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Balance the following chemical equations:

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Step-By-Step Solution

Question 1

Balance: Fe2(SO4)3 + NH3 + H2O rightarrow Fe(OH)3 + (NH4)2SO4

Step 1

Write atoms and their counts for each compound:

  • Fe2(SO4)3 has 2 Fe, 3 S, 12 O
  • NH3 has 1 N, 3 H
  • H2O has 2 H, 1 O
  • Fe(OH)3 has 1 Fe, 3 O, 3 H
  • (NH4)2SO4 has 2 N, 8 H, 1 S, 4 O

Step 2

Assign coefficients as variables:

  • a Fe2(SO4)3
  • b NH3
  • c H2O
  • d Fe(OH)3
  • e (NH4)2SO4

Step 3

Set up element balance equations:

  • Fe: 2a = d
  • S: 3a = e
  • N: b = 2e
  • H: 3b + 2c = 3d + 8e
  • O: 12a + c = 3d + 4e

Step 4

From Fe: d = 2a From S: e = 3a From N: b = 2e = 6a Substitute in H balance: 3b + 2c = 3d + 8e 3(6a) + 2c = 3(2a) + 8(3a) 18a + 2c = 6a + 24a 18a + 2c = 30a 2c = 12a c = 6a

Substitute in O balance: 12a + c = 3d + 4e 12a + 6a = 3(2a) + 4(3a) 18a = 6a + 12a 18a = 18a (True)

Step 5

Choose a lowest integer value for a, a = 1 Then:

  • d = 2
  • e = 3
  • b = 6
  • c = 6

Step 6

Write balanced equation: 1 Fe2(SO4)3 + 6 NH3 + 6 H2O rightarrow 2 Fe(OH)3 + 3 (NH4)2SO4

Question 2

Balance: NaOH + Cl2 rightarrow NaCl + NaClO3 + H2O

Step 1

Let coefficients be: a NaOH + b Cl2 rightarrow c NaCl + d NaClO3 + e H2O

Step 2

Balance Na: Na from left = a Na on right = c + d So, a = c + d

Balance Cl: From left: 2b From right: c + 3d So, 2b = c + 3d

Balance H: From left: a (from NaOH has one H) From right: 2e (in H2O) So, a = 2e

Balance O: From left: a (NaOH has one O) From right: 3d + e So, a = 3d + e

Step 3

From H and O equations: a = 2e (H) a = 3d + e (O) Set equal: 2e = 3d + e => e = 3d

From Na: a = c + d From Cl: 2b = c + 3d

Use e = 3d and a = 2e = 2(3d) = 6d Therefore a = 6d

Since a = c + d, 6d = c + d => c = 5d Also, 2b = c + 3d = 5d + 3d = 8d => b = 4d

Step 4

Choose d=1 (lowest integer) Then: a = 6 b = 4 c = 5 d = 1 e = 3

Step 5

Balanced equation: 6 NaOH + 4 Cl2 rightarrow 5 NaCl + 1 NaClO3 + 3 H2O

Question 3

Balance: KMnO4 + HCl rightarrow KCl + MnCl2 + H2O + Cl2

Step 1

Assign coefficients: a KMnO4 + b HCl rightarrow c KCl + d MnCl2 + e H2O + f Cl2

Step 2

Balance K: a = c

Balance Mn: a = d

Balance O: Left: 4a Right: e (water) So, 4a = e

Balance H: Left: b Right: 2e So, b = 2e = 2 (4a) = 8a

Balance Cl: Left: b = 8a Right: c + 2d + 2f = a + 2a + 2f = 3a + 2f So, 8a = 3a + 2f => 5a = 2f => f = (5/2)a

Step 3

Choose a=2 to get integer f: f = 5

Now:

  • a=2
  • c=2
  • d=2
  • e=4a=8
  • b=8a=16
  • f=5

Step 4

Write balanced equation: 2 KMnO4 + 16 HCl rightarrow 2 KCl + 2 MnCl2 + 8 H2O + 5 Cl2

Final Answer

  1. Fe2(SO4)3 + 6 NH3 + 6 H2O rightarrow 2 Fe(OH)3 + 3 (NH4)2SO4

  2. 6 NaOH + 4 Cl2 rightarrow 5 NaCl + NaClO3 + 3 H2O

  3. 2 KMnO4 + 16 HCl rightarrow 2 KCl + 2 MnCl2 + 8 H2O + 5 Cl2