Question

The gas from a certain volcano had the following composition in mole percent (that is, mole fraction \(\times 100\) ): \(65.0 \%\) \(\mathrm{CO}_{2}, 25.0 \% \mathrm{H}_{2}, 5.4 \% \mathrm{HCl}, 2.8 \% \mathrm{HF}, 1.7 \% \mathrm{SO}_{2},\) and \(0.1 \%\) \(\mathrm{H}_{2} \mathrm{~S} .\) What would be the partial pressure of each of these gases if the total pressure of volcanic gas were \(760 \mathrm{mmHg}\) ?

Short answer

Partial pressures: CO2 = 494 mmHg, H2 = 190 mmHg, HCl = 41 mmHg, HF = 21.3 mmHg, SO2 = 12.9 mmHg, H2S = 0.76 mmHg.

Step-by-step solution

Understand Mole Percent

Mole percent is a way to express the composition of a mixture in terms of the proportion (in percent) of moles of each component. So, if we have 65.0% CO2, it means that CO2 makes up 65.0% of the total moles present in the gas mixture.

Convert Mole Percent to Mole Fraction

To find the mole fraction, divide the mole percent by 100. The mole fraction of a component is calculated as: \[ x_{i} = \frac{\text{mole percent}}{100} \] Thus: - CO2: \( x_{CO2} = \frac{65.0}{100} = 0.650 \) - H2: \( x_{H2} = \frac{25.0}{100} = 0.250 \) - HCl: \( x_{HCl} = \frac{5.4}{100} = 0.054 \) - HF: \( x_{HF} = \frac{2.8}{100} = 0.028 \) - SO2: \( x_{SO2} = \frac{1.7}{100} = 0.017 \) - H2S: \( x_{H2S} = \frac{0.1}{100} = 0.001 \)

Calculate Partial Pressures

Partial pressure is calculated using the formula: \[ P_{i} = x_{i} \times P_{\text{total}} \] where \( P_{i} \) is the partial pressure and \( P_{\text{total}} \) is the total pressure (760 mmHg). - CO2: \( P_{CO2} = 0.650 \times 760 = 494.0 \, \text{mmHg} \) - H2: \( P_{H2} = 0.250 \times 760 = 190.0 \, \text{mmHg} \) - HCl: \( P_{HCl} = 0.054 \times 760 = 41.0 \, \text{mmHg} \) - HF: \( P_{HF} = 0.028 \times 760 = 21.3 \, \text{mmHg} \) - SO2: \( P_{SO2} = 0.017 \times 760 = 12.9 \, \text{mmHg} \) - H2S: \( P_{H2S} = 0.001 \times 760 = 0.76 \, \text{mmHg} \)

Key concepts

Mole Fraction

In chemistry, the mole fraction is a way of expressing the composition of a mixture or solution. It refers to the proportion of moles of a particular component compared to the total number of moles in the mixture. This is calculated by dividing the number of moles of the component by the total number of moles.

For instance, if a mixture contains gases like carbon dioxide (CO2), hydrogen (H2), and others, the mole fraction of CO2 can be found by dividing the moles of CO2 by the total moles of all gases in the mixture.- To calculate the mole fraction (\( x_i \)), you take the mole percent and divide it by 100. For example, with 65% CO2, the mole fraction is: \[ x_{CO2} = \frac{65.0}{100} = 0.650 \]

The mole fraction is unitless and is particularly useful in calculations involving the properties of gases because it directly relates to quantities such as vapor pressure and chemical reaction weights.

Gas Laws

Gas laws are an essential part of chemistry and physics that describe the behavior of gases under various conditions. They relate the properties of pressure, volume, temperature, and the number of particles. Understanding these principles is critical for comprehending how gases will behave in different environments.

The main gas laws include:

• Boyle's Law: At constant temperature, the pressure of a gas is inversely proportional to its volume.
• Charles's Law: At constant pressure, the volume of a gas is directly proportional to its absolute temperature.
• Avogadro's Law: At a given temperature and pressure, the volume of a gas is directly proportional to the number of moles of gas.

These laws are combined in the ideal gas law, expressed as: \[ PV = nRT \]where \( P \) is pressure, \( V \) is volume, \( n \) is the number of moles, \( R \) is the gas constant, and \( T \) is the temperature in Kelvin.

Applying these laws can help calculate the partial pressure of individual gases in a mixture, using their mole fraction and the total pressure. The relationship is given by Dalton's Law of Partial Pressures, where each gas in a mixture exerts a pressure that is proportionate to its mole fraction of the total pressure.

Volcanic Gas Composition

Volcanic gas composition refers to the types and quantities of gas that are emitted from a volcano. These gases are often critical in studying volcanic activity and predicting volcanic events.

Typical volcanic gases include:

• Carbon Dioxide (CO2): A major component, it comprises a significant portion of volcanic emissions.
• Water Vapor (H2O): This is one of the most prevalent gases released during eruptions.
• Sulfur Dioxide (SO2): Known for its sharp odor, it's a significant indicator of volcanic activity.
• Hydrogen Sulfide (H2S): Though emitted in smaller quantities, it can be hazardous due to its toxicity.
• Hydrochloric Acid (HCl): This gas can contribute to acid rain and environmental harm.
• Hydrofluoric Acid (HF): Although minor, it has a potent environmental impact.

Understanding the composition of these gases and their partial pressures helps scientists monitor volcanic activity and its potential impacts on the environment. In the study of volcanic gases, one seeks to measure both their overall output and changes in specific components over time, as these can provide insights into the behavior of the volcano's subterranean magma.