Problem 131 - Chemistry: An Atoms-Focused Approach

Question

Uranus has a total atmospheric pressure of \(130 \mathrm{kPa}\) and consists of the following gases: \(83 \% \mathrm{H}_{2}, 15 \% \mathrm{He},\) and \(2 \%\) \(\mathrm{CH}_{4}\) by volume. Calculate the partial pressure of each gas in Uranus's atmosphere.

Step-by-Step Solution

Answer

Answer: The partial pressures of each gas in Uranus's atmosphere are as follows: - Partial pressure of H2: 107.9 kPa - Partial pressure of He: 19.5 kPa - Partial pressure of CH4: 2.6 kPa

Step 1: Understand Partial Pressure

Partial pressure is the pressure that each gas would exert if it were alone in the container. In a mixture of gases, the total pressure is the sum of the partial pressures of each individual gas. Mathematically, this can be represented as: Total Pressure = P1 + P2 + P3 where P1, P2, and P3 are the partial pressures of the individual gases.

Step 2: Calculate the partial pressure of H2

To calculate the partial pressure of H2, we can use the following formula: Partial Pressure of H2 = (Percentage of H2) * (Total Pressure) Here, the percentage of H2 is given as 83%, so we can write this as 0.83. The total pressure of Uranus is given as 130 kPa. Now we can find the partial pressure of H2: Partial Pressure of H2 = 0.83 * 130 kPa = 107.9 kPa

Step 3: Calculate the partial pressure of He

Similarly, we'll calculate the partial pressure of He using the formula: Partial Pressure of He = (Percentage of He) * (Total Pressure) The percentage of He is given as 15%, so we can write this as 0.15. Now we can find the partial pressure of He: Partial Pressure of He = 0.15 * 130 kPa = 19.5 kPa

Step 4: Calculate the partial pressure of CH4

Finally, we'll calculate the partial pressure of CH4 using the same formula: Partial Pressure of CH4 = (Percentage of CH4) * (Total Pressure) The percentage of CH4 is given as 2%, so we can write this as 0.02. Now we can find the partial pressure of CH4: Partial Pressure of CH4 = 0.02 * 130 kPa = 2.6 kPa

Step 5: State the final result

We have successfully calculated the partial pressures of each gas in Uranus's atmosphere: Partial pressure of H2: 107.9 kPa Partial pressure of He: 19.5 kPa Partial pressure of CH4: 2.6 kPa

Key Concepts

Atmospheric Composition

Atmospheric composition refers to the mixture of different gases that are present in the atmosphere of a planet. Each planet has a unique atmospheric composition that can give us insights into its climate, weather patterns, and potential for supporting life. Earth's atmosphere, for example, includes large amounts of nitrogen and oxygen, essential for life as we know it.
On the other hand, planets like Uranus have atmospheres dominated by different gases. The composition of Uranus's atmosphere mainly consists of:

• Hydrogen (\(H_2\)) - 83% by volume.
• Helium (\(He\)) - 15% by volume.
• Methane (\(CH_4\)) - 2% by volume.

Understanding these proportions is vital for astronomical studies, enabling scientists to comprehend the atmospheric dynamics and physical conditions of these celestial bodies. When scientists refer to partial pressures, these percentages play a critical role in determining the contribution of each gas to the total atmospheric pressure.

Ideal Gas Law

The ideal gas law is one of the cornerstone principles in chemistry and physics, used to relate the pressure, volume, and temperature of a gas. It is expressed as:\[PV = nRT\]where:

• \(P\) represents the pressure of the gas,
• \(V\) is the volume,
• \(n\) is the number of moles of gas,
• \(R\) is the universal gas constant,
• \(T\) is the temperature in Kelvin.

By applying the ideal gas law, one can derive critical insights into the behavior of gases under various conditions.
In the context of calculating partial pressures, although the ideal gas law itself is not directly used in the solution, understanding it helps to lay the foundation of gas behaviors and interactions. It illustrates how gases expand to fill their container and how total pressure in a mixture can be understood in terms of individual gas contributions through their mole fractions and conditions specified by this principle.

Uranus Atmosphere

Uranus is the seventh planet from the Sun and is notable for its gaseous atmosphere. Unlike Earth, which is primarily composed of nitrogen and oxygen, Uranus's atmosphere comprises a large portion of hydrogen and helium, with traces of methane giving it a blue hue.
The atmospheric pressure on Uranus is around 130 kPa, significantly higher than Earth's standard atmospheric pressure of 101.3 kPa. This indicates a denser mixture of gases at Uranus's atmospheric heights. The presence of methane (\(CH_4\)) is particularly interesting as it absorbs red light, leaving the planet with its characteristic blue-green color.
Much knowledge about Uranus and its atmosphere has come from telescopic observations and data from space missions including Voyager 2. Continuous research seeks to understand more about Uranus, including its atmospheric dynamics, composition, and how it relates to the planet's unique features, such as its sideways rotation and extreme axial tilt. Exploring these gas compositions and their roles helps us comprehend the atmospheric evolution and current state of this distant ice giant.