Question

Venus's atmosphere is composed of 96.5 percent \(\mathrm{CO}_{2}\), 3.5 percent \(\mathrm{N}_{2}\), and 0.015 percent \(\mathrm{SO}_{2}\) by volume. Its standard atmospheric pressure is \(9.0 \times 10^{6} \mathrm{~Pa}\). Calculate the partial pressures of the gases in pascals.

Short answer

The partial pressures are 8.685 × 10⁶ Pa for CO₂, 3.15 × 10⁵ Pa for N₂, and 1.35 × 10³ Pa for SO₂.

Step-by-step solution

Understand Partial Pressure Concept

Partial pressure is the pressure that a single component of a mixture of gases would exert if it occupied the entire volume alone at the same temperature. We can find the partial pressure by multiplying the total pressure by the fraction of each gas in the mixture.

Convert Percentages to Fractions

Convert the percentage of each gas into its fractional form. For CO₂, use 0.965, for N₂, use 0.035, and for SO₂, use 0.00015.

Calculate Partial Pressure of CO₂

Calculate the partial pressure of CO₂ using its fraction: \( p_{CO_2} = 9.0 \times 10^6 \, Pa \times 0.965 = 8.685 \times 10^6 \, Pa \).

Calculate Partial Pressure of N₂

Calculate the partial pressure of N₂ using its fraction: \( p_{N_2} = 9.0 \times 10^6 \, Pa \times 0.035 = 3.15 \times 10^5 \, Pa \).

Calculate Partial Pressure of SO₂

Calculate the partial pressure of SO₂ using its fraction: \( p_{SO_2} = 9.0 \times 10^6 \, Pa \times 0.00015 = 1.35 \times 10^3 \, Pa \).

Key concepts

Atmospheric Pressure

Atmospheric pressure is a crucial concept in understanding planetary atmospheres. It refers to the force exerted by the weight of the atmosphere over a unit area. This pressure is measured in units called Pascals (Pa). For example, Earth's standard atmospheric pressure at sea level is approximately 101,325 Pa. In contrast, Venus has a much thicker atmosphere, resulting in a significantly higher pressure. Its standard atmospheric pressure is about 9.0 x 10^6 Pa, indicating a dense atmosphere which can influence both weather and surface conditions. Understanding atmospheric pressure is essential as it helps us decipher weather patterns, climate conditions, and potential for habitation on other planets.

Gas Mixture

A gas mixture is a collection of different gases that are combined without any chemical bonding. Each gas in the mixture retains its original properties while contributing to the overall characteristics of the mixture. For example, the air we breathe on Earth is a mixture primarily composed of nitrogen, oxygen, and smaller amounts of other gases. Similarly, the atmosphere of Venus is a mixture primarily made up of carbon dioxide (96.5%), nitrogen (3.5%), and trace amounts of sulfur dioxide (0.015%).

• Homogeneous Mixture: In gas mixtures, the distribution is generally uniform, making them homogeneous.
• Non-reactive: The gases in the mixture do not react chemically with each other.

Understanding gas mixtures is key to studying atmospheric composition and calculating partial pressures.

Partial Pressure Calculation

Partial pressure calculation is integral to understanding how each gas in a mixture behaves independently. It is determined by the equation:
\[ p_i = P_{total} \times x_i \] where

• \( p_i \) represents the partial pressure of a particular gas,
• \( P_{total} \) is the total pressure of the gas mixture,
• \( x_i \) is the mole fraction of the gas in the mixture.

In the case of Venus's atmosphere, given that its total pressure is 9.0 x 10^6 Pa, the partial pressures are calculated by multiplying each gas's percentage as a fraction by this total pressure. For example, the partial pressure of carbon dioxide, with a fraction of 0.965, would be calculated as \( 9.0 \times 10^6 \, Pa \times 0.965 = 8.685 \times 10^6 \, Pa \). Similar calculations can be applied to find the partial pressures of nitrogen and sulfur dioxide in Venus's atmosphere.

Venus Atmosphere Composition

The composition of Venus's atmosphere is quite different from that of Earth. It is predominantly composed of carbon dioxide (CO₂), which makes up about 96.5% of the atmosphere by volume. This high concentration of CO₂ contributes to Venus's intense greenhouse effect, leading to surface temperatures high enough to melt lead. Venus's atmosphere also contains about 3.5% nitrogen (N₂), which, despite being a minor component, plays a role in atmospheric pressure and density.
Additionally, sulfur dioxide (SO₂) is present in trace amounts (0.015%), contributing to cloud formation and the planet's yellowish appearance. This mixture of gases creates an environment that is both hot and hostile. Understanding the gas composition of Venus helps scientists investigate not only planetary atmospheres but also climates and potential habitability of other celestial bodies.