In Exercise 107 in Chapter 5 , the pressure of CO2 in a...

In Exercise 107 in Chapter 5 , the pressure of $\mathrm{CO}_{2}$ in a bottle of sparkling wine was calculated assuming that the $\mathrm{CO}_{2}$ was insoluble in water. This was a bad assumption. Redo this problem by assuming $\mathrm{CO}_{2}$ obeys Henry's law. Use the data given in that problem to calculate the partial pressure of $\mathrm{CO}_{2}$ in the gas phase and the solubility of $\mathrm{CO}_{2}$ in the wine at $25^{\circ} \mathrm{C}$. The Henry's law constant for $\mathrm{CO}_{2}$ is $3.1 \times 10^{-2} \mathrm{~mol} / \mathrm{L} \cdot \mathrm{atm}$ at $25^{\circ} \mathrm{C}$ with Henry's law in the form $C=k P$, where $C$ is the concentration of the gas in $\mathrm{mol} / \mathrm{L}$.

In Exercise 107 in Chapter 5 , the pressure of $\mathrm{CO}_{2}$ in a bottle of sparkling wine was calculated assuming that the $\mathrm{CO}_{2}$ was insoluble in water. This was a bad assumption. Redo this problem by assuming $\mathrm{CO}_{2}$ obeys Henry's law. Use the data given in that problem to calculate the partial pressure of $\mathrm{CO}_{2}$ in the gas phase and the solubility of $\mathrm{CO}_{2}$ in the wine at $25^{\circ} \mathrm{C}$. The Henry's law constant for $\mathrm{CO}_{2}$ is $3.1 \times 10^{-2} \mathrm{~mol} / \mathrm{L} \cdot \mathrm{atm}$ at $25^{\circ} \mathrm{C}$ with Henry's law in the
form $C=k P$, where $C$ is the concentration of the gas in $\mathrm{mol} / \mathrm{L}$.

Key Concepts

Gas Solubility in Liquids

The solubility of gases in liquids describes how much of a gas can dissolve at a specific temperature and pressure. This concept is influenced by factors such as the nature of the gas, the properties of the liquid, and environmental conditions, and it is directly described by the relationship given by Henry's Law.

Chemical Equilibrium in Gas-Liquid Systems

Chemical equilibrium in gas-liquid systems occurs when the rate of gas dissolving into the liquid equals the rate of gas escaping from it. This equilibrium is essential for accurately applying Henry's Law, as it ensures that the concentrations of the dissolved gas and the gas in the headspace remain constant under a given set of conditions.

Henry's Law

Henry's Law states that at a constant temperature, the amount of a gas dissolved in a liquid is directly proportional to the partial pressure of that gas in contact with the liquid. This concept is fundamental in predicting how gases like CO2 behave when dissolved in liquids, such as in carbonated beverages or natural water bodies.

Partial Pressure

Partial pressure refers to the pressure exerted by a single component of a gas mixture, and it is crucial when considering gas solubility in liquids. It determines the driving force for the dissolution of gases under equilibrium conditions as described by Henry's Law.

Transcript

00:01 In this problem, you have to refer back to example 107 or problem 107 in chapter 5.

00:07 And when we were doing that problem, that would have been bad assumptions.

00:12 And we're going to redo this, assuming that carbon dioxide obeys henry's law.

00:16 We're going to use the data to calculate the partial pressure of carbon dioxide in the gas space and the solubility of carbon dioxide in wine or grape juice at 25 degrees c.

00:28 And we're given the henry's law constant and the form of henry's law.

00:35 Okay.

00:38 So let's get started.

00:42 And i'm going to go get a different color to get started here.

00:49 And i'm on problem 1965.

00:54 Okay.

00:56 So we're told that we have, i'll be jotting some information down, 750 milliliters of grape juice.

01:08 Or wine, whatever.

01:13 And we're going to call this from now on grape juice.

01:19 And let's go ahead and do 12 milliliters per 100 milliliters.

01:29 And that's going to be my alcohol.

01:34 I'm going to have to make myself a little bit more room here.