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.

First, we need to find the total volume of 1000 ml (1L) of water and the total volume of the water molecules in 1 mole of water. Then we can find the % empty space.

1. Find the mass of 1 mole of water.
Molar mass of water (H2O) = 2 * molar mass of H + molar mass of O
Molar mass of water = 2 * 1 g/mol (Hydrogen) + 16 g/mol (Oxygen) = 18 g/mol

2. Find the mass of 1 L (1000 ml) of water at 25 °C.
Density at 25°C = 0.9971 g/ml
Mass = Volume * Density
Mass = 1000 ml * 0.9971 g/ml = 997.1 g

3. Calculate the number of moles in 1L of water.
Number of moles = mass / molar mass = 997.1 g / 18 g/mol = 55.39 moles

4. Calculate the volume of one water molecule.
Volume of 1 H atom = 4/3 * pi * r^3 = 4/3 * pi * (37 pm)^3
Volume of 1 O atom = 4/3 * pi * r^3 = 4/3 * pi * (66 pm)^3
We assume that the H2O molecule is formed by overlapping volumes of 2 H atoms and 1 O atom.
Volume of 1 water molecule = (1 * Volume of O atom) + (2 * Volume of H atom)

5. Calculate the total volume of 1 mole of water molecules.
Total volume of water molecules = (number of moles) * (volume of 1 water molecule)

6. Calculate the volume of water containing 1 mole of water at 25 °C (assuming 1 mole occupies 1000 ml).
Total volume of 1 L water = 1000 ml

7. Calculate the % empty space.
% empty space = ((total volume of 1 L water - total volume of water molecules) / total volume of 1 L water) * 100

Let's calculate these values:

Volume of 1 H atom = 4/3 * pi * (37*10^-12 m)^3 = 2.11 * 10^-28 m^3
Volume of 1 O atom = 4/3 * pi * (66*10^-12 m)^3 = 1.20 * 10^-27 m^3
Volume of 1 water molecule = (1 * 1.20*10^-27) + (2 * 2.11*10^-28) = 1.54 * 10^-27 m^3
Total volume of water molecules = 55.39 moles * 1.54 * 10^-27 m^3/mole = 8.52 * 10^-26 m^3 (divide by 1000 to convert to liters)
Total volume of 1 L water = 1000 ml / 1000 = 1 L = 1 m^3
% empty space = ((1 - 8.52 * 10^-26) / 1) * 100 = 99.99999991 %

The % empty space in 1 mole of water at 25 °C is approximately 99.99999991 %.

To calculate the % empty space in 1 mole of water at 25 degrees Celsius, we need to first determine the total volume occupied by water molecules and then calculate the empty space.

Step 1: Calculate the volume of one water molecule:
The volume of a water molecule can be calculated as the sum of the volumes of the two hydrogen atoms and one oxygen atom.

Volume of one water molecule = Volume of 2 hydrogen atoms + Volume of 1 oxygen atom

The formula for the volume of a sphere is V = 4/3 * π * r^3, where r is the radius.

The radius of a hydrogen atom (single-bonded covalent radius) is given as 37 pm (picometers). Converting this to meters: 37 pm = 37 * 10^-12 m.

Similarly, the radius of an oxygen atom (single-bonded covalent radius) is given as 66 pm. Converting this to meters: 66 pm = 66 * 10^-12 m.

Using these values, we can calculate the volume of one water molecule.

Volume of one hydrogen atom = 4/3 * π * (37 * 10^-12 m)^3
Volume of two hydrogen atoms = 2 * Volume of one hydrogen atom
Volume of oxygen atom = 4/3 * π * (66 * 10^-12 m)^3

Step 2: Calculate the total volume occupied by water molecules:
Since 1 mole of water contains Avogadro's number (6.022 x 10^23) of water molecules, we can multiply the volume of one water molecule by Avogadro's number to get the total volume occupied by water molecules.

Total volume occupied by water molecules = Volume of one water molecule * Avogadro's number

Step 3: Calculate the empty space:
The empty space is the difference between the total volume occupied by water molecules and the volume of 1 mole of water.

Empty space = Volume of 1 mole of water - Total volume occupied by water molecules

Step 4: Calculate the % empty space:
Finally, we can convert the empty space into a percentage.

% Empty space = (Empty space / Volume of 1 mole of water) * 100

Now, let's put these values into the equations and calculate the % empty space.

Volume of one hydrogen atom = 4/3 * π * (37 * 10^-12 m)^3
Volume of two hydrogen atoms = 2 * Volume of one hydrogen atom
Volume of oxygen atom = 4/3 * π * (66 * 10^-12 m)^3

Total volume occupied by water molecules = Volume of one water molecule * Avogadro's number

Empty space = Volume of 1 mole of water - Total volume occupied by water molecules

% Empty space = (Empty space / Volume of 1 mole of water) * 100

By substituting the given values and performing the calculations, you can find the % empty space in 1 mole of water at 25 degrees Celsius.

To calculate the % empty space in 1 mole of water, we first need to determine the volume occupied by a water molecule.

The volume of a water molecule can be calculated by summing the volumes of the two hydrogen atoms and the oxygen atom.

Volume of a water molecule = 2 * (volume of hydrogen atom) + volume of oxygen atom

The volume of a sphere can be calculated using the formula:

Volume of a sphere = (4/3) * π * r^3

Where r is the radius of the sphere.

Given that the single bonded covalent radii of hydrogen and oxygen are 37 pm and 66 pm respectively, we can convert these values to meters.

Radius of hydrogen atom (in meters) = 37 pm * (1 m / 10^12 pm)
Radius of oxygen atom (in meters) = 66 pm * (1 m / 10^12 pm)

We can then substitute these values into the formula to calculate the volumes of the hydrogen and oxygen atoms:

Volume of hydrogen atom = (4/3) * π * (radius of hydrogen atom)^3
Volume of oxygen atom = (4/3) * π * (radius of oxygen atom)^3

Next, we need to determine the molar mass of water. Water (H2O) consists of 2 hydrogen atoms and 1 oxygen atom.

Molar mass of water = (2 * atomic mass of hydrogen) + atomic mass of oxygen

Finally, using the density of water at 25 degrees Celsius (d = 0.9971 g/mL), we can calculate the volume occupied by 1 mole of water.

Volume occupied by 1 mole of water = (1 mole water) * (molar mass of water) / (density of water)

To calculate the % empty space, we subtract the volume of a water molecule from the volume occupied by 1 mole of water. We then divide this difference by the volume occupied by 1 mole of water and multiply by 100.

% empty space = [(Volume occupied by 1 mole of water) - (Volume of a water molecule)] / (Volume occupied by 1 mole of water) * 100

Let's calculate the % empty space step by step.