An unopened soda can has an aqueous CO2 concentration of 0.0506 m (molality) at 25 C. What is the pressure of CO2 gas in the can?
To find the pressure of CO2 gas in the can, we can use Henry's law, which states that the pressure of a gas above a liquid is directly proportional to the concentration of the gas in the liquid.
The equation for Henry's law is P = kH * C, where P is the partial pressure of the gas, kH is the Henry's law constant, and C is the concentration of the gas in the liquid.
In this case, we are given the concentration of aqueous CO2 in molality, which is different from molarity. Molality (m) is the number of moles of solute per kilogram of solvent, while molarity (M) is the number of moles of solute per liter of solution.
To convert molality to molarity, we need to know the density of the solution. However, the density of the soda is not provided in the question. Therefore, we cannot directly convert the given concentration from molality to molarity.
As a result, we cannot calculate the pressure of CO2 gas in the can based on the information provided in the question. We need either the density of the soda or additional information to obtain the molarity of CO2 before we can use Henry's law to calculate the pressure of CO2 gas.
To determine the pressure of CO2 gas in the can, we need to use Henry's Law. Henry's Law states that the partial pressure of a gas above a liquid is directly proportional to the concentration of the gas in the liquid.
In this case, the aqueous CO2 concentration is given as 0.0506 m (molality). However, we need to convert this concentration to a molar concentration (molarity) in order to use Henry's Law. The molality (m) can be converted to molarity (M) using the density of the solution.
First, we need to find the density of the solution. The density (ρ) can be determined using the equation:
ρ = m/V
Where m is the mass of the solution and V is the volume of the solution.
Since we are dealing with an unopened soda can, we can assume the solution is mostly water. The density of water at 25 °C is approximately 0.997 g/mL.
Let's assume we have 1 L of the solution. The mass of the solution (m) is then:
m = density of water × volume of water
m = 0.997 g/mL × 1000 mL
m = 997 g
Now we can calculate the molar concentration (M) using the molality (m) and the mass of the solvent (water).
M = m / (molar mass of CO2 × mass of solvent in kg)
The molar mass of CO2 is approximately 44.01 g/mol.
M = 0.0506 m / (44.01 g/mol × 0.997 kg)
M = 0.0506 m / 43.83 g
M ≈ 0.00116 M
Now we can use Henry's Law, which states that the partial pressure of a gas above a liquid is directly proportional to the concentration of the gas in the liquid.
P = K × M
Where P is the partial pressure of the gas, K is the Henry's Law constant for the gas in that solvent, and M is the molar concentration of the gas.
For CO2 in water at 25 °C, the Henry's Law constant is approximately 3.3 x 10^(-2) mol/(L·atm).
P = (3.3 x 10^(-2) mol/(L·atm)) × (0.00116 M)
P ≈ 3.8 x 10^(-5) atm
Therefore, the pressure of CO2 gas in the can is approximately 3.8 x 10^(-5) atm.