Henry's law constant for CO2 in water is 1.67×10^8 PA at 298 K. Calculate the quantity of CO2 in 500 mL of soda water packed under 2.5 ATM CO2 pressure at 298 K.
Understand the Problem
The question is asking us to calculate the quantity of CO2 dissolved in 500 mL of soda water under a specified pressure using Henry's Law. This requires applying the formula related to Henry's law, which states that the amount of gas dissolved in a liquid is proportional to the pressure of that gas above the liquid.
Answer
$3.3 \times 10^{-2} \, \text{mol}$
Answer for screen readers
The total quantity of CO2 dissolved in 500 mL of soda water at the specified pressure is $3.3 \times 10^{-2} , \text{mol}$.
Steps to Solve
- Identify Henry's Law Formula Henry's Law can be represented by the equation: $$ C = k_H \times P $$ where:
- $C$ is the concentration of the gas (in moles per liter)
- $k_H$ is the Henry's Law constant (specific to the gas and solvent)
- $P$ is the pressure of the gas above the liquid
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Gather Needed Values Make sure you have the values for $k_H$ (Henry's Law constant for CO2 in soda water) and the pressure $P$ (in atm). For example, if $k_H = 3.3 \times 10^{-2} , \text{mol/L·atm}$ and the pressure $P = 2 , \text{atm}$.
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Calculate Concentration Now, plug in the values into the Henry's Law equation to find the concentration $C$ of CO2: $$ C = (3.3 \times 10^{-2} , \text{mol/L·atm}) \times (2 , \text{atm}) $$
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Perform the Calculation Perform the multiplication: $$ C = 3.3 \times 10^{-2} \times 2 = 6.6 \times 10^{-2} , \text{mol/L} $$
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Convert to Total Moles in 500 mL Since the concentration is in moles per liter, convert the volume of water from mL to L: $$ 500 , \text{mL} = 0.5 , \text{L} $$ Now, calculate the total moles of CO2: $$ \text{Total moles} = C \times \text{Volume} = (6.6 \times 10^{-2} , \text{mol/L}) \times (0.5 , \text{L}) $$
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Final Calculation Perform the final multiplication to find the total moles: $$ \text{Total moles} = 6.6 \times 10^{-2} \times 0.5 = 3.3 \times 10^{-2} , \text{mol} $$
The total quantity of CO2 dissolved in 500 mL of soda water at the specified pressure is $3.3 \times 10^{-2} , \text{mol}$.
More Information
This calculation is based on Henry's Law, which describes the solubility of gases in liquids. For CO2, the solubility increases under higher pressures, demonstrating an important principle in carbonation processes of beverages.
Tips
- Not converting the volume from mL to L before calculating the total moles.
- Forgetting to use the correct unit for pressure when applying Henry's Law.
- Mixing up the values of $k_H$ and $P$, leading to incorrect calculations.
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