Respuesta :
Answer :
The number of atoms of copper are [tex]3.540\times 10^{24}[/tex]
The number of atoms of zinc are [tex]6.197\times 10^{24}[/tex]
Explanation :
First we have to calculate the total mass of brass.
Formula used :
[tex]Density=\frac{Mass}{Volume}[/tex]
[tex]8.48g/cm^3=\frac{Mass}{122.5cm^3}[/tex]
[tex]Mass=(8.48g/cm^3)\times (122.5cm^3)=1038.8g[/tex]
Total mass of brass = 1038.8 g
Now we have to calculate the mass of zinc and copper.
As we are given that, 37 % zinc by mass that means 37 g of zinc present in 100 g of mixture.
Mass of zinc = 37 g
Total mass of mixture (brass) = 100 g
Mass of copper = 100 - 37 = 63 g
Mass of zinc = [tex]1038.8g\times \frac{37}{100}=384.36g[/tex]
Mass of copper = [tex]1038.8g\times \frac{63}{100}=654.44g[/tex]
Now we have to calculate the moles of zinc and copper.
Molar mass of zinc = 65.38 g/mole
Molar mass of copper = 63.55 g/mole
[tex]\text{ Moles of }Zn=\frac{\text{ Mass of }Zn}{\text{ Molar mass of }Zn}=\frac{384.36g}{65.38g/mole}=5.879moles[/tex]
[tex]\text{ Moles of }Cu=\frac{\text{ Mass of }Cu}{\text{ Molar mass of }Cu}=\frac{654.44g}{63.55g/mole}=10.29moles[/tex]
Now we have to calculate the number of atoms of copper.
As, 1 mole of copper contains [tex]6.022\times 10^{23}[/tex] number of copper atoms
So, 5.879 moles of copper contains [tex]5.879\times 6.022\times 10^{23}=3.540\times 10^{24}[/tex] number of copper atoms
The number of atoms of copper are [tex]3.540\times 10^{24}[/tex]
Now we have to calculate the number of atoms of zinc.
As, 1 mole of zinc contains [tex]6.022\times 10^{23}[/tex] number of zinc atoms
So, 10.29 moles of zinc contains [tex]10.29\times 6.022\times 10^{23}=6.197\times 10^{24}[/tex] number of zinc atoms
The number of atoms of zinc are [tex]6.197\times 10^{24}[/tex]
