- Verify the conservation of atoms: carbon and hydrogen are balanced with the current coefficients (2, 8, 10).
- Calculate the correct requirement for oxygen: the right side has 26 oxygen atoms (16 from \(CO_2\), 10 from \(H_2O\)).
- Identify the error: the left side only provides 24 oxygen atoms (from \(12O_2\)), but 26 are required.
- Conclude the change: the coefficient 12 must be changed to 13.
- Final Answer: \(\boxed{12}\)
Explanation
- Analyzing the Balanced Chemical Equation
To determine which coefficient Leslie needs to change in her equation \(2C_4H_{10} + 12O_2 \rightarrow 8CO_2 + 10H_2O\), we must check the balance of atoms for carbon, hydrogen, and oxygen on both sides of the equation. A balanced chemical equation must have an equal number of atoms for every element on both sides.
- Checking Atomic Balance
First, we check the number of carbon (C) atoms:
- On the left: \(2 \times 4 = 8\) atoms.
- On the right: \(8 \times 1 = 8\) atoms.
The carbon atoms are balanced.
Next, we check the number of hydrogen (H) atoms:
- On the left: \(2 \times 10 = 20\) atoms.
- On the right: \(10 \times 2 = 20\) atoms.
The hydrogen atoms are balanced.
Finally, we check the number of oxygen (O) atoms:
- On the left: \(12 \times 2 = 24\) atoms.
- On the right: \(8 \times 2 + 10 \times 1 = 16 + 10 = 26\) atoms.
The oxygen atoms are not balanced, as there are 24 on the left and 26 on the right.
- Determining the Correct Coefficient
Since the number of atoms for carbon and hydrogen is already fixed by the coefficients 2, 8, and 10, we must determine the correct coefficient for oxygen, \(b\), in the general form \(2C_4H_{10} + bO_2 \rightarrow 8CO_2 + 10H_2O\).
The conservation of oxygen atoms dictates:
\(2b = (8 \times 2) + (10 \times 1) = 16 + 10 = 26\).
Dividing by 2, we find \(b = 13\).
Since Leslie used 12 instead of 13, the coefficient that needs to be changed is 12.
Examples
Balancing chemical equations is essential in fields like pharmacology and environmental science to ensure accurate dosage calculations or to predict the environmental impact of chemical reactions. For example, in a combustion reaction, knowing the exact amount of oxygen required prevents incomplete combustion, which could produce toxic carbon monoxide instead of carbon dioxide. Precision in these coefficients ensures safety and efficiency in all chemical processes.