Question

The number of moles of $CuO$, that will be utilized in Dumas method for estimating nitrogen in a sample of 57.5 g of N,N-dimethylaminopentane is $x \times 10^{-2}$. (Nearest integer)

Hint:

The oxygen required for oxidation comes solely from $CuO$. One $O$ atom from $CuO$ is needed for every half $CO_2$ or half $H_2O$ unit formed. Sum the oxygen requirements to find the $CuO$ moles.

Answer 1

Correct Answer: 1125

Step 1: Understanding the Concept:
In Dumas method, the organic compound is oxidized by $CuO$. Carbon is converted to $CO_2$, Hydrogen to $H_2O$, and Nitrogen to $N_2$.
Step 2: Detailed Explanation:
1. Molecular Formula:
N,N-dimethylaminopentane consists of a pentane chain ($C_5$) and a dimethylamino group ($N(CH_3)_2$).
Total Carbons = $5 + 2 = 7$.
Total Hydrogens = $11 (\text{from pentyl}) + 6 (\text{from methyls}) = 17$.
Molecular Formula = $C_7H_{17}N$.
2. Stoichiometry with CuO:
General reaction: $C_xH_yN_z + (2x + y/2) CuO \to x CO_2 + (y/2) H_2O + (z/2) N_2 + (2x + y/2) Cu$.
Moles of $CuO$ needed for 1 mole of $C_7H_{17}N$ = $2(7) + 17/2 = 14 + 8.5 = 22.5$ moles.
3. Calculation for Given Mass:
Molar mass of $C_7H_{17}N = (7 \times 12) + (17 \times 1) + 14 = 84 + 17 + 14 = 115$ g/mol.
Moles of compound $= \frac{57.5}{115} = 0.5$ mol.
Moles of $CuO = 0.5 \times 22.5 = 11.25$ mol.
$11.25 = 1125 \times 10^{-2}$.
Step 3: Final Answer:
The value of $x$ is 1125.