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
Question
1 Answer

1. User Answers JalenOblong
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