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Balance the following chemical equations:


  1. \_ Na + \_ F_2 \rightarrow \_ NaF
  2. \_ CO_2 + \_ H_2O \rightarrow \_ O_2 + \_ C_6H_{12}O_6
  3. \_ K + \_ B_2O_3 \rightarrow \_ K_2O + \_ B
  4. \_ C + \_ S_8 \rightarrow \_ CS_2
  5. \_ FeS + \_ HCl \rightarrow \_ FeCl_2 + \_ H_2S
  6. \_ PCl_5 + \_ H_2O \rightarrow \_ H_3PO_4 + \_ HCl

Verified Answer :

  • Balance Equation 1: \(2\text{Na} + \text{F}_2 \rightarrow 2\text{NaF}\).
  • Balance Equation 2: \(6\text{CO}_2 + 6\text{H}_2\text{O} \rightarrow 6\text{O}_2 + \text{C}_6\text{H}_{12}\text{O}_6\).
  • Balance Equations 3 and 4: \(6\text{K} + \text{B}_2\text{O}_3 \rightarrow 3\text{K}_2\text{O} + 2\text{B}\) and \(4\text{C} + \text{S}_8 \rightarrow 4\text{CS}_2\).
  • Balance Equations 5 and 6: \(\text{FeS} + 2\text{HCl} \rightarrow \text{FeCl}_2 + \text{H}_2\text{S}\) and \(\text{PCl}_5 + 4\text{H}_2\text{O} \rightarrow \text{H}_3\text{PO}_4 + 5\text{HCl}\).

Explanation

  1. Analysis of the Problem

Balancing chemical equations requires ensuring that the law of conservation of mass holds: the number of atoms of each element must be equal on both sides of the reaction. We will analyze each equation by setting stoichiometric coefficients as variables and solving the resulting system of linear equations to find the smallest set of whole numbers. The first row contains arithmetic expressions which evaluate to 6 (c-3=3 -> c=6) and 6 (C-3=3 -> C=6); while these are provided, our primary objective is to balance the chemical equations listed in the subsequent rows.

  1. Balancing the First and Second Equations

For each chemical equation, we represent the reactants and products with variables.

  1. Equation 1: \(\text{Na} + \text{F}_2 \rightarrow \text{NaF}\)

Equating atoms: Na: \(a = c\), F: \(2b = c\). Let \(c=2\), then \(a=2, b=1\).
Balanced equation: \(2\text{Na} + \text{F}_2 \rightarrow 2\text{NaF}\).

  1. Equation 2: \(\text{CO}_2 + \text{H}_2\text{O} \rightarrow \text{O}_2 + \text{C}_6\text{H}_{12}\text{O}_6\)

Equating atoms: C: \(a = 6d\), H: \(2b = 12d \Rightarrow b = 6d\), O: \(2a + b = 2c + 6d\).
Substituting \(a=6d\) and \(b=6d\): \(2(6d) + 6d = 2c + 6d \Rightarrow 18d = 2c + 6d \Rightarrow 12d = 2c \Rightarrow c = 6d\).
Let \(d=1\), then \(a=6, b=6, c=6\).
Balanced equation: \(6\text{CO}_2 + 6\text{H}_2\text{O} \rightarrow 6\text{O}_2 + \text{C}_6\text{H}_{12}\text{O}_6\).

  1. Balancing the Third and Fourth Equations
  2. Equation 3: \(\text{K} + \text{B}_2\text{O}_3 \rightarrow \text{K}_2\text{O} + \text{B}\)

Equating atoms: K: \(a = 2c\), B: \(2b = d\), O: \(3b = c\).
Let \(b=1\), then \(d=2\), \(c=3\), \(a=6\).
Balanced equation: \(6\text{K} + \text{B}_2\text{O}_3 \rightarrow 3\text{K}_2\text{O} + 2\text{B}\).

  1. Equation 4: \(\text{C} + \text{S}_8 \rightarrow \text{CS}_2\)

Equating atoms: C: \(a = c\), S: \(8b = 2c \Rightarrow 4b = c\).
Let \(b=1\), then \(c=4, a=4\).
Balanced equation: \(4\text{C} + \text{S}_8 \rightarrow 4\text{CS}_2\).

  1. Balancing the Fifth and Sixth Equations
  2. Equation 5: \(\text{FeS} + \text{HCl} \rightarrow \text{FeCl}_2 + \text{H}_2\text{S}\)

Equating atoms: Fe: \(a = c\), S: \(a = d\), H: \(b = 2d\), Cl: \(b = 2c\).
Setting \(a=1\), then \(c=1, d=1, b=2\).
Balanced equation: \(\text{FeS} + 2\text{HCl} \rightarrow \text{FeCl}_2 + \text{H}_2\text{S}\).

  1. Equation 6: \(\text{PCl}_5 + \text{H}_2\text{O} \rightarrow \text{H}_3\text{PO}_4 + \text{HCl}\)

Equating atoms: P: \(a = c\), Cl: \(5a = d\), H: \(2b = 3c + d\), O: \(b = 4c\).
Substitute \(a=1\): \(c=1\), \(d=5\).
H equation: \(2b = 3(1) + 5 = 8 \Rightarrow b=4\).
O equation: \(b = 4(1) = 4\). (Matches!)
Balanced equation: \(\text{PCl}_5 + 4\text{H}_2\text{O} \rightarrow \text{H}_3\text{PO}_4 + 5\text{HCl}\).

  1. Conclusion

The balanced equations are:

  1. \(2\text{Na} + \text{F}_2 \rightarrow 2\text{NaF}\)
  2. \(6\text{CO}_2 + 6\text{H}_2\text{O} \rightarrow 6\text{O}_2 + \text{C}_6\text{H}_{12}\text{O}_6\)
  3. \(6\text{K} + \text{B}_2\text{O}_3 \rightarrow 3\text{K}_2\text{O} + 2\text{B}\)
  4. \(4\text{C} + \text{S}_8 \rightarrow 4\text{CS}_2\)
  5. \(\text{FeS} + 2\text{HCl} \rightarrow \text{FeCl}_2 + \text{H}_2\text{S}\)
  6. \(\text{PCl}_5 + 4\text{H}_2\text{O} \rightarrow \text{H}_3\text{PO}_4 + 5\text{HCl}\)

Final answer confirmed by checking atom counts on both sides.

Examples

Balancing chemical equations is essential in industrial chemistry and laboratory work. For instance, when manufacturing pharmaceuticals or fertilizers, chemists must calculate the precise amounts of reactants to ensure that the reaction proceeds efficiently, minimizing waste and predicting the yield of the product. By using stoichiometry, manufacturers save resources and ensure safety in chemical processing.

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