Sealed flask with carbon dioxide. Need number of moles

Question

You have a sealed 2 liter flask that contains nothing but water and carbon dioxide. The flask is half-filled with liquid water, has a temperature of 25°C, and the overall pressure within the flask is 0.1 atm. How many moles of CO₂ are in the flask? At this temperature, you may take the K_H value for CO₂ as 0.033 M / atm.

Answer 1

Henry's Law: C = K_HP

C = concentration = ?

K_H = Henry's law constant = 0.033 M/atm

P = partial pressure of CO₂ = 0.07 atm (see below)

Before we can find the concentration of CO₂ (and hence the moles of CO₂), we first need to find its partial pressure. We look up the vapor pressure of water at 25º and find it to be 0.03 atm. Since the total pressure = 0.1 atm, this mean the partial pressure of CO₂ = 0.1 atm - 0.03 atm = 0.07 atm

Now using Henry's law, we find the concentration of CO₂:

C = 0.033 M/atm x 0.07 atm = 2.31x10^-3 M

Converting to moles of CO₂, we have...

2.31x10^-3 mol/L x 2 L = 4.6x10^-3 mols CO₂