# How to convert CO2 ppm volume to ppm weight?

I'm using a sensor that measures $\ce{CO2}$ in ppm by volume aka atmosphere. What I'm using it for is to measure $\ce{CO2}$ concentration in water which is measured in ppm by weight.

This is what I have so far

$$\text{Ppmwco2} = \text{ppmvco2} \times 0.8317 \times 44.01 / 10000;$$

This is quicker than $\text{co2}/1000000 \times 0.8317 \times 44.01 / 1000000$. 0.8317 accounts for Henry's Law and max ppmw will be 36.6 with 10,000 ppmv.

The sensor floats on the waterline detecting any $\ce{CO2}$ bouncing out of the water. Do I even need to account for Henry's law? Is the math right?

## 2 Answers

You can't determine the concentration of CO2 in the water just from measuring the concentration in the air above the water.

The solubility of CO2 is extremely dependent upon pH. See: http://ion.chem.usu.edu/~sbialkow/Classes/3650/CO2%20Solubility/DissolvedCO2.html

There is no indication you are considering pH at all.

Solubility of CO2 also depends upon temperature.

Also, you need to consider whether or not the phases are in equilibrium.

• Actually from the link you provided, your statement is false. pH is dependent on CO2 species like HCO3, not CO2. After reading further on wikipedia, Henri's law can't be used accurately because CO2 reacts with water to form HCO3 and the like. – Mistergreen Apr 12 '14 at 22:54
• From wikipedia:The hydration equilibrium constant at 25°C is called Kh, which in the case of carbonic acid is [H2CO3]/[CO2] ≈ 1.7×10−3 in pure water[3] and ≈ 1.2×10−3 in seawater.[4] Hence, the majority of the carbon dioxide is not converted into carbonic acid, remaining as CO2 molecules – Mistergreen Apr 12 '14 at 23:07

For those looking, I think I solved it.

$$\text{ppmw} = \frac{(\text{ppmv})(\text{MW})}{((0.08205) (¦K))(\text{density of Water})}$$

where:

• ppmv = air pollutant ($\ce{CO2}$) concentration, in parts per million by volume

• mg/m3 = milligrams of pollutant per cubic meter of air - (ppmv)(MW) / [(0.08205) (¦K)]

• ¦K = atmospheric temperature in degrees Kelvin = 273.15 + ¦C
• 0.08205 = universal gas law constant in (atm+liter)/(gmol+¦K)
• MW = molecular weight of the air pollutant (dimensionless) - mol weight of $\ce{CO2}$ ($\pu{44.01g/mol}$)
• $\pu{1000 kg/m^3}$ (density of water)

density of Water = $\pu{1000 kg/m3}$ - use 1000 as default since you'll need to measure the density to get accurate numbers. The density does vary due to temperature but very minor.

400ppmv of CO2 = 0.720ppmw