A lead atom has a mass of 3.4x10^-9g. How many lead atoms are in a cube of lead that has a volume of 2.00cm^3 if the density of lead is 11.3g/cm^3?
Mass = volume x density
Solve for mass.
3.4E-9 g/atom x # atoms = mass
Solve for # atoms.
Thank you!!
To solve this problem, you will need to use the formula:
Number of atoms = (mass of substance / molar mass) * Avogadro's number
1. Calculate the mass of the cube of lead using its density and volume:
Mass = Density * Volume
Mass = 11.3 g/cm^3 * 2.00 cm^3
Mass = 22.6 g
2. Use the mass of the cube to find the number of moles of lead:
Moles = Mass / Molar mass
Molar mass of lead (Pb) = 207.2 g/mol
Moles = 22.6 g / 207.2 g/mol
Moles ≈ 0.109 mol
3. Calculate the number of lead atoms using Avogadro's number (6.022 x 10^23 atoms/mol):
Number of atoms = (Moles * Avogadro's number) / 1
Number of atoms = (0.109 mol * 6.022 x 10^23 atoms/mol) / 1
Number of atoms ≈ 6.573 x 10^22 atoms
Therefore, there are approximately 6.573 x 10^22 lead atoms in the given cube of lead.
To find the number of lead atoms in a given volume, we need to follow these steps:
Step 1: Calculate the mass of the lead cube.
Given that the density of lead is 11.3g/cm^3 and the volume of the lead cube is 2.00cm^3, we can find the mass using the formula:
mass = density x volume
mass = 11.3g/cm^3 x 2.00cm^3
mass = 22.6g
Step 2: Determine the number of moles of lead in the cube.
To calculate the number of moles, we will use the molar mass of lead, which is approximately 207.2g/mol.
moles = mass / molar mass
moles = 22.6g / 207.2g/mol
moles ≈ 0.109mol
Step 3: Calculate the number of lead atoms in the cube.
Avogadro's number tells us that there are 6.022 x 10^23 atoms in one mole of any substance.
So, to find the number of lead atoms:
number of atoms = moles x Avogadro's number
number of atoms ≈ 0.109mol x 6.022 x 10^23 atoms/mol
number of atoms ≈ 6.56 x 10^22 atoms
Therefore, there are approximately 6.56 x 10^22 lead atoms in the given cube of lead.