One particle(atom) of gold weight 197 atomic mass units. One atomic mass unit is approximately 1.6601 x 10^-24 grams. How many particles of gold are there in 197 grams of gold? Use scientific notation where and when appropriate.
hint
197g * 1atom/1.6601*10^-24 g = ? atoms
To find out the number of particles of gold in 197 grams, we need to calculate the number of moles of gold first using the atomic mass unit and then convert moles into particles.
Given:
Weight of one particle of gold = 197 atomic mass units
1 atomic mass unit = 1.6601 x 10^-24 grams
Mass of gold = 197 grams
Step 1: Calculate the number of moles of gold
To calculate the number of moles, we need to use the molar mass of gold. The molar mass of gold is the atomic mass in grams.
Molar mass of gold = 197 atomic mass units x (1.6601 x 10^-24 grams/1 atomic mass unit)
Molar mass of gold = 197 x 1.6601 x 10^-24 grams
Step 2: Calculate the number of moles of gold
Now we can calculate the number of moles of gold by dividing the given mass of gold by the molar mass of gold.
Number of moles of gold = Mass of gold / Molar mass of gold
Number of moles of gold = 197 grams / (197 x 1.6601 x 10^-24 grams)
Step 3: Convert moles into number of particles
Finally, we need to convert moles into the number of particles.
Avogadro's number states that there are 6.022 x 10^23 particles in one mole of any substance.
Number of particles of gold = Number of moles of gold x Avogadro's number
Number of particles of gold = (197 grams / (197 x 1.6601 x 10^-24 grams)) x (6.022 x 10^23 particles/mole)
Now you can plug in the values and calculate the number of particles of gold.