Measurements of CO2 Molar Mixing Ratio

by Infrared Absorption Spectroscopy

C, mole fraction (μmole mole-1 = ppm)

LI-COR analyzers measure absorbance at 4.26 μm

V = kA (voltage proportional to absorbance)

ρc = Pc/RT = CP/RT (molar density of absorber)

ρcL = CPL/RT (absorber amount in absorption cell)

LiCor internal schematic

100 cc/min

Virial Equation of State (REAL not IDEAL):

PV = nRT(1 + nB(T)/V + nC(T)/V2 + …)

neglect higher order terms

Solve for n:

n = -(V/2B){1 – (1 + 4PB/RT)1/2}

B (10-6 m3 mole-1) (in air at T = 300 K)

air -7.7

CO2 -42.3

Using this, we find the equivalence of (at 300 K and 1 Bar):

volume mixing ratio 370.0 x 10-6 m3 CO2 / m3 air

molar mixing ratio 370.5 x 10-6 mole CO2 / mole air

• LiCor Analyzer Response Curve:

C = [a0 + a1 (V P0/P) + a2 (V P0/P)2] T/T0

C is CO2 mole fraction

P0, T0 are pressure and temperature during calibration

Pressure Broadening

effective pressure: Pe = PN2 + Σbi Pi

Gas Coef (bi) % of air

N2 1.00 78.084

O2 0.81 20.946

Ar 0.78 0.934

H2O ≈1.57 ≈1

Pressure Broadening

Example calibration curve in air (PO2 = 20 kPA, PN2 = 80 kPA):

Pe = 80 kPa x 1.00 + 20 kPa x 0.81 = 96.2 kPa

C = 326.61 + 0.1738 V + 4.5095 x 10-5 V2

A LiCor response of 300 mV implies CO2 = 382.82 ppm

What if you calibrated using pure N2? (PN2 = Pe = 100 kPa)

C = 326.61 + 0.1807 V + 4.8723 x 10-5 V2

Now a response of 300 mV gives CO2 = 385.21 ppm !

What error is made using synthetic (no Argon) vs. real air?

Water Vapor

(1) Pressure broadening of CO2 line

bH2O ≈ 1.57

(2) Dilution of air – adding 1% H2O displaces 1% of CO2 (≈ 3.7 ppm)

Solution: DRY THE AIR! How dry is dry enough?

0.1 ppm / 370 ppm = 0.027% → H2O ≤ 0.00027 m3/m3 air

Error in CO2 Dewpoint

0.1 ppm -36.5oC

0.2 ppm -29.4oC

What if we had 3 standard gases instead of 4 ???

The results differ for different LiCor CO2

analyzers under the same conditions!!!