Q. \( \mathrm{C_6H_{12}O_6} + 6\,\mathrm{O_2} \rightarrow 6\,\mathrm{CO_2} + 6\,\mathrm{H_2O} \).

Step 1: Identify what the problem is showing

The given chemical equation is:

\[\mathrm{C_6H_{12}O_6 + 6O_2 \rightarrow 6CO_2 + 6H_2O}\]

This is the balanced chemical equation for the combustion (oxidation) of glucose.

Step 2: Understand the meaning of each coefficient

In a balanced equation, the numbers in front of formulas are coefficients that tell you the relative number of molecules (or moles) reacting.

Here:

• 1 molecule (or 1 mole) of glucose reacts.
• 6 molecules (or 6 moles) of oxygen gas react.
• 6 molecules (or 6 moles) of carbon dioxide are produced.
• 6 molecules (or 6 moles) of water are produced.

Step 3: Verify atom balance (check each element separately)

Carbon (C):

• Left side: glucose contains 6 carbon atoms, so total carbon is \(6\).
• Right side: there are 6 molecules of \(CO_2\), and each \(CO_2\) has 1 carbon atom, so total carbon is \(6 \times 1 = 6\).

So carbon is balanced.

Hydrogen (H):

• Left side: glucose is \(H_{12}\), so total hydrogen is \(12\).
• Right side: there are 6 molecules of \(H_2O\), and each \(H_2O\) has 2 hydrogen atoms, so total hydrogen is \(6 \times 2 = 12\).

So hydrogen is balanced.

Oxygen (O):

• Left side:
  • glucose has 6 oxygen atoms, so that contributes \(6\).
  • oxygen gas \(6O_2\) has \(6 \times 2 = 12\) oxygen atoms.

  Total oxygen on the left is \(6 + 12 = 18\).

• Right side:
  • \(6CO_2\) has \(6 \times 2 = 12\) oxygen atoms.
  • \(6H_2O\) has \(6 \times 1 = 6\) oxygen atoms.

  Total oxygen on the right is \(12 + 6 = 18\).

So oxygen is balanced.

Step 4: Conclusion

Since the numbers of \(C\), \(H\), and \(O\) atoms match on both sides, the equation is already correctly balanced.

Final balanced equation:

\[\mathrm{C_6H_{12}O_6 + 6O_2 \rightarrow 6CO_2 + 6H_2O}\]