Question

The Henry's law constant for CO₂ is 3.4 × 10⁻2 M/atm at 25 °C. Assuming ideal solution behavior, what pressure of carbon dioxide is needed to maintain a CO₂ concentration of 0.10 M in a can of lemon-lime soda?

a) 2.94 atm
b) 2.94 × 10² atm
c) 0.294 atm
d) 2.94 × 10⁻3 atm

Answer 1

To maintain a CO₂ concentration of 0.10 M in soda using a Henry's law constant of 3.4 × 10⁻² M/atm at 25°C, a pressure of 2.94 atm is required, which indicates a saturated solution state for the beverage.

Step-by-step explanation:

The question involves calculating the pressure of carbon dioxide (CO₂) gas required to maintain a specific concentration of CO₂ in a solution using Henry's law. With a known Henry's law constant (3.4 × 10⁻² M/atm), to maintain a 0.10 M concentration of CO₂, we must solve the equation derived from Henry's law: Concentration = Henry's law constant × Pressure. Therefore, the pressure needed would be Concentration / Henry's law constant.

Pressure = 0.10 M / (3.4 × 10⁻² M/atm) = 2.94 atm

c) Regarding the soda's saturation state, if the pressure applied is just enough to maintain the 0.10 M concentration (the given condition), the beverage can be considered to be saturated with CO₂ at that pressure. Additional CO₂ would make it supersaturated, and less CO₂ would lead to unsaturation as the CO₂ would escape until the saturated concentration is reached again.