Question

What would be the number value for the conversion factor that would take the slope of 0.0026 in kPa/s to moles of CO₂/s (assuming again that the change in pressure is entirely due to CO₂production)?​

Answer 1

The ideal gas equation is:

PV = nRT --------(1)

where P = pressure

V = volume

n = number of moles

R = gas constant

T = temperature

Given:

Rate of change of pressure i.e. dP/dt = kPa/s

Here the value of gas constant R = 8.314 L-kPa/K-mol

Explanation:

Based on equation (1) we can write

n = PV/RT

At constant V and T, differentiating w.r.t time 't' we get

dn/dT = (V/RT)dP/dt

where dn/dt = rate of change in the # moles of CO2 i.e. moles CO2/s

dn/dt = (V/T)*(1/R)*dP/dt = (V/T) *(1/8.314)*0.0026

Therefore:

moles CO2/s = dn/dt = 3.127*10^-4 (V/T)