How many atoms are in a drop of mercury that has a diameter of 1.0 mm? (Volume of a sphere is 4ðr3/3; density of mercury = 13.6 g/cm3)
Molar mass of Mercury = 200g/mole, look it up.
Assume drop of mercury is a sphere, apply the formula pi * r^3 * 4/3 = volume.
Use the density.
Should be fairly simple.
(4π/3 * 0.05^3 cm^3) * 13.6g/cm^3 * 1mol/200g * 6.023*10^23atom/mol = 2.144x10^19 atoms
To calculate the number of atoms in a drop of mercury, we need to follow these steps:
1. Find the volume of the drop using the formula for the volume of a sphere:
Volume = (4πr³) / 3,
where r is the radius of the sphere (half the diameter). Given that the diameter is 1.0 mm, the radius would be 0.5 mm.
Radius = 0.5 mm = 0.05 cm.
Substituting the values:
Volume = (4π * (0.05 cm)³) / 3.
2. Convert the volume from cm³ to mL since density is given in g/cm³:
1 cm³ = 1 mL.
Therefore, Volume = (4π * (0.05 mL)³) / 3.
3. Calculate the mass of the drop using the formula:
Mass = Density * Volume.
Given that the density of mercury is 13.6 g/cm³, substitute the values:
Mass = 13.6 g/cm³ * Volume.
4. Convert the mass from grams to atomic mass units (amu):
1 g = 6.022 x 10²³ amu.
Therefore, Mass_amu = Mass * (6.022 x 10²³ amu / 1 g).
5. Find the molar mass of mercury (Hg):
The atomic mass of mercury is approximately 200.59 g/mol.
6. Calculate the number of moles of mercury in the drop using the formula:
Moles = Mass / Molar mass.
Substitute the values:
Moles = Mass_amu / (200.59 g/mol).
7. Calculate the number of atoms in the drop using Avogadro's number:
1 mole = 6.022 x 10²³ atoms.
Therefore, Number of atoms = Moles * (6.022 x 10²³ atoms / 1 mole).
Now, let's calculate step-by-step:
Step 1: Compute the volume
Volume = (4π * (0.05 cm)³) / 3.
= (4π * 0.000125 cm³) / 3.
= 0.0005236 cm³.
Step 2: Convert the volume to mL
Volume (mL) = 0.0005236 cm³.
Step 3: Calculate the mass of the drop
Mass = 13.6 g/cm³ * Volume (mL).
= 13.6 g/cm³ * 0.0005236 mL.
≈ 0.00712 g.
Step 4: Convert the mass to amu
Mass_amu = Mass * (6.022 x 10²³ amu / 1 g).
= 0.00712 g * (6.022 x 10²³ amu / 1 g).
≈ 4.29 x 10²¹ amu.
Step 5: Find the molar mass of mercury (Hg)
Molar mass = 200.59 g/mol.
Step 6: Calculate the number of moles of mercury in the drop
Moles = Mass_amu / Molar mass.
= 4.29 x 10²¹ amu / 200.59 g/mol.
≈ 2.14 x 10²¹ mol.
Step 7: Calculate the number of atoms in the drop
Number of atoms = Moles * (6.022 x 10²³ atoms / 1 mole).
= 2.14 x 10²¹ mol * (6.022 x 10²³ atoms / 1 mole).
≈ 1.29 x 10⁴⁴ atoms.
Therefore, there are approximately 1.29 x 10⁴⁴ atoms in a drop of mercury with a diameter of 1.0 mm.
To find the number of atoms in a drop of mercury, we need to follow these steps:
Step 1: Calculate the volume of the drop
Using the formula for the volume of a sphere, we have V = (4/3)πr^3. Since the diameter is given as 1.0 mm, the radius (r) is half of that, so r = 0.5 mm = 0.05 cm.
V = (4/3)π(0.05 cm)^3
V ≈ 0.0005236 cm^3
Step 2: Calculate the mass of the drop
Given that the density of mercury is 13.6 g/cm^3, we can calculate the mass (m) of the drop using the formula m = density × volume.
m = 13.6 g/cm^3 × 0.0005236 cm^3
m ≈ 0.0071296 g
Step 3: Convert mass to moles
To convert the mass of the drop into moles, we need to use the molar mass of mercury. The molar mass of mercury is approximately 200.59 g/mol.
moles = mass / molar mass
moles ≈ 0.0071296 g / 200.59 g/mol
moles ≈ 3.555 × 10^-5 mol
Step 4: Calculate the number of atoms
One mole contains 6.022 × 10^23 atoms (Avogadro's number), so we can calculate the number of atoms in the drop:
number of atoms = moles × Avogadro's number
number of atoms ≈ 3.555 × 10^-5 mol × 6.022 × 10^23 atoms/mol
number of atoms ≈ 2.138 × 10^19 atoms
Therefore, there are approximately 2.138 × 10^19 atoms in a drop of mercury with a diameter of 1.0 mm.