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Step-by-Step Solution
Step 1: Write the Balanced Chemical Equation
The combustion reaction for butane (C4H10) is:
C_4H_{10} + \frac{13}{2}O_2 \rightarrow 4CO_2 + 5H_2O
Step 2: Determine the Moles of Water Formed
Given the mass of water is 72.0 g. The molar mass of water ( H_2O ) is 18 g/mol.
\text{Moles of } H_2O = \frac{72.0\,\text{g}}{18\,\text{g/mol}} = 4\,\text{mol}
Step 3: Relate the Moles of Water to the Moles of Butane
From the balanced equation, 1 mole of C_4H_{10} produces 5 moles of H_2O . Hence,
\text{If }5\text{ moles of }H_2O \text{ come from }1\text{ mole of }C_4H_{10},
\text{then }4\text{ moles of }H_2O \text{ come from } \frac{4}{5}\text{ moles of }C_4H_{10}.
Step 4: Calculate the Moles of Butane Used
Therefore, the moles of butane ( C_4H_{10} ) required are:
\text{Moles of } C_4H_{10} = \frac{4}{5} = 0.8\,\text{mol}
Step 5: Convert Moles of Butane to Mass
The molar mass of butane ( C_4H_{10} ) is 58\,\text{g/mol} . So,
\text{Mass of } C_4H_{10} = 0.8\,\text{mol} \times 58\,\text{g/mol} = 46.4\,\text{g}
Final Answer
Expressed in terms of 10^{-1} grams, the mass of butane required is:
46.4\,\text{g} = 464 \times 10^{-1}\,\text{g}
