Answered

Carbon dioxide and water are produced when pentane $\left( C _5 H _{12}\right)$ reacts with oxygen. What is the balanced equation for this reaction?


A$C _5 H _{12}(g)+ O _2(g) \rightarrow CO _2(g)+ H _2 O (g)$
B$C _5 H _{12}(g)+ O _2(g) \rightarrow 5 CO _2(g)+ H _2 O (g)$
C$C _5 H _{12}(g)+8 O _2(g) \rightarrow 5 CO _2(g)+6 H _2 O (g)$
D$5 CO _2(g)+6 H _2 O (g) \rightarrow C _5 H _{12}(g)+8 O _2(g)$

Verified Answer :

  • Analyze the reaction: \(C_5H_{12}(g) + O_2(g) \rightarrow CO_2(g) + H_2O(g)\).
  • Balance Carbon: Place a coefficient of 5 before \(CO_2\).
  • Balance Hydrogen: Place a coefficient of 6 before \(H_2O\).
  • Balance Oxygen: Calculate total oxygen on products side (\(10+6=16\)) and place a coefficient of 8 before \(O_2\).
  • Balanced Equation: \(\boxed{C_5H_{12}(g) + 8O_2(g) \rightarrow 5CO_2(g) + 6H_2O(g)}\).

Explanation

  1. Analysis of the Reaction

The combustion reaction of pentane \(C_5H_{12}\) involves the substance reacting with oxygen \(O_2\) to produce carbon dioxide \(CO_2\) and water \(H_2O\). The principle of conservation of mass dictates that the number of atoms of each element must remain the same on both sides of the equation. We start with the skeletal equation:
\[C_5H_{12}(g) + O_2(g) \rightarrow CO_2(g) + H_2O(g)\]

  1. Balancing Carbon Atoms

First, we balance the carbon atoms. There are 5 carbon atoms in one molecule of pentane (\(C_5H_{12}\)), so we must have 5 molecules of carbon dioxide (\(CO_2\)) on the product side:
\[C_5H_{12}(g) + O_2(g) \rightarrow 5CO_2(g) + H_2O(g)\]

  1. Balancing Hydrogen Atoms

Next, we balance the hydrogen atoms. There are 12 hydrogen atoms in one molecule of pentane (\(C_5H_{12}\)). Each water molecule (\(H_2O\)) contains 2 hydrogen atoms. Therefore, we need \(12 \div 2 = 6\) molecules of water:
\[C_5H_{12}(g) + O_2(g) \rightarrow 5CO_2(g) + 6H_2O(g)\]

  1. Balancing Oxygen Atoms

Finally, we balance the oxygen atoms. On the product side, we have \(5 \times 2 = 10\) oxygen atoms from the carbon dioxide and \(6 \times 1 = 6\) oxygen atoms from the water molecules, giving a total of \(10 + 6 = 16\) oxygen atoms. To balance this on the reactant side, we need 16 oxygen atoms, which corresponds to \(16 \div 2 = 8\) molecules of oxygen gas (\(O_2\)):
\[C_5H_{12}(g) + 8O_2(g) \rightarrow 5CO_2(g) + 6H_2O(g)\]

  1. Conclusion

The balanced equation is \(C_5H_{12}(g) + 8O_2(g) \rightarrow 5CO_2(g) + 6H_2O(g)\). Comparing this to the given options, we identify the third option as the correct balanced chemical equation. The final answer is \(\boxed{C_5H_{12}(g) + 8O_2(g) \rightarrow 5CO_2(g) + 6H_2O(g)}\).

Examples

Chemical equations are vital in everyday life, such as in the combustion of fuel in your car. When gasoline, which contains hydrocarbons like pentane, burns in an engine, it reacts with oxygen to release energy. Balancing these equations allows chemists and engineers to calculate exactly how much fuel and oxygen are needed for optimal performance and to predict the emissions produced, helping us design cleaner and more efficient vehicles.