# Hydrostatic pressure

Hi

I am to calculate the hydrostatic pressure difference - given by the

\Delta P = n*f/A

where f = 0.4 kcal/mol/Å. The unit cell has the dimension 23Å x 19.9Å x 30.4 Å and the number of water molecules are 5.4 Å in the z-direction with a molar volume of 55.5 mol/l.

I start by calculating the moles of water
n = 23Å*19.9Å*5.4Å*55.5 mol/l 1000 l/Å^3 = 1.37*10^-19 mol

Than I assume that the force is acting on the 5.4Å depth of water which gives a pressure of

\Delta P = 5.4Å*0.4 kcal/mol/Å*1.37*10^-19 mol /(23*10^-10*19.9*10¯10)m² = 6.47*10^-18 kcal/m^2

It seems a little strange and how to convert into Pascal? Any help or comments appreciated. Thanks in advance

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Gokul43201
Staff Emeritus
Gold Member
1. Homework & Coursework is the correct place for this question (not the Chemistry subforum).

2. What is the context for all this?

3. Why have you substituted the depth, d=5.4A into the equation?

4. Once you make the correction in 3, you will find you have the correct dimensions to convert to units of Pa.

so this should be okay

0.4 kcal/mol/Å*1.37*10^-19 mol /(23*10^-10*19.9*10¯10)m² = 1.1988e-08 kcal/Å /m^2

and than convert this to Pa? Thanks in advance

Gokul43201
Staff Emeritus
Gold Member
I can't attest to the correctness of the calculation without knowing what the question is, but now it is at least dimensionally correct.

Hi

Sorry if it is bit unclear.

I should calculate the pressure difference with a nanotube and on water on both sides. So I will use the formula \Delta P = n*f/A where f = 0.4 kcal/mol/Å and the unit cell of the system is 23Å*19.9Å*30.4Å and the number of water is in the 5.4 Å thick layer with a molar volume of 55.5 mol/l. So I end up with this

\Delta P = 10^10 Å/m 0.4 kcal/mol/Å*1.37*10^-19 mol /(23*10^-10*19.9*10¯10)m² = 119.88 kcal/m m^2

which I convert to MPascal with 1 kcal/m = 4184 N

4184 m/kcal N * 119.88 kcal/m m^2 / 10^6 = 0.50 MPa

Does this seems correct? Thanks in advance