A lead atom has a mass of 3.40×10−22 g. How many lead atoms are in a cube of lead that has a volume of 1.40 cm^3 if the density of lead is 11.3 g/cm^3?
To find the number of lead atoms in a given volume of lead, we need to follow these steps:
Step 1: Calculate the mass of the cube of lead.
Given:
Density of lead = 11.3 g/cm³
Volume of the cube = 1.40 cm³
Mass = Density × Volume
Mass = 11.3 g/cm³ × 1.40 cm³
Step 2: Convert the mass of the cube from grams to atomic mass units (amu).
1 g = 6.022 × 10^23 amu
Mass in amu = Mass in grams × (1 mole/atomic mass of lead) × (6.022 × 10^23 atoms/mole)
Note: The atomic mass of lead is 207.2 amu.
Step 3: Calculate the number of lead atoms in the cube.
Number of atoms = Mass in amu × (1 atom/atomic mass in amu)
Let's perform the calculations:
Step 1:
Mass = 11.3 g/cm³ × 1.40 cm³
Mass = 15.82 g
Step 2:
Mass in amu = 15.82 g × (1 mole/207.2 amu) × (6.022 × 10^23 atoms/mole)
Mass in amu = 15.82 g × (1/207.2) × (6.022 × 10^23)
Mass in amu = 4.866 × 10^22 amu
Step 3:
Number of atoms = 4.866 × 10^22 amu × (1 atom/207.2 amu)
Number of atoms = 2.35 × 10^21 atoms
Therefore, there are approximately 2.35 × 10^21 lead atoms in the given cube of lead.
To find the number of lead atoms in a cube of lead, we need to use the given information about the mass, volume, and density of lead.
1. First, let's use the density of lead to find the mass of the lead cube. The formula for density is:
Density = Mass / Volume
Rearranging the formula, we can solve for mass:
Mass = Density * Volume
Plugging in the values:
Mass = 11.3 g/cm^3 * 1.40 cm^3
= 15.82 g
Therefore, the mass of the lead cube is 15.82 grams.
2. Next, we need to convert the lead mass from grams to atomic mass units (amu). The atomic mass unit is defined as 1/12th the mass of a carbon-12 atom, which is approximately 1.66 × 10^-24 grams.
Mass (in amu) = Mass (in grams) / Atomic mass unit (in grams)
Plugging in the values:
Mass (in amu) ≈ 15.82 g / 1.66 × 10^-24 g
= 9.54 × 10^23 amu
Therefore, the mass of the lead cube is approximately 9.54 × 10^23 atomic mass units.
3. Finally, we need to find the number of lead atoms in the lead cube using the atomic mass of lead. The atomic mass of lead (Pb) is approximately 207.2 amu.
Number of lead atoms = Mass (in amu) / Atomic mass of lead
Plugging in the values:
Number of lead atoms = 9.54 × 10^23 amu / 207.2 amu
≈ 4.61 × 10^21 lead atoms
Therefore, there are approximately 4.61 × 10^21 lead atoms in the given cube of lead.
Is the mass of the lead 3.4 x 10^(-22)
or literally 3.4 x 10 - 22 or just 22g?
The problem has given you volume and density.
D = mass/ volume
You're trying to find mass, so your equation's going to be m= dv
m= 15. 82 g
Divide this by whatever your mass was, either 3.4 x 10^(-22)
or 3.4 x 10 - 22 or just 22g.
That number will be the number of lead atoms in the cube.