To calculate the number of N, C, O, and H atoms in 1.78*10^4g of urea, we need to first calculate the number of moles of urea, and then use the mole ratios between the elements and the compound.
The molar mass of urea can be calculated by adding up the atomic masses of its constituent elements:
Molar mass of urea = 2(14.01 g/mol N) + 2(1.01 g/mol H) + 12.01 g/mol C + 1(16.00 g/mol O)
= 60.06 g/mol
To calculate the number of moles of urea, we can divide the given mass by the molar mass:
Number of moles of urea = 1.78*10^4 g / 60.06 g/mol
= 296.26 mol
Using the chemical formula (NH2)2CO, we can see that there are 2 nitrogen atoms (N), 1 carbon atom (C), 1 oxygen atom (O), and 2 hydrogen atoms (H) in one molecule of urea.
Therefore, in 296.26 moles of urea, there are:
- 2 nitrogen atoms x 296.26 moles = 592.52 moles of N
- 1 carbon atom x 296.26 moles = 296.26 moles of C
- 1 oxygen atom x 296.26 moles = 296.26 moles of O
- 2 hydrogen atoms x 296.26 moles = 592.52 moles of H
To convert from moles to atoms, we can use Avogadro's number, which is the number of atoms in one mole of a substance:
1 mole = 6.022 x 10^23 atoms
Therefore, in 1.78*10^4g of urea, there are:
- 2 nitrogen atoms x 296.26 moles x 6.022 x 10^23 atoms/mole = 7.16 x 10^26 atoms of N
- 1 carbon atom x 296.26 moles x 6.022 x 10^23 atoms/mole = 1.79 x 10^26 atoms of C
- 1 oxygen atom x 296.26 moles x 6.022 x 10^23 atoms/mole = 1.79 x 10^26 atoms of O
- 2 hydrogen atoms x 296.26 moles x 6.022 x 10^23 atoms/mole = 7.16 x 10^26 atoms of H
Therefore, there are approximately 7.16 x 10^26 atoms of N, 1.79 x 10^26 atoms of C, 1.79 x 10^26 atoms of O, and 7.16 x 10^26 atoms of H in 1.78*10^4g of urea.