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Question: which of the following contains the greater number of atoms? A) One gram of butane B) One gram o...

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

Explanation

Solution

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 butaneCH3CH2CH2CH3C{H_3}C{H_2}C{H_2}C{H_3}
    Molecular mass of one mole of butane=(12g×4)+(1g×10)=48+10=58g = \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 6.023×10236.023 \times {10^{23}} number of molecules of butane
    Therefore, 1g of butane contains =1g×6.022×102358g=0.1038×1023 = \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,0.1038×10230.1038 \times {10^{23}} molecules of butane contains=0.1038×1023×14=1.4532×1023 = 0.1038 \times {10^{23}} \times 14 = 1.4532 \times {10^{23}}atoms
    2)Molecular formula of nitrogen N2{N_2}
    Molecular mass of one mole of nitrogen=14g×2=28g = 14g \times 2 = 28g
    Therefore, 1g of nitrogen contains=1g×6.022×102328g=0.2150×1023 = \dfrac{{1g \times 6.022 \times {{10}^{23}}}}{{28g}} = 0.2150 \times {10^{23}} molecules
    Each molecule of nitrogen contains 2 atoms
    Thus,0.2150×10230.2150 \times {10^{23}} molecules of nitrogen contains=0.2150×1023×2=0.43×1023 = 0.2150 \times {10^{23}} \times 2 = 0.43 \times {10^{23}}atoms
  2. 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 = 107.9g
    Therefore 1g of silver contains=1g×6.022×1023107.9g=0.0558×1023 = \dfrac{{1g \times 6.022 \times {{10}^{23}}}}{{107.9g}} = 0.0558 \times {10^{23}} atoms.
  3. Molecular formula of water isH2O{H_2}O
    Molecular mass of one mole of water=(1g×2)+(16g×1)=2+16=18g = \left( {1g \times 2} \right) + \left( {16g \times 1} \right) = 2 + 16 = 18g
    Therefore, 1g of water contains=1g×6.022×102318g=0.3345×1023 = \dfrac{{1g \times 6.022 \times {{10}^{23}}}}{{18g}} = 0.3345 \times {10^{23}} of molecules
    Each molecule of water contains 3 atoms
    Thus,0.3345×10230.3345 \times {10^{23}} molecules of water contain=0.3345×1023×3=1.0035×1023 = 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.