Zn + VO3 ^- --> Zn ^2+ + V^+3

Fe ^2+ + H2O2 + OH- --> Fe (OH) 3
V2O5 + I- + H^+ --> VO2 + I2 + H20
P + H+ + NO3- + H2O -->'NO + H3PO4

All of the equations are balanced.

1. Zn + VO3^- → Zn^2+ + V^3+

To balance the equation, we need to ensure that the number of each type of atom is the same on both sides of the equation.

Step 1: Balance the metals on both sides:
Zn + VO3^- → Zn^2+ + V^3+

Step 2: Balance the oxygen atoms by adding water molecules on the right side:
Zn + VO3^- + H2O → Zn^2+ + V^3+ + H2O

Step 3: Balance the hydrogen atoms by adding H+ ions on the left side:
Zn + VO3^- + H2O → Zn^2+ + V^3+ + H2O + H+

Step 4: Balance the charges by adding electrons (e^-) as needed:
Zn + VO3^- + 2H2O → Zn^2+ + V^3+ + 2H2O + H+ + 2e^-

Step 5: Combine the electrons on one side of the equation to simplify:
Zn + VO3^- + 2H2O + H+ + 2e^- → Zn^2+ + V^3+ + 2H2O

2. Fe^2+ + H2O2 + OH^- → Fe(OH)3
To balance the equation:

Step 1: Balance the hydrogen atoms by adding H2O molecules on the left side:
Fe^2+ + H2O2 + OH^- → Fe(OH)3 + H2O

Step 2: Balance the oxygen atoms by adding water molecules on the left side:
Fe^2+ + H2O2 + 2OH^- → Fe(OH)3 + 2H2O

Step 3: Balance the charges by adding electrons (e^-) as needed:
Fe^2+ + H2O2 + 2OH^- → Fe(OH)3 + 2H2O + 2e^-

Step 4: Combine the electrons on one side of the equation to simplify:
Fe^2+ + H2O2 + 2OH^- + 2e^- → Fe(OH)3 + 2H2O

3. V2O5 + 5I^- + 4H^+ → 2VO2 + 5I2 + 2H2O
To balance the equation:

Step 1: Balance the vanadium (V) atoms by multiplying VO2 by 2 on the right side:
V2O5 + 5I^- + 4H^+ → 2VO2 + 5I2 + 2H2O

Step 2: Balance the iodine (I) atoms by multiplying I2 by 5 on the right side:
V2O5 + 5I^- + 4H^+ → 2VO2 + 5I2 + 2H2O

Step 3: Balance the hydrogen atoms by adding H2O molecules on the left side:
V2O5 + 5I^- + 4H^+ + 4H2O → 2VO2 + 5I2 + 2H2O

Step 4: Balance the oxygen atoms by adding water molecules on the left side:
V2O5 + 5I^- + 4H^+ + 4H2O → 2VO2 + 5I2 + 6H2O

Step 5: Simplify the equation by removing common factors:
V2O5 + 5I^- + 4H^+ + 4H2O → 2VO2 + 5I2 + 6H2O

4. P + H+ + NO3^- + H2O → NO + H3PO4
To balance the equation:

Step 1: Balance the phosphorus (P) atoms by multiplying H3PO4 by 1 on the right side:
P + H+ + NO3^- + H2O → NO + H3PO4

Step 2: Balance the hydrogen atoms by adding H2O molecules on the left side:
P + 3H+ + NO3^- + H2O → NO + H3PO4

Step 3: Balance the oxygen atoms by adding water molecules on the left side:
P + 3H+ + NO3^- + 2H2O → NO + H3PO4

Step 4: Simplify the equation by removing common factors:
P + 3H+ + NO3^- + 2H2O → NO + H3PO4

To balance the chemical equations given, we need to ensure that the number of each type of atom on both sides of the equation is the same. Here's how to balance each equation step by step:

1. Zn + VO3^ - -> Zn^2+ + V^+3:
- Start by balancing the metals. There is one Zn atom on the left side, so place a coefficient of 1 in front of Zn on the right side.
- Count the number of oxygens on each side. There are three oxygens in VO3^ -, so place a coefficient of 3 in front of VO3^ - on the left side.
- Now, check the charge balance. On the left, we have a neutral zinc (Zn) and a -1 charge from VO3^ -. On the right, we have Zn^2+ and V^+3. To balance the charges, place a coefficient of 2 in front of V^+3 on the right side.
The balanced equation is:
2 Zn + 3 VO3^ - -> 2 Zn^2+ + 3 V^+3.

2. Fe^2+ + H2O2 + OH- -> Fe(OH)3:
- Begin by balancing the metals. There is one Fe on the left, so place a coefficient of 1 in front of Fe(OH)3 on the right side.
- Next, balance the oxygens by adding water (H2O) to the left side. We need three more oxygens, so add three H2O to the left.
- Now, balance the hydrogens. There are six hydrogens on the left (two from H2O2 and four from OH-). Place a coefficient of 6 in front of H2O2 on the left side.
- Finally, check the overall charge balance. On the left, we have a +2 charge from Fe^2+ and a -1 charge from OH-. On the right, we have a +3 charge from Fe(OH)3. To balance the charges, place a coefficient of 3 in front of OH- on the left side.
The balanced equation is:
Fe^2+ + 3 H2O2 + 3 OH- -> Fe(OH)3.

3. V2O5 + I- + H+ -> VO2 + I2 + H2O:
- Begin by balancing the vanadium atoms. There are two vanadium atoms on the left, so place a coefficient of 2 in front of VO2 on the right side.
- Next, balance the iodine atoms. There is one iodine atom on the left, so place a coefficient of 1 in front of I2 on the right side.
- Balance the hydrogens. There are six hydrogens on the right (two from VO2 and four from H2O). Place a coefficient of 6 in front of H+ on the left side.
- Now, balance the oxygens. There are 10 oxygens on the left (five from V2O5), and four oxygens on the right (two from VO2 and two from H2O). Add three H2O to the right side.
The balanced equation is:
V2O5 + 12 I- + 10 H+ -> 4 VO2 + 6 I2 + 5 H2O.

4. P + H+ + NO3- + H2O -> NO + H3PO4:
- Start by balancing the phosphorus atoms. There is one phosphorus atom on the left, so place a coefficient of 1 in front of H3PO4 on the right side.
- Balance the hydrogens. There are four hydrogens on the right (three from H3PO4 and one from NO). Place a coefficient of 4 in front of H+ on the left side.
- Next, balance the oxygens. There are four oxygens on the right (one from NO and three from H3PO4). Place a coefficient of 4 in front of NO3- on the left side.
- Check the charge balance. On the left, you have a neutral phosphorus (P), a +1 charge from H+, and a -1 charge from NO3-. On the right, you have a +1 charge from H3PO4 and a neutral NO. To balance the charges, place a coefficient of 2 in front of H3PO4 on the right side.
The balanced equation is:
P + 4 H+ + 4 NO3- + 6 H2O -> 2 NO + 2 H3PO4.