Calculate the % empty space in 1 mole of water at 25 degree C (d=0.9971g/ml). The volume of a water molecule can be taken as the sum of the volumes of the 2 hydrogen molecules and the oxygen atom. Use the single bonded covalent radii of 37pm for hydrogen and 66pm for oxygen.
Oh, calculating empty space in water? That's like trying to find a fish in an empty bathtub! But hey, I'll give it a shot for you.
First, let's calculate the total volume of a mole of water. We can use its density. The density of water at 25 degrees Celsius is 0.9971 g/mL. Since 1 mole of water is equal to its molar mass (18.015 g/mol) in grams, we can divide it by the density to find the volume.
Volume of 1 mole of water = (Molar mass of water) / (Density of water)
= 18.015 g/mol / 0.9971 g/mL
≈ 18.095 mL
Next, let's calculate the volume occupied by the water molecules. The volume of a water molecule is the sum of the volumes of two hydrogen atoms and one oxygen atom. The volume of a sphere can be calculated using the formula (4/3) π r^3, where r is the radius.
Volume of 1 water molecule = 2 * (4/3) π (37 pm)^3 (for hydrogen atoms)
+ (4/3) π (66 pm)^3 (for oxygen atom)
≈ 71.6 ų
Now, to find the percentage empty space in water, we can subtract the volume occupied by the water molecules from the total volume of a mole of water and then divide by the total volume.
% Empty space = [(Total volume - Volume occupied by molecules) / Total volume] x 100
= [(18.095 mL - 71.6 ų) / 18.095 mL] x 100
Hold on, I need to switch units here... Ahhh, the joy of conversions!
% Empty space = [(18.095 mL - 71.6 × 10¯² ų) / 18.095 mL] x 100
After plugging in the values and calculating, you should get the approximate % empty space in 1 mole of water at 25 degrees Celsius. Just remember, water molecules are quite snug in their arrangements, so these calculations may not represent swimming pool-sized gaps.
To calculate the % empty space in 1 mole of water, we need to determine the total volume occupied by the water molecules and subtract it from the total volume available.
First, let's calculate the volume of one water molecule.
1. Calculate the volume of the hydrogen molecules:
The covalent radius of hydrogen (H) is given as 37 pm. We can assume a spherical shape for each hydrogen atom.
Volume of one hydrogen atom = 4/3 * pi * (radius of H)^3 = 4/3 * 3.14 * (37 pm / 1000)^3 = 4.07 x 10^-5 mL
Since there are two hydrogen molecules in one water molecule, the total volume of the hydrogen molecules is:
Volume of hydrogen atoms = 2 * 4.07 x 10^-5 mL
2. Calculate the volume of the oxygen atom:
The covalent radius of oxygen (O) is given as 66 pm. We can assume a spherical shape for the oxygen atom.
Volume of oxygen atom = 4/3 * pi * (radius of O)^3 = 4/3 * 3.14 * (66 pm / 1000)^3 = 1.44 x 10^-4 mL
3. Calculate the total volume of one water molecule:
Total volume of one water molecule = Volume of hydrogen atoms + Volume of oxygen atom
Next, let's calculate the total volume occupied by 1 mole of water molecules.
4. Calculate the molar mass of water (H2O):
The molar mass of H2O = 2 * molar mass of H (hydrogen) + 1 * molar mass of O (oxygen)
= 2 * 1 g/mol + 1 * 16 g/mol
= 18 g/mol
5. Calculate the number of moles in 1 mole of water:
Since the molar mass of water is 18 g/mol, 1 mole of water contains 1 mole of water molecules.
6. Calculate the total volume occupied by 1 mole of water molecules:
Total volume = Total volume of one water molecule * number of moles in 1 mole of water
= Total volume of one water molecule * 1
Finally, let's calculate the % empty space:
7. Calculate the % empty space:
% empty space = (Total volume available - Total volume occupied) / Total volume available * 100
Remember to convert all volumes in the same units (ml in this case), and you should be able to plug in the values from the previous steps to perform the final calculations.
To calculate the % empty space in 1 mole of water, we need to find the total volume occupied by the water molecules and compare it to the volume of the container containing 1 mole of water.
1. Calculate the molar mass of water (H2O):
- The atomic mass of hydrogen (H) is approximately 1 g/mol.
- The atomic mass of oxygen (O) is approximately 16 g/mol.
- Since there are two hydrogen atoms and one oxygen atom in water, the molar mass of water is:
Molar mass of H2O = (2 * 1 g/mol) + (1 * 16 g/mol) = 18 g/mol.
2. Calculate the mass of 1 mole of water (m):
- Given that the density (d) of water is 0.9971 g/mL, this means that 1 mL of water will have a mass of 0.9971 grams.
- Since 1 mole of water is equal to its molar mass (18 g), the mass of 1 mole of water is:
m = d * V = 0.9971 g/mL * 18 mL = 17.9478 g.
3. Calculate the total volume of the molecules in 1 mole of water (V_molecules):
- The volume of a water molecule can be taken as the sum of the volumes of the two hydrogen molecules and the oxygen atom.
- The volume of a sphere is given by the formula: V = (4/3) * π * r^3.
- Convert the radii to picometers (pm) to ensure consistent units.
- For hydrogen (H), with a radius of 37 pm:
V_hydrogen = (4/3) * π * (37 pm)^3.
- For oxygen (O), with a radius of 66 pm:
V_oxygen = (4/3) * π * (66 pm)^3.
- Since there are two hydrogen atoms in a water molecule and one oxygen atom, the total volume of the molecules in 1 mole of water is:
V_molecules = 2 * V_hydrogen + V_oxygen.
4. Calculate the % empty space (E) in 1 mole of water:
- The volume of the container containing 1 mole of water is equal to the molar volume of water, which is approximately 18 mL/mol.
- The % empty space can be calculated using the formula:
E = ((V_container - V_molecules) / V_container) * 100.
- Here, V_container is the volume of the container containing 1 mole of water, which is equal to the molar volume of water.
Let's plug in the values and calculate:
V_hydrogen = (4/3) * π * (37 pm)^3
V_oxygen = (4/3) * π * (66 pm)^3
V_molecules = 2 * V_hydrogen + V_oxygen
V_container = 18 mL
% empty space (E) = ((V_container - V_molecules) / V_container) * 100
Now, you can substitute the values into the equations and calculate the % empty space in 1 mole of water at 25 degrees Celsius.