Animated Solution for Chemistry - Purification and Characterisation of Organic Compounds: The number of moles of CuO, that will be utilised in Dumas method for estimation nitrogen in a sample of $57.5\text{ g}$ of N, N-dimethylaminopentane is ......... $\times 10^{-2}$. (Nearest integer)

To solve this problem, our first task is to decipher the molecular formula of the given organic compound: N,N-dimethylaminopentane.

Imagine a straight chain of five carbon atoms—this forms our pentane backbone. Attached to the nitrogen atom, we have two methyl ($-C{H}_3$) groups. Let's count the atoms systematically to find the molecular formula. We have $5$ carbons from the main chain and $2$ from the methyl groups, giving us $7$ carbons in total. Counting the hydrogens, we get $17$, and there is exactly $1$ nitrogen atom.

So, our molecular formula is $C_7{H}_{17}N$.

Now, let's recall the core principle of the Dumas method. In this method, the organic compound is heated with copper oxide ($CuO$), which acts as an oxidizing agent. The carbon is oxidized to carbon dioxide ($C{O}_2$), the hydrogen to water ($H_{2}O$), and the nitrogen is liberated as free nitrogen gas ($N_2$).

The general balanced equation is crucial here. For a compound with the formula $C_x{H}_y{N}_z$, the combustion reaction is:

Notice how nitrogen doesn't consume any oxygen from the copper oxide. The number of moles of $CuO$ required per mole of the compound is simply $\left(2x+\frac{y}{2}\right)$.

With our general formula ready, let's substitute the values for our specific compound. We found that $x=7$ and $y=17$. Plugging these into our coefficient expression, we get:

This means that for every single mole of our organic compound, we need exactly $22.5$ moles of copper oxide to completely oxidize it.

Before we can find the total copper oxide needed, we must determine how much of our organic compound we actually have in the given $57.5\text{ g}$ sample. Let's calculate its molar mass.

To convert the given mass into moles, we simply divide the given mass by the molar mass we just found:

We have exactly $0.5$ moles of N,N-dimethylaminopentane in our sample.

We are almost there! We know that $1$ mole of our compound requires $22.5$ moles of copper oxide. Therefore, $0.5$ moles of the compound will require half of that amount.

Finally, let's format our answer to match the question's requirement. The question asks for the value in the form of an integer multiplied by $10^{-2}$. We can rewrite $11.25$ by shifting the decimal point two places to the right:

Thus, our final integer answer is $1125$.