Chemistry

Question

What is the difference in mass between 3.01×10^24 atoms of gold and a gold bar with the dimensions 6.00 cm X 4.25 cm X 2.00 cm

1 Answer

  • Answer:

    The difference in mass between 3.01×10^24 atoms of gold and a gold bar with the dimensions 6.00 cm X 4.25 cm X 2.00 cm is :

    Difference  in mass = 985.32 - 984.5 = 0.82 g

    Explanation:

    Part I :

    [tex]n =\frac{3.01\times 10^{24}}{6.022\times 10^{23}}[/tex]

    n = 4.9983

    n = 4.99 moles

    (Note : You can also take n = 5 mole )

    Molar mass of gold = 196.96 g/mole

    This means, 1 mole of gold(Au) contain = 196.96 grams

    So, 4.99 moles of gold contain = [tex]5\times 196.96[/tex] g

    4.99 moles of gold contain = 984.8 g

    Mass of [tex]{3.01\times 10^{24}}[/tex] atoms of gold = 984.5 g

    Part II :

    Density of Gold = [tex]19.32 g/cm^{3}[/tex]

    Volume of the cuboid = [tex]length\times breadth\times height[/tex]

    Volume of the gold bar =[tex]6.00\times 4.25\times 2.00[/tex]

    Volume of the gold bar = 51[tex]cm^{3}[/tex]

    Using formula,

    [tex]Density = \frac{mass}{Volume}[/tex]

    [tex]Mass = Density\times Volume[/tex]

    [tex]Mass = 19.32 \times 51[/tex]

    Mass = 985.32 g

    So, A  gold bar with the dimensions 6.00 cm X 4.25 cm X 2.00 cm has mass of 985.32 g

    Difference  in mass = 985.32 - 984.5 = 0.82 g

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