Question

Urea, chemical formula${\left( {{\text{N}}{{\text{H}}_{\text{2}}}} \right)_{\text{2}}}{\text{CO}}$, is used for fertilizer and many other things. How do you calculate the number of N, C, O and H atoms in $1.68 \times {10^4}$g of urea?

Answer 1

Hint: Here, first we have to calculate the number moles of urea. The formula used to calculate the number of moles is, ${\text{Number}}\,{\text{of}}\,{\text{moles = }}\dfrac{{{\text{Mass}}}}{{{\text{Molar}}\,{\text{mass}}}}$. Then, we have to calculate the number atoms of each element using Avogadro's number.

Complete step by step answer:
Let’s first calculate the molar mass of urea. Atomic mass of nitrogen is 14, hydrogen is 1, carbon is 1 and oxygen is 16.
Molar mass of ${\left( {{\text{N}}{{\text{H}}_{\text{2}}}} \right)_{\text{2}}}{\text{CO = 2}} \times {\text{14 + 4}} \times {\text{1 + 12 + 16 = 60}}\,{\text{g}}\,{\text{mo}}{{\text{l}}^{ - 1}}$
The mass of urea is given as $1.68 \times {10^4}$g
Now, we calculate the number of moles of urea.
Moles of urea$ = \dfrac{{16800\,{\text{g}}\,{\text{mo}}{{\text{l}}^{ - 1}}}}
{{60\,{\text{g}}}} = 280\,{\text{moles}}$
Now, we have to calculate the number of atoms of every element of urea. We know Avogadro's number represents the number of atoms of every element in 1 mole of substance. The Avogadro’s number is $6.022 \times {10^{23}}$.
Number of nitrogen atom:
1 mole of urea contains N atoms = $2 \times 6.022 \times {10^{23}}$
280 mole of urea contains N atoms = $2 \times 6.022 \times {10^{23}} \times 280 = 3372 \times {10^{23}}$
Number of carbon atom:
1 mole of urea contains C atoms = $1 \times 6.022 \times {10^{23}}$
280 mole of urea contains C atoms = $1 \times 6.022 \times {10^{23}} \times 280 = 1686.16 \times {10^{23}}$
Number of oxygen atom:
1 mole of urea contains O atoms = $1 \times 6.022 \times {10^{23}}$
280 mole of urea contains O atoms = $1 \times 6.022 \times {10^{23}} \times 280 = 1686.16 \times {10^{23}}$
Number of hydrogen atom:
1 mole of urea contains H atoms = $4 \times 6.022 \times {10^{23}}$
280 mole of urea contains H atoms = $4 \times 6.022 \times {10^{23}} \times 280 = 6744.64 \times {10^{23}}$

Note: The number $6.022 \times {10^{23}}$is named in honor of the Italian physicist Amedeo Avogadro. The Avogadro's number aids in counting very small particles. Different kinds of particles, such as molecules, atoms, ions, electrons are representative particles. One mole of anything consists of $6.022 \times {10^{23}}$ representative particles.