Calculating Hydrostatic Pressure Difference: A Step-by-Step Guide

[greisen]

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

 

[Gokul43201]

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.

 

[greisen]

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]

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

 

[greisen]

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