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Step-by-Step Solution
Step 1: Identify the given data
We have 57.5 g of N,N-dimethylaminopentane (molecular formula C_7H_{17}N ).
Step 2: Calculate moles of the organic compound
Molar mass of C_7H_{17}N is approximately 115 g/mol.
Number of moles of C_7H_{17}N in 57.5 g
= \frac{57.5 \,\text{g}}{115 \,\text{g/mol}} = 0.5 \text{ mol}
Step 3: Write the reaction for Dumas method
In the Dumas method, the organic compound is heated with copper(II) oxide ( \text{CuO} ). A simplified balanced reaction for 1 mole of C_7H_{17}N can be written as:
C_7H_{17}N + \frac{45}{2} \, CuO \;\longrightarrow\; 7\,CO_2 + \frac{17}{2}\,H_2O + \frac{1}{2}\,N_2 + \frac{45}{2}\, Cu
From this stoichiometry, 1 mole of C_7H_{17}N consumes \frac{45}{2} = 22.5 moles of CuO .
Step 4: Find moles of CuO required
Since we have 0.5 moles of C_7H_{17}N , the moles of CuO needed are:
n_{\text{CuO}} = 22.5 \times 0.5 = 11.25 \text{ moles}
Step 5: Express the final answer in the requested form
The question asks for an expression of the form "_____ \times 10^{-2} (Nearest integer)".
11.25 moles = 1125 \times 10^{-2} moles.
The nearest integer to fill in the blank is 1125.
