density of gold is 19.32 g/cm^3.A piece of gold leaf is 2.50 cm on each side and 0.100 mm thick,How many atoms of gold are in this piece of gold leaf?
To find the number of atoms in the given piece of gold leaf, we need to follow these steps:
1. Calculate the volume of the gold leaf:
- The gold leaf is a rectangular prism, with dimensions 2.50 cm on each side and 0.100 mm thick.
- Since the volume formula for a rectangular prism is V = l × w × h, we can plug in the values and convert the thickness from millimeters to centimeters:
- V = 2.50 cm × 2.50 cm × 0.100 cm
2. Calculate the mass of the gold leaf:
- The density of gold is given as 19.32 g/cm^3.
- Since density = mass/volume, we can rearrange the formula to find the mass:
- mass = density × volume
3. Find the molar mass of gold:
- The molar mass of an element tells us the mass of one mole of that element. In this case, we need the molar mass of gold.
- According to the periodic table, the atomic mass of gold (Au) is 196.97 g/mol.
4. Use the molar mass to calculate the number of moles of gold:
- The number of moles can be calculated using the formula:
- moles = mass/molar mass
5. Determine Avogadro's number:
- Avogadro's number is the number of atoms or molecules per mole, and it is approximately equal to 6.022 × 10^23.
6. Calculate the number of atoms:
- The number of atoms can be calculated using the formula:
- atoms = moles × Avogadro's number
Now, let's follow these steps to find the number of atoms in the given piece of gold leaf:
1. Calculate the volume of the gold leaf:
- V = 2.50 cm × 2.50 cm × 0.100 cm = 0.625 cm^3
2. Calculate the mass of the gold leaf:
- mass = density × volume = 19.32 g/cm^3 × 0.625 cm^3
3. Find the molar mass of gold:
- The molar mass of gold is 196.97 g/mol.
4. Use the molar mass to calculate the number of moles of gold:
- moles = mass/molar mass
5. Determine Avogadro's number:
- Avogadro's number is approximately 6.022 × 10^23.
6. Calculate the number of atoms:
- atoms = moles × Avogadro's number
By following these steps and plugging in the appropriate values, you can find the number of atoms in the given piece of gold leaf.
To find the number of atoms in a piece of gold leaf, we first need to calculate the volume of the gold leaf using its dimensions and then use the density of gold to find the mass. Finally, we can determine the number of atoms using Avogadro's number.
1. Calculate the volume of the gold leaf:
The gold leaf is a rectangle with dimensions 2.50 cm x 2.50 cm x 0.100 mm. To find the volume, we multiply the three dimensions:
Volume = (2.50 cm) x (2.50 cm) x (0.100 mm)
Note: We need to convert the thickness from millimeters to centimeters to ensure consistent units.
Thickness = 0.100 mm = 0.100 mm x (1 cm / 10 mm) = 0.0100 cm
Volume = (2.50 cm) x (2.50 cm) x (0.0100 cm) = 0.0625 cm^3
2. Calculate the mass:
To find the mass of the gold leaf, we multiply the volume by the density of gold:
Mass = Volume x Density
Mass = 0.0625 cm^3 x 19.32 g/cm^3 = 1.205 g
3. Determine the number of atoms:
To find the number of atoms, we need to use Avogadro's number, which states that there are 6.022 x 10^23 atoms in one mole of any substance. The molar mass of gold (Au) is 197.0 g/mol.
First, calculate the number of moles of gold:
Moles = Mass / Molar mass
Moles = 1.205 g / 197.0 g/mol = 0.00612 mol
Next, use Avogadro's number to find the number of atoms:
Number of atoms = Moles x Avogadro's number
Number of atoms = 0.00612 mol x (6.022 x 10^23 atoms/mol)
Number of atoms = 3.68 x 10^21 atoms
Therefore, there are approximately 3.68 x 10^21 atoms of gold in the given piece of gold leaf.
volume = 2.5x2.5x.01 cm^3=.0625cm^3
mass of gold=density*volume=you do it.
massofoneatome*numberHere=massgold
numberHere=massofgold/atomicmassAu
and you can look up the atomic mass of Gold.