Sure! Let's determine the amount in moles of carbon dioxide (CO₂) dissolved in an aqueous Sprite solution. The problem provides the following information:
- Volume of the Sprite solution: [tex]\( V = 1.25 \, \text{L} \)[/tex]
- Pressure of CO₂ gas: [tex]\( P = 253 \, \text{kPa} \)[/tex]
- Henry's law constant for CO₂: [tex]\( k_{CO₂} = 3.4 \times 10^{-4} \, \text{mol L}^{-1} \text{kPa}^{-1} \)[/tex]
We are using Henry's Law for this calculation. Henry's Law states that the amount of gas dissolved in a liquid is directly proportional to its partial pressure above the liquid. The mathematical expression for Henry's Law is:
[tex]\[ C = k_H \cdot P \][/tex]
Where:
- [tex]\( C \)[/tex] is the concentration of the dissolved gas in mol/L.
- [tex]\( k_H \)[/tex] is Henry's Law constant in mol/L·kPa.
- [tex]\( P \)[/tex] is the partial pressure of the gas in kPa.
First, we calculate the concentration [tex]\( C \)[/tex] of CO₂ in the Sprite solution:
[tex]\[ C = k_{CO₂} \cdot P \][/tex]
[tex]\[ C = (3.4 \times 10^{-4} \, \text{mol/L·kPa}) \times (253 \, \text{kPa}) \][/tex]
[tex]\[ C = 0.08602 \, \text{mol/L} \][/tex]
Now, we need to find the total amount of CO₂ in moles dissolved in the entire volume of the Sprite solution. Since the concentration [tex]\( C \)[/tex] is in mol/L, we use the volume [tex]\( V \)[/tex] to find the moles of CO₂.
[tex]\[ \text{Moles of CO₂} = C \cdot V \][/tex]
[tex]\[ \text{Moles of CO₂} = 0.08602 \, \text{mol/L} \times 1.25 \, \text{L} \][/tex]
[tex]\[ \text{Moles of CO₂} = 0.107525 \, \text{mol} \][/tex]
Thus, the amount of carbon dioxide dissolved in the aqueous Sprite solution is approximately [tex]\( 0.108 \, \text{mol} \)[/tex] when rounded to three significant figures.
