If Gold sells for $1200.00 an ounce, how many atoms of gold can you buy for a penny? Please, Show work.
I think Au is sold in TROY ounces and 1 Troy ounce = 31.1 grams.
There are 6.02E23 Au atoms in 197 g Au (actually 196.97 and you can use that number if you wish).
So 31.1 g Au costs $1200 and contains 6.02E23 Au atoms x (31.1/197)= about 9.5E22 atoms.
atoms/dollar = 9.5E22 atoms/1200 = about 7.2E19.
So (7.2E19 atoms/$1) x $0.01 dollars = ?
To determine how many atoms of gold can be purchased for a penny, we will need to calculate the number of moles of gold that can be bought with a penny. Then, we can use Avogadro's number to convert the moles to atoms.
1. Determine the price per ounce of gold: $1200.00/ounce.
2. Convert the price to cents per ounce: $1200.00 * 100 cents/dollar = 120,000 cents/ounce.
3. Determine the weight of gold in one mole: The molar mass of gold is 196.97 grams/mole.
4. Convert the weight of gold in one mole to ounces: 196.97 grams/mole * 1 ounce/28.35 grams = 6.9484 ounces/mole.
5. Calculate the number of moles of gold that can be bought for the given price: 1 penny / 120,000 cents/ounce * 1 ounce/6.9484 ounces/mole = 1.436 * 10^(-8) moles.
6. Convert the moles of gold to atoms using Avogadro's number:
1.436 * 10^(-8) moles * 6.022 * 10^23 atoms/mole = 8.65 * 10^15 atoms.
Therefore, for a penny, you can buy approximately 8.65 * 10^15 atoms of gold.