Question

Steam at 300 degree C has a density of 7.132 kg/m^3. Find a) the pressure using the ideal gas equation, b) the pressure using the steam tables, and c) the error in the calculation of pressure using ideal gas equation. Write all units in all quantities. How many molecules of air are there in a nanometer cube volume (nm^3) at standard conditions?

Answer 1

part (a)

mw = molecular weight

d = density

P = pressure

T = temperature

R = universal gas constant

V = volume

The ideal gas equation is:

PV = nRT

PV = (mass/molecular weight)*RT

P*(mw) = (mass/volume)*RT

P*(mw) = (density)*RT

P = dRT/mw

Given that,

T = 300 celsius = 300+273.15 = 573.15 K

d = 7.132 kg/m³

R = 8.314*1000 (1000 is multiplied to maintain consistency of units) m³Pa/K mol

mw = 18 kg/kmol

Hence, P = (7.132*8.314*1000*573.15)/18

P = 1888065.89 Pa

P = 1888.065 kPa

From steam tables, the pressure comes out to be: 8.5879 MPa = 8587.9 kPa

Error = 8587.9 - 1888.065 = 6699.835 kPa

Part (b):

Assuming STP conditions:

T = temperature = 273.15 K

P = Pressure = 1 atm

V = Volume = 1 nm³ = 10^-27 m³ = 10^-24 L

R = 0.082 L-atm/K-mol

PV = nRT

n = 4.46*10^-26 moles of air

1 mole = 6.022*10²³ molecules

Hence, number of molecules of air in 4.46*10^-26 = 0.02688 molecues