A student carried out the following procedure to measure the pressure of carbon dioxide in a soft drink bottle. First, she weighed the bottle \((853.5 \mathrm{~g})\). Next, she carefully removed the cap to let the \(\mathrm{CO}_{2}\) gas escape. She then reweighed the bottle with the cap \((851.3 \mathrm{~g})\). Finally, she measured the volume of the soft drink ( \(452.4 \mathrm{~mL}\) ). Given that Henry's law constant for \(\mathrm{CO}_{2}\) in water at \(25^{\circ} \mathrm{C}\) is \(3.4 \times 10^{-2}\) \(\mathrm{mol} / \mathrm{L} \cdot \mathrm{atm},\) calculate the pressure of \(\mathrm{CO}_{2}\) in the original bottle. Why is this pressure only an estimate of the true value?

Understanding how gases dissolve in liquids is essential for a wide variety of scientific and practical applications. Henry's law describes the relationship between the solubility of a gas in a liquid and the pressure of the gas above the liquid.

The statement of Henry's law can be expressed mathematically as: \[ P = C \times k_{H} \] Where \( P \) is the pressure of the gas above the liquid, \( C \) is the concentration (molarity) of the gas in the liquid, and \( k_{H} \) is the Henry's law constant for the gas in that specific liquid at a given temperature.

The ability to estimate the gas pressure using Henry's law requires accurate readings of the gas concentration within the liquid, the correct Henry's law constant at the temperature being measured, and the assumption that the system is at equilibrium. These factors dictate the precision of the pressure estimation, emphasizing the importance of detailed measurements and constants.

When working with gases like carbon dioxide (\(CO_2\)), it's important to be able to convert between mass and moles. The molar mass is a key concept that facilitates this conversion, representing the mass of one mole of a substance.

For \(CO_2\), the molar mass is approximately 44.01 grams per mole (\(44.01 \, \mathrm{g/mol}\)). This molar mass allows scientists and students to calculate how many moles are present in a given mass of carbon dioxide. Calculating moles from mass involves dividing the mass of the \(CO_2\) by its molar mass. The accuracy of the molar mass is crucial for any subsequent calculations, including those in molarity and gas pressure estimations using Henry's law.

Molarity is a measure of concentration for solutions. It is defined as the number of moles of a solute (in this case, \(CO_2\)) present in one liter of solution. The formula for molarity is: \[ \text{Molarity (M)} = \frac{\text{moles of solute}}{\text{volume of solution in liters}} \]

In the context of the exercise, after calculating the moles of \(CO_2\), converting the volume of the soft drink from milliliters to liters is necessary for the molarity calculation. The resulting molarity is then used in conjunction with Henry's law to estimate the pressure of the dissolved gas in the solution. Thus, understanding how to calculate molarity is fundamental for accurately applying Henry's law and finding gas pressures in solutions.

Gas laws are principles that describe the behavior of gases, and they are fundamental to understanding chemistry, especially when dealing with gases in various conditions. Among these laws, Henry's law is specific to the solubility of gases in liquids, but there are others that impact how gases behave under different temperatures, volumes, and pressures.

Examples include Boyle's law, which explains the inverse relationship between pressure and volume, Charles's law that describes how gases expand as the temperature increases, and the Ideal Gas Law, which is a comprehensive equation incorporating pressure, volume, temperature, and the number of moles of a gas.

• Boyle's Law: \( P_1V_1 = P_2V_2 \)
• Charles's Law: \( \frac{V_1}{T_1} = \frac{V_2}{T_2} \)
• Ideal Gas Law: \( PV = nRT \)

These laws are instrumental in predicting and explaining the behavior of gases, and they are applied alongside calculations such as those found in the exercise to measure gas pressure in solutions.