How many atoms are there in a 5.2-g copper

Accepted Solution

Answer:There are [tex]4.93\times 10^{22}[/tex] copper atoms in 5.2 gram of metallic copper.Step-by-step explanation:Start by finding the number of moles of copper atoms in that 5.2 gram of metallic copper. Look up the relative atomic mass of copper on a modern periodic table.Cu: 63.546.In other words, the mass of one mole of copper atoms is 63.546 gram. [tex]M(\mathrm{Cu}) = \rm 63.546\; g\cdot mol^{-1}[/tex].How many moles of copper atoms in that 5.2 gram sample?[tex]\displaystyle n = \frac{m}{M} =\rm \frac{5.2\; g}{63.546\; g\cdot mol^{-1}} = 0.0818305\; mol[/tex].Now, how many atoms is [tex]\rm 0.0818305\; mol[/tex]?The Avogadro's Number gives the number of particles in one mole:[tex]N_A \approx \rm 6.022\times 10^{23}\;mol^{-1}[/tex]. (Encyclopedia Britannica)There are [tex]6.022\times 10^{23}[/tex] particles (a very large number) in one mole. [tex]\rm 0.0818305\; mol[/tex] of copper atoms will thus contain[tex]N = n\cdot N_A \approx \rm 0.0818305\; mol\times 6.023\times 10^{23}\;mol^{-1} \approx 4.93\times 10^{22}[/tex] copper atoms.