Question

Rhodium, a metal used as a catalyst and in jewelry, currently sells for $1500. per troy ounce. If 6.022 x 10^23 rhodium atoms have a mass of 102.9 grams, how many rhodium atoms could you buy for exactly one nickel

Answer 1

Answer:

$2.19 \times 10^{-4} \mathrm{Rh}$

Explanation:

Atomic mass of Nickel = 58.69 g/mol

Mass of 1 mole of nickel atom = 58.69 gm

Now, mass of 1 nickel atom = Gram atomic mass/Avogadro number

=$\frac{58.69}{6.023\times10^{22}} =9.744\times10^{23} g/atom$

Now, price of Rhodium =$1500 per troy ounce

Price of nickel in market  = 0.577$/oz

No. of rhodium atoms needed to buy 1 nickel atom is

$9.744 \times 10^{-23} \mathrm{g} \times \frac{1 \mathrm{oz}}{31.1035 \mathrm{g}} \times \frac{0.577 \mathrm{s}}{1 \mathrm{oz}} \times \frac{1 \mathrm{oz}}{1500 \mathrm{s}}$

$\quad \times \frac{31.1035 \mathrm{g}}{1 \mathrm{oz}} \times \frac{6.023 \times 10^{23} \mathrm{Rh} \text { atoms }}{102.9 \mathrm{g}}=2.19 \times 10^{-4} \mathrm{Rh} \text { atoms }$