Chapter 18: Problem 5
(a) Calculate the density of the atmosphere at the surface of Mars (where the pressure is 650 Pa and the temperature is typically 253 \(K\), with a \(CO_2\) atmosphere), Venus (with an average temperature of 730 \(K\) and pressure of 92 atm, with a \(CO_2\) atmosphere), and Saturn's moon Titan (where the pressure is 1.5 atm and the temperature is -178\(^\circ\)C, with a \(N_2\) atmosphere). (b) Compare each of these densities with that of the earth's atmosphere, which is 1.20 kg/m\(^3\). Consult Appendix D to determine molar masses.
Short Answer
Step by step solution
Understand the Ideal Gas Law
Determine Molar Masses
Mars Density Calculation
Venus Density Calculation
Titan Density Calculation
Compare with Earth's Density
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Key Concepts
These are the key concepts you need to understand to accurately answer the question.
Ideal Gas Law
- Pressure (P) is the force exerted by the gas particles on the walls of its container, measured in Pascals (Pa) or atmospheres (atm).
- Volume (V) is the amount of space that the gas occupies, usually measured in cubic meters (m³) or liters (L).
- Number of Moles (n) indicates the quantity of gas particles.
- Universal Gas Constant (R) has a value of 8.314 J/(mol·K) and connects all these variables.
- Temperature (T) is expressed in Kelvin (K) and affects how fast the gas particles move.
Molar Mass
For example:
- Carbon dioxide \( (CO_2) \) has a molar mass of approximately 44.01 g/mol. It's the main component of both Mars and Venus atmospheres.
- Nitrogen \( (N_2) \), which primarily makes up Titan's atmosphere, has a molar mass of about 28.02 g/mol.
Planetary Atmospheres
- Mars: Dominated by \( CO_2 \), it has a high-altitude, thin atmosphere, with low pressure at 650 Pa and a temperature of around 253 K. This leads to a very low density of around 0.020 kg/m³.
- Venus: Has an incredibly dense atmosphere composed mainly of \( CO_2 \). The pressure is immense at 92 atm, and the average temperature is a scorching 730 K, resulting in a much higher density of approximately 67.97 kg/m³.
- Titan (moon of Saturn): The atmosphere is primarily \( N_2 \), with a pressure of 1.5 atm and a surface temperature of -178 °C (95.15 K), leading to a density of about 5.38 kg/m³.
Pressure Conversion
The common units of pressure include:
- Pascal (Pa), the SI unit of pressure, commonly used in scientific calculations.
- Atmosphere (atm), a unit based on the average atmospheric pressure at sea level on Earth.