The density of (Hg) is 13.53 g/mL. How many liters will 4.2x10^21 atoms of Hg occupy?
mols Hg = 4.2E21/6.02E23 = ?
grams Hg = mols x atomic mass = ?
Since mass = volume x density that can be rearranged to volume = mass/density. Substitute mass from above and density in the problem and solve for mL as the volume and convert to L.
To find the volume, in liters, occupied by a given number of atoms of Hg, we need to follow these steps:
Step 1: Determine the molar mass of Hg (mercury).
Step 2: Convert the number of atoms of Hg into moles.
Step 3: Calculate the mass of Hg using the moles and molar mass.
Step 4: Use the density of Hg to find the volume in milliliters.
Step 5: Convert the volume from milliliters to liters.
Let's go through the steps in detail:
Step 1: Determine the molar mass of Hg (mercury).
The molar mass of Hg is found on the periodic table. The atomic mass of mercury (Hg) is approximately 200.59 g/mol.
Step 2: Convert the number of atoms of Hg into moles.
Given: 4.2 x 10^21 atoms of Hg
Avogadro's number states that 1 mole of any substance contains 6.022 x 10^23 atoms. We can use this to convert the atoms into moles:
(4.2 x 10^21 atoms of Hg) x (1 mol/6.022 x 10^23 atoms) ≈ 6.97 x 10^-3 mol of Hg
Step 3: Calculate the mass of Hg using the moles and molar mass.
To find the mass of Hg, we multiply the moles of Hg by the molar mass:
Mass of Hg = (6.97 x 10^-3 mol of Hg) x (200.59 g/mol) ≈ 1.395 g of Hg
Step 4: Use the density of Hg to find the volume in milliliters.
Given density of Hg: 13.53 g/mL
Density is defined as mass/volume, so we can rearrange the formula to solve for volume:
Volume (in milliliters) = Mass/Density
Volume (in milliliters) = 1.395 g of Hg / 13.53 g/mL ≈ 0.103 mL of Hg
Step 5: Convert the volume from milliliters to liters.
Since there are 1000 mL in 1 L, we can convert the volume from milliliters to liters:
Volume (in liters) = 0.103 mL / 1000 ≈ 1.03 x 10^-4 L
Therefore, 4.2 x 10^21 atoms of Hg will occupy approximately 1.03 x 10^-4 liters of space.