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Henry's Law Example Problem

Calculate Concentration of Gas in Solution

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You can calculate the amount of carbon dioxide in a can of soda.

You can calculate the amount of carbon dioxide in a can of soda.

Carlos Paes, stock.xchng
This example problem demonstrates how to use Henry's Law to calculate the concentration of a gas in solution under pressure.

Problem:

How many grams of carbon dioxide gas is dissolved in a 1 L bottle of carbonated water if the manufacturer uses a pressure of 2.4 atm in the bottling process at 25 °C?
Given: KH of CO2 in water = 29.76 atm/(mol/L) at 25 °C

Solution

When a gas is dissolved in a liquid, the concentrations will eventually reach equilibrium between the source of the gas and the solution. Henry's Law shows the concentration of a solute gas in a solution is directly proportional to the partial pressure of the gas over the solution.

P = KHC where

P is the partial pressure of the gas above the solution
KH is the Henry's Law constant for the solution
C is the concentration of the dissolved gas in solution

C = P/KH
C = 2.4 atm/29.76 atm/(mol/L)
C = 0.08 mol/L

since we only have 1 L of water, we have 0.08 mol of CO2.

Convert moles to grams

mass of 1 mol of CO2 = 12+(16x2) = 12+32 = 44 g

g of CO2 = mol CO2 x (44 g/mol)
g of CO2 = 8.06 x 10-2 mol x 44 g/mol
g of CO2 = 3.52 g

Answer:

There are 3.52 g of CO2 dissolved in a 1 L bottle of carbonated water from the manufacturer.

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