What pressure of carbon dioxide is needed to maintain a CO2.

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?

Final Answer: 

The pressure of carbon dioxide needed to maintain a CO₂ concentration of 0.10 M in a can of lemon-lime soda is approximately 2.94 atm. This is calculated using Henry’s Law, relating concentration and pressure. The equation used is

Examples & Evidence:

To find the pressure of carbon dioxide (CO₂) required to maintain a concentration of 0.10 M in a lemon-lime soda can, we will use Henry’s Law, which relates the concentration of a gas in a liquid to the partial pressure of that gas above the liquid.

Henry’s Law is expressed by the equation:

CCO2​​=  concentration of carbon dioxide in molarity (M)

CO2= partial pressure of carbon dioxide in atm

​Given:

CCO2 =0.10M
KH=3.4×10-2 M/atm​

We can rearrange the formula to solve for​ 2      

p_{\mathrm{CO}_2}=\frac{C_{C O_2}}{K_H}

Now substituting the values into the equation:

p_{\mathrm{CO}_2}=\frac{0.10 \mathrm{M}}{3.4 \times 10^{-2} \mathrm{M} / \mathrm{atm}}

​Calculating this gives:

p_{C O_2}=\frac{0.10}{0.034} \approx 2.94 \mathrm{~atm}

Thus, the pressure of carbon dioxide needed to maintain a CO₂ concentration of 0.10 M in the soda is approximately 2.94 atm.

Explanation:

For example, if the concentration of CO₂ in a different beverage is 0.20 M and using the same Henry’s Law constant, you would calculate the required pressure accordingly using p_{C O_2}=\frac{0.20 \mathrm{M}}{3.4 \times 10^{-2} \mathrm{M} / \mathrm{atm}}, resulting in a different pressure value.

Henry’s Law is a well-established principle in chemistry that accurately describes the relationship between the pressure of a gas above a liquid and its concentration in that liquid. This law is commonly applied in various fields, including environmental science and beverage technology, supporting its validity.

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