Question

which of the following contains the greater number of atoms?
A) One gram of butane
B) One gram of nitrogen
C) One gram of silver
D) One gram of water

Answer 1

Hint: Here first write down the molecular formula of each compound, then calculate the molecular mass of the given molecule, the molecular mass gives the mass of one mole of the substance. Since one mole of any substance contains Avogadro's number of molecules, calculate how many molecules are present in one gram of each compound and then calculate how many atoms are present in one gram and compare the values to get the answer.

 Complete step by step answer:
1) Molecular formula of butane$C{H_3}C{H_2}C{H_2}C{H_3}$
Molecular mass of one mole of butane$ = \left( {12g \times 4} \right) + \left( {1g \times 10} \right) = 48 + 10 = 58g$
One mole of any substance contains Avogadro's number of particles
Thus, 58g of butane contains $6.023 \times {10^{23}}$ number of molecules of butane
Therefore, 1g of butane contains \[ = \dfrac{{1g \times 6.022 \times {{10}^{23}}}}{{58g}} = 0.1038 \times {10^{23}}\] molecules
They have asked us calculate number of atoms not just number of molecules, therefore each molecule of butane contains 14 atoms
Thus,\[0.1038 \times {10^{23}}\] molecules of butane contains$ = 0.1038 \times {10^{23}} \times 14 = 1.4532 \times {10^{23}}$atoms
2)Molecular formula of nitrogen ${N_2}$
Molecular mass of one mole of nitrogen$ = 14g \times 2 = 28g$
Therefore, 1g of nitrogen contains\[ = \dfrac{{1g \times 6.022 \times {{10}^{23}}}}{{28g}} = 0.2150 \times {10^{23}}\] molecules
Each molecule of nitrogen contains 2 atoms
Thus,\[0.2150 \times {10^{23}}\] molecules of nitrogen contains$ = 0.2150 \times {10^{23}} \times 2 = 0.43 \times {10^{23}}$atoms
3) Silver is a noble metal so it can exist as pure silver metal, therefore we here take atomic mass and not molecular mass of silver
Atomic mass of one mole of silver$ = 107.9g$
Therefore 1g of silver contains\[ = \dfrac{{1g \times 6.022 \times {{10}^{23}}}}{{107.9g}} = 0.0558 \times {10^{23}}\] atoms.
4) Molecular formula of water is${H_2}O$
Molecular mass of one mole of water$ = \left( {1g \times 2} \right) + \left( {16g \times 1} \right) = 2 + 16 = 18g$
 Therefore, 1g of water contains\[ = \dfrac{{1g \times 6.022 \times {{10}^{23}}}}{{18g}} = 0.3345 \times {10^{23}}\] of molecules
Each molecule of water contains 3 atoms
Thus,\[0.3345 \times {10^{23}}\] molecules of water contain$ = 0.3345 \times {10^{23}} \times 3 = 1.0035 \times {10^{23}}$atoms.
When we compare answers of each option we see that one gram of butane has the highest number of atoms in it.
Therefore option A is correct.

Note: while reading the question be careful and see whether they have asked the number of molecules or number of atoms, if they had asked us which option has greater number of molecules than it would be option D.