15.0 moles of gas are in a 4.00 l tank at 23.9 ∘c . calculate the difference in pressure between methane and an ideal gas under these conditions. the van der waals constants for methane are a=2.300l2⋅atm/mol2 and b=0.0430 l/mol.

14.8 atm  

Step-by-step explanation:

(a) Ideal Gas Law

The equation for the Ideal Gas Law is

pV = nRT     Divide each side by V

 p = (nRT)/V

Data:

n = 15.0 mol

R = 0.082 06 L·atm·K⁻¹mol⁻¹

T = 23.9 °C

V = 4.00 L

Calculations:

(i) Convert temperature to Kelvins

T = (23.9 + 273.15) K

  = 297.05 K

(ii) Calculate the pressure

p = (15.0 × 0.082 06 × 297.05)/4.00

  = 91.4 atm

The pressure predicted by the Ideal Gas Law is 91.4 atm.

(b) van der Waals gas

The van der Waals equation is

[p + (n²a)/V²)](V - nb) = nRT                   Divide each side by (V - nb)

             p + (n²a)/V² = (nRT)/(V - nb)     Subtract (n²a)/V² from each side

                                         p = (nRT)/(V - nb) - (n²a)/V²

(i) Data:

a=2.300 L²⋅atm·mol⁻²

b=0.0430 L·mol⁻¹

(ii) Calculation:

p = (15.0 × 0.082 06 × 297.05)/(4.00 – 15.0 × 0.0430)

      - (15.0² × 2.300)/4.00²

  = 365.6/(4.00 - 0.645) - 517.5/16

  = 365.6/3.355 - 32.34

  = 109.0 - 32.34

  = 76.6 atm

The pressure predicted by the van der Waals equation is 76.6 atm.

(iii) The pressure difference

p(Ideal) - p(vdW) = 91.4 - 76.6

                           = 14.8 atm

the ideal gas law equation is as follows

pv = nrt

where p - pressure

v - volume

n - number of moles

r - universal gas constant

t - temperature

so if the pressure, volume and temperature are already known

we are left with n and r

since r is the universal gas constant that has a known fixed value then r too is known

so we are left with 'n'

once we know temperature volume and pressure

we can find the number of moles of gas present using the ideal gas law equation

this is not my own answer, this is an answer for the same question by the user blahblahmali. i do not claim ownership of this account.