Math  /  Algebra

QuestionQuestion 7 of 10
Balance the following chemical equation (if necessary): MnO2( s)+H2O(l)+Zn( s)Mn(OH)2( s)+Zn(OH)2( s)\mathrm{MnO}_{2}(\mathrm{~s})+\mathrm{H}_{2} \mathrm{O}(\mathrm{l})+\mathrm{Zn}(\mathrm{~s}) \rightarrow \mathrm{Mn}(\mathrm{OH})_{2}(\mathrm{~s})+\mathrm{Zn}(\mathrm{OH})_{2}(\mathrm{~s}) \qquad \square 4- 3{ }^{3-} 222^{2-} \square^{-} \square +\square^{+} 2+{ }^{2+} 3+\square^{3+} 74+7^{4+} 1 2 3 4 5 6 7 8 9 0 1\square 1 \square 2 3\square_{3} 4\square_{4} 5\square_{5} 6\square_{6} 7\square_{7} \square 8 9\square 9 9 \square 0 ++ ( ) D \rightarrow \rightleftharpoons (s) (I) (g) (aq) MnO2\mathrm{MnO}_{2} Mn(OH)2\mathrm{Mn}(\mathrm{OH})_{2} Zn(OH)2\mathrm{Zn}(\mathrm{OH})_{2} Zn H2O\mathrm{H}_{2} \mathrm{O} 甾 - xH2Ox \mathrm{H}_{2} \mathrm{O}

Studdy Solution

STEP 1

1. The chemical equation provided may not be balanced.
2. Balancing a chemical equation involves ensuring the same number of each type of atom appears on both sides of the equation.
3. The physical states of the compounds are given and should be maintained.

STEP 2

1. List the number of each type of atom on both sides of the equation.
2. Adjust coefficients to balance the atoms.
3. Verify that the equation is balanced.

STEP 3

List the number of each type of atom on both sides of the equation.
Left side: - Mn: 1 - O: 3 (2 from MnO2\mathrm{MnO}_{2} and 1 from H2O\mathrm{H}_{2}\mathrm{O}) - H: 2 - Zn: 1
Right side: - Mn: 1 - O: 4 (2 from Mn(OH)2\mathrm{Mn}(\mathrm{OH})_{2} and 2 from Zn(OH)2\mathrm{Zn}(\mathrm{OH})_{2}) - H: 4 - Zn: 1

STEP 4

Adjust coefficients to balance the atoms.
To balance the oxygen and hydrogen atoms, we can adjust the coefficients of H2O\mathrm{H}_{2}\mathrm{O} on the left side and Mn(OH)2\mathrm{Mn}(\mathrm{OH})_{2} and Zn(OH)2\mathrm{Zn}(\mathrm{OH})_{2} on the right side.
Let's start by balancing the oxygen and hydrogen atoms:
- Add a coefficient of 2 in front of H2O\mathrm{H}_{2}\mathrm{O} on the left side to balance the hydrogen atoms. - This gives us 4 hydrogen atoms on both sides, but now we have 4 oxygen atoms on the left side.
Now, the equation looks like this:
MnO2(s)+2H2O(l)+Zn(s)Mn(OH)2(s)+Zn(OH)2(s)\mathrm{MnO}_{2}(\mathrm{s}) + 2\mathrm{H}_{2}\mathrm{O}(\mathrm{l}) + \mathrm{Zn}(\mathrm{s}) \rightarrow \mathrm{Mn}(\mathrm{OH})_{2}(\mathrm{s}) + \mathrm{Zn}(\mathrm{OH})_{2}(\mathrm{s})

STEP 5

Verify that the equation is balanced.
Left side: - Mn: 1 - O: 4 (2 from MnO2\mathrm{MnO}_{2} and 2 from H2O\mathrm{H}_{2}\mathrm{O}) - H: 4 - Zn: 1
Right side: - Mn: 1 - O: 4 (2 from Mn(OH)2\mathrm{Mn}(\mathrm{OH})_{2} and 2 from Zn(OH)2\mathrm{Zn}(\mathrm{OH})_{2}) - H: 4 - Zn: 1
The equation is now balanced with the same number of each type of atom on both sides.

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