"Suppose you had a mole of gold atoms (radius=144pm) and could link the atoms together like a string of pearls. How many of these gold necklaces could you make using 1 mole of gold atoms so that each necklace would stretch from the earth to the sun? (Distance from earth to the sun =92.58 million miles; 1 mile=1.6093km)."
Au has a radius of 144 pm so the diameter is 288 pm and that is 288 x 10^-12 meters. Convert that to km, convert 92.58 million miles to km, and divide distance by the diameter. Post your work if you get stuck.
6.53*10-20
92.58*10^6 = 148,988,994km
148988994/2.88*10^-13=5.17*10^20
This doesn't seem right?
I got 1164.07 necklaces. The answer above is how many gold atoms it takes to go around the earth, but you have to divide that into Avagadro's number because that is how many atoms you have to work with. Idk. I could be wrong.
To solve this problem, we need to calculate the total length of one gold necklace made from a mole of gold atoms and then determine how many necklaces it would take to stretch from the earth to the sun.
First, let's calculate the length of one gold necklace made from a mole of gold atoms:
1. Calculate the molar mass of gold (Au): The molar mass of gold is approximately 197 grams per mole (g/mol).
2. Convert grams to moles: Since we have 1 mole of gold atoms, we don't need to convert anything.
3. Calculate the number of gold atoms: Avogadro's number tells us that there are approximately 6.022 x 10^23 atoms in 1 mole of any substance. So, we have 6.022 x 10^23 gold atoms.
4. Calculate the length of a single necklace: Each gold atom in the necklace is treated like a sphere with a radius of 144 picometers (pm). The total length of the necklace can be approximated by approximating the atoms as touching each other.
To calculate the length of one gold necklace, we can consider each molecule as a diameter, assuming they are arranged in a straight line.
Length of one atom = 2 x radius = 2 x 144 pm = 288 pm
For each necklace, we have (6.022 x 10^23 - 1) links connecting the atoms (since the first atom has no link on one side).
Length of one necklace = (6.022 x 10^23 - 1) x 288 pm
Now, let's convert the length of one necklace from picometers to kilometers:
1 kilometer (km) = 1,000,000,000,000 picometers (pm)
Length of one necklace in kilometers = [(6.022 x 10^23 - 1) x 288 pm] / (1,000,000,000,000 pm/km)
Next, let's calculate the distance from the earth to the sun in kilometers:
Distance from earth to sun = 92.58 million miles × 1.6093 km/mile
Finally, we can calculate how many gold necklaces can stretch from the earth to the sun:
Number of necklaces = Distance from earth to the sun / Length of one necklace in kilometers
By substituting the values of the distance from earth to the sun and the length of one necklace into the equation, we can find the answer.