Question
A soda can is sealed at 3 atm and contaisn 1.5 g/L of Co2, what would the solubility be if opened at 1 atm
Answers
GPT-4o mini
To find the solubility of CO2 in the soda can when the pressure is released from 3 atm to 1 atm, we can use Henry's Law. Henry's Law states that the solubility of a gas in a liquid is directly proportional to the partial pressure of that gas above the liquid.
The formula for Henry's Law is:
\[ C = k_H \cdot P \]
where:
- \( C \) = concentration (solubility) of the gas (in grams per liter, g/L)
- \( k_H \) = Henry's Law constant (specific to the gas-liquid combination)
- \( P \) = partial pressure of the gas (in atm)
Given that the soda can is sealed at 3 atm and has a concentration of 1.5 g/L of CO2, we can use this information to find the Henry's Law constant.
1. **Find the Henry's Law constant (\( k_H \)) at 3 atm:**
\[ k_H = \frac{C}{P} = \frac{1.5 \, \text{g/L}}{3\, \text{atm}} = 0.5 \, \text{g/L/atm} \]
2. **Now, calculate the solubility when the pressure is 1 atm:**
\[ C_{1 \, \text{atm}} = k_H \cdot P_{1 \, \text{atm}} = 0.5 \, \text{g/L/atm} \times 1 \, \text{atm} = 0.5 \, \text{g/L} \]
Therefore, the solubility of CO2 when the soda can is opened and the pressure drops to 1 atm is **0.5 g/L**.
The formula for Henry's Law is:
\[ C = k_H \cdot P \]
where:
- \( C \) = concentration (solubility) of the gas (in grams per liter, g/L)
- \( k_H \) = Henry's Law constant (specific to the gas-liquid combination)
- \( P \) = partial pressure of the gas (in atm)
Given that the soda can is sealed at 3 atm and has a concentration of 1.5 g/L of CO2, we can use this information to find the Henry's Law constant.
1. **Find the Henry's Law constant (\( k_H \)) at 3 atm:**
\[ k_H = \frac{C}{P} = \frac{1.5 \, \text{g/L}}{3\, \text{atm}} = 0.5 \, \text{g/L/atm} \]
2. **Now, calculate the solubility when the pressure is 1 atm:**
\[ C_{1 \, \text{atm}} = k_H \cdot P_{1 \, \text{atm}} = 0.5 \, \text{g/L/atm} \times 1 \, \text{atm} = 0.5 \, \text{g/L} \]
Therefore, the solubility of CO2 when the soda can is opened and the pressure drops to 1 atm is **0.5 g/L**.