Bond energy between two water molecules

[FaraDazed]

Homework Statement

Estimate the bond energy between two water molcules (liquid) in the following way

A: From the density of water and its molecular weight calculate the average distance between the molecules

B:hence show that there are 10^19 molcules per m^2 of surace

C:from the suraface tension of water, assuming this to be the same as the suraface energy, fine the value of U_0

Homework Equations

[tex]N_s ≈ \frac{1}{r_0^2} \\
\frac{1}{4}nU_0N_s \\
\gamma = \frac{F}{L} \\
[/tex]

The Attempt at a Solution

I am stuck straight away on part A. I know the density of water (1000 kg/m^3) and the molecular weight of H2O is 18 but have no idea how these are supposed to help me calculate the average distance between the molecules.

I am not looking for the answer but any hints on where to start would be very much appreciated.

 

[GregoryS]

The volume of one molecule (in m^3):
$$
V_1 = \frac {μ}{ρ N_A}
$$
where ## μ = 18×10^3 kg/mole##
## ρ = 10^3 kg/m^3##
## N_A = 6×10^{23} mole^{-1}##

 

[FaraDazed]

The volume of one molecule (in m^3):
$$
V_1 = \frac {μ}{ρ N_A}
$$
where ## μ = 18×10^3 kg/mole##
## ρ = 10^3 kg/m^3##
## N_A = 6×10^{23} mole^{-1}##

OK Thank you, what is mu called? (For example rho is density)

 

[haruspex]

OK Thank you, what is mu called? (For example rho is density)

I think it's supposed to be the molar mass of water (2xH+1xO = 18). But I believe it should be 18g/mol, the molar unit having been defined in terms of grammes before the old cgs units were replaced by MKS units. So that's 18 10^-3 kg/mol, not 18 10⁺³ kg/mol.

 

[Nickie]

I would approach this problem by first understanding the concept of bond energy between two molecules. Bond energy is the amount of energy required to break a bond between two atoms or molecules. In the case of water, we are looking at the bond energy between two water molecules.

To calculate the bond energy between two water molecules, we need to understand the average distance between them. This can be determined by using the given density of water (1000 kg/m^3) and its molecular weight (18 g/mol). By using the formula for density, we can convert the given density to units of molecules per cubic meter (m^-3). This will give us the number of water molecules present in one cubic meter of water.

Next, we can use the Avogadro's number (6.022 x 10^23 molecules/mol) to convert the number of molecules per cubic meter to the number of moles per cubic meter (mol/m^3). This will give us the number of moles of water molecules present in one cubic meter of water.

Now, we can use the ideal gas law (PV=nRT) to determine the volume occupied by one mole of water molecules at a given temperature and pressure. By using the given density of water and the ideal gas law, we can calculate the volume occupied by one mole of water molecules. This volume will give us an estimate of the average distance between two water molecules.

Moving on to part B, we can use the calculated average distance between two water molecules to determine the number of molecules present per unit surface area. This can be done by using the formula N_s ≈ 1/r_0^2, where N_s is the number of molecules per unit surface area and r_0 is the average distance between the molecules.

Finally, in part C, we can use the given surface tension of water (assuming it is the same as surface energy) to determine the value of U_0. This can be done by using the formula γ = 1/4nU_0N_s, where γ is the surface tension, n is the number of molecules per unit volume, and N_s is the number of molecules per unit surface area.

Overall, the process of estimating the bond energy between two water molecules involves understanding the concepts of density, molecular weight, Avogadro's number, ideal gas law, surface tension, and surface energy. By using these concepts and the given information, we can calculate an