div>
<p>
There is <code>1 \space X</code> on the left and <code>2 \space X</code>
on the right, so multiply
<code>\text{H}_2X</code> by <code>\blue{2}</code>.
</p>
<p><code>\qquad
\blue{2}\text{H}_2X + \text{Pb(OH)}_4 \rightarrow \text{Pb}X_2 + \text{H}_2\text{O}
</code></p>
</div>
<div>
<p>
That gives us <code>8 \text{ H}</code> on the left and
only <code>2</code> on the right, so multiply
<code>\text{H}_2\text{O}</code> by <code>\red{4}</code>.
</p>
<p><code>\qquad
2\text{H}_2X + \text{Pb(OH)}_4 \rightarrow \text{Pb}X_2 + \red{4}\text{H}_2\text{O}
</code></p>
</div>
<div>
<p>Everything is now balanced. Replacing <code>\text{SO}_4</code> for <code>X</code>, the balanced equation is:</p>
<p><code>\qquad
2\text{H}_2\text{SO}_4 + \text{Pb(OH)}_4 \rightarrow \text{Pb(}\text{SO}_4\text{)}_2 + 4\text{H}_2\text{O}
</code></p>
</div>
</div>
</div>
<div id="as4s6-o2---as4o6-so2">
<div class="vars">
<var id="SOLUTION">[1, 9, 1, 6]</var>
</div>
<div class="solution" data-type="multiple">
<code>\qquad</code>
<span class="sol coefficient" data-forms="integer, coefficient"><var>SOLUTION[0]</var></span><code>\text{As}_4\text{S}_6 +</code>
<span class="sol coefficient" data-forms="integer, coefficient"><var>SOLUTION[1]</var></span><code>\text{O}_2 \rightarrow</code>
<span class="sol coefficient" data-forms="integer, coefficient"><var>SOLUTION[2]</var></span><code>\text{As}_4\text{O}_6 +</code>
<span class="sol coefficient" data-forms="integer, coefficient"><var>SOLUTION[3]</var></span><code>\text{SO}_2</code>
</div>
<div class="hints">
<p>
<code>\text{As}</code> is already balanced.
</p>
<div>
<p>
There are <code>6 \text{ S}</code> on the left and
only <code>1</code> on the right, so multiply
<code>\text{SO}_2</code> by <code>\blue{6}</code>.
</p>
<p><code>\qquad
\text{As}_4\text{S}_6 + \text{O}_2 \rightarrow \text{As}_4\text{O}_6 + \blue{6}\text{SO}_2
</code></p>
</div>
<div>
<p>
That gives us <code>18 \text{ O}</code> on the right and
only <code>2</code> on the left, so multiply
<code>\text{O}_2</code> by <code>\red{9}</code>.
(Since oxygen is by itself on the left, it should be done
at the end because you can give it a coefficient without
affecting another element.)
</p>
<p><code>\qquad
\text{As}_4\text{S}_6 + \red{9}\text{O}_2 \rightarrow \text{As}_4\text{O}_6 + 6\text{SO}_2
</code></p>
</div>
<div>
<p>The balanced equation is:</p>
<p><code>\qquad
\text{As}_4\text{S}_6 + 9\text{O}_2 \rightarrow \text{As}_4\text{O}_6 + 6\text{SO}_2
</code></p>
</div>
</div>
</div>
<div id="cr2o3-mg---cr-mgo">
<div class="vars">
<var id="SOLUTION">[1, 3, 2, 3]</var>
</div>
<div class="solution" data-type="multiple">
<code>\qquad</code>
<span class="sol coefficient" data-forms="integer, coefficient"><var>SOLUTION[0]</var></span><code>\text{Cr}_2\text{O}_3 +</code>
<span class="sol coefficient" data-forms="integer, coefficient"><var>SOLUTION[1]</var></span><code>\text{Mg} \rightarrow</code>
<span class="sol coefficient" data-forms="integer, coefficient"><var>SOLUTION[2]</var></span><code>\text{Cr} +</code>
<span class="sol coefficient" data-forms="integer, coefficient"><var>SOLUTION[3]</var></span><code>\text{MgO}</code>
</div>
<div class="hints">
<div>
<p>
There are <code>2 \text{ Cr}</code> on the left and
only <code>1</code> on the right, so multiply
<code>\text{Cr}</code> by <code>\blue{2}</code>.
</p>
<p><code>\qquad
\text{Cr}_2\text{O}_3 + \text{Mg} \rightarrow \blue{2}\text{Cr} + \text{MgO}
</code></p>
</div>
<div>
<p>
There are <code>3 \text{ O}</code> on the left and
only <code>1</code> on the right, so multiply
<code>\text{MgO}</code> by <code>\red{3}</code>.
</p>
<p><code>\qquad
\text{Cr}_2\text{O}_3 + \text{Mg} \rightarrow 2\text{Cr} + \red{3}\text{MgO}
</code></p>
</div>
<div>
<p>
That gives us <code>3 \text{ Mg}</code> on the right and
only <code>1</code> on the left, so multiply
<code>\text{Mg}</code> by <code>\pink{3}</code>.
</p>
<p><code>\qquad
\text{Cr}_2\text{O}_3 + \pink{3}\text{Mg} \rightarrow 2\text{Cr} + 3\text{MgO}
</code></p>
</div>
<div>
<p>The balanced equation is:</p>
<p><code>\qquad
\text{Cr}_2\text{O}_3 + 3\text{Mg} \rightarrow 2\text{Cr} + 3\text{MgO}
</code></p>
</div>
</div>
</div>
</div>
</div>
</body>
</html>