Ch.10 - Gases: Their Properties & Behavior

Problem 45

Chapter 10, Problem 45

The surface temperature of Venus is about 1050 K, and the pressure is about 75 Earth atmospheres. Assuming that these conditions represent a Venusian 'STP,' what is the standard molar volume in liters of a gas on Venus?

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1. The standard molar volume of a gas at standard temperature and pressure (STP) on Earth is 22.4 L. This is based on the ideal gas law, PV = nRT, where P is the pressure, V is the volume, n is the number of moles, R is the ideal gas constant, and T is the temperature.

2. On Venus, the conditions are different. The temperature is 1050 K and the pressure is 75 atmospheres. We can use these values to calculate the standard molar volume on Venus.

3. First, we need to rearrange the ideal gas law to solve for V: V = nRT/P. In this case, n is 1 mole (since we're looking for the molar volume), R is 0.0821 L·atm/(K·mol) (the value of the ideal gas constant in these units), T is 1050 K, and P is 75 atm.

4. Substitute these values into the rearranged ideal gas law to calculate the molar volume on Venus.

5. Remember, the result will be in liters, as the units of the ideal gas constant we used are in liters.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Ideal Gas Law

The Ideal Gas Law relates the pressure, volume, temperature, and number of moles of a gas through the equation PV = nRT. This law is fundamental for understanding gas behavior under various conditions. In this context, it allows us to calculate the molar volume of a gas at the extreme conditions present on Venus.

Standard Molar Volume

Standard molar volume is the volume occupied by one mole of an ideal gas at standard temperature and pressure (STP), typically defined as 0°C (273.15 K) and 1 atm. However, in this question, we are asked to determine the molar volume under Venusian conditions, which differ significantly from typical STP.

Conditions on Venus

Venus has extreme surface conditions, with high temperatures (around 1050 K) and pressures (about 75 atmospheres). These conditions significantly affect gas behavior and properties, necessitating adjustments to the Ideal Gas Law to calculate the molar volume accurately. Understanding these unique conditions is crucial for solving the problem.

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