Question

The mass of nitrogen in ${\rm{1000}}\;{\rm{kg}}$ of urea $\left[ {{\rm{CO}}{{\left( {{\rm{N}}{{\rm{H}}_{\rm{2}}}} \right)}_{\rm{2}}}} \right]$ is:
A. ${\rm{467}}\;{\rm{kg}}$
B. $700.5\;{\rm{kg}}$
C. $350.25\;{\rm{kg}}$
D. $592.34\;{\rm{kg}}$

Answer 1

Hint: We know that the mass of any substance is the amount of moles to the molar mass of that species.

Complete step by step answer:
The formula of urea is $\left[ {{\rm{CO}}{{\left( {{\rm{N}}{{\rm{H}}_{\rm{2}}}} \right)}_{\rm{2}}}} \right]$. It has one carbon atom, one oxygen atom, two nitrogen atoms and four hydrogen atoms. The chemical name of urea is carbamide. It has a carbonyl group as the functional group.
The given mass of urea is ${\rm{1000}}\;{\rm{kg}}$.
The molar mass of urea is ${\rm{60}}\;{\rm{g/mol}}$.
The molar mass of dinitrogen is ${\rm{28}}\;{\rm{g/mol}}$.
The conversion of mass of urea from kilograms to grams is done as follows.
$\begin{array}{c}
{\rm{1}}\;{\rm{kg}} = 1000\;{\rm{g}}\\
{\rm{1000}}\;{\rm{kg}} = 1000 \times {\rm{1000}}\;{\rm{g}}\\
 = {\rm{1000000}}\;{\rm{g}}
\end{array}$
We can see that, ${\rm{60}}\;{\rm{g}}$ of urea consist $28\;{\rm{g}}$.
So, ${\rm{1000000}}\;{\rm{g}}$ of urea consisting of the nitrogen atom can be calculated as shown below.
$\begin{array}{c}
{\rm{Mass}}\;{\rm{of}}\;{\rm{nitrogen}} = \dfrac{{{\rm{1000000}}\;{\rm{g}}}}{{{\rm{60}}\;{\rm{g}}}} \times 28\;{\rm{g}}\\
 = 466666.66\;{\rm{g}}
\end{array}$
The conversion of mass of nitrogen from grams to kilograms is done as follows.
$\begin{array}{c}
{\rm{1}}\;{\rm{g}} = \dfrac{1}{{1000}}\;{\rm{kg}}\\
466666.66\;{\rm{g}} = \dfrac{{466666.66}}{{1000}}\;{\rm{kg}}\\
 = 466.66666\;{\rm{kg}}\\
 \approx 467\;{\rm{kg}}
\end{array}$
Thus, the calculated mass of nitrogen is ${\rm{467}}\;{\rm{kg}}$.

Hence, the correct answer for this question is A.

Note:
The mass of any species can be calculated through the molar mass of that species by comparing them. It is one of the easiest methods to evaluate the mass.