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Chapter 18: Problem 34

The conditions of standard temperature and pressure (STP) are a temperature of \(0.00^{\circ} \mathrm{C}\) and a pressure of 1.00 \(\mathrm{atm}\) . (a) How many liters does 1.00 \(\mathrm{mol}\) of any ideal gas occupy at STP? (b) For a scientist on Venus, an absolute pressure of 1 Venusian-atmosphere is 92 Earth- atmospheres. Of course she would use the Venusian-atmosphere to define STP. Assuming she kept the same temperature, how many liters would 1 mole of ideal gas occupy on Venus?

Short Answer

Expert verified
(a) 22.4 L at STP on Earth; (b) 0.244 L on Venus at 92 Earth-atmospheres.

Step by step solution

01

Calculate Volume at STP on Earth

At STP on Earth, 1 mole of an ideal gas occupies 22.4 liters. This is a standard result derived from the Ideal Gas Law, \(PV = nRT\), where \(P = 1.00\,\mathrm{atm}\), \(T = 273.15\,\mathrm{K}\), and \(R\) is the gas constant.
02

Determine Pressure on Venus

On Venus, 1 Venusian-atmosphere is equivalent to 92 Earth-atmospheres. Thus, if the pressure is 1 Venusian-atmosphere, this translates to a pressure of \(92\,\mathrm{atm}\) in Earth terms.
03

Apply Ideal Gas Law on Venus

Using the Ideal Gas Law again, \(PV = nRT\). Here, \(P = 92\,\mathrm{atm}\), \(n = 1\,\mathrm{mol}\), \(R = 0.0821\,\mathrm{L}\cdot\mathrm{atm}\cdot\mathrm{mol^{-1}}\cdot\mathrm{K^{-1}}\), and \(T = 273.15\,\mathrm{K}\) (since the temperature remains the same on Venus).Rearrange to find \(V\):\[ V = \frac{nRT}{P} = \frac{1\times 0.0821\times 273.15}{92} \approx 0.244\,\mathrm{L} \]
04

Compare Volume on Earth and Venus

On Earth, 1 mole of gas at STP occupies 22.4 L, whereas on Venus with the same temperature but a higher pressure, it occupies approximately 0.244 L.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

standard temperature and pressure (STP)
Standard Temperature and Pressure (STP) is a set of conditions used in gas calculations to make it easier to compare results from different experiments. It is defined as a temperature of 0.00掳颁 (273.15 K) and a pressure of 1.00 atm (atmosphere). Under these conditions, scientists and students can predict the behavior of gases using the Ideal Gas Law. This standardization allows for consistent and comparable results worldwide.
  • Temperature: 0掳颁
  • Pressure: 1 atm
Applying the Ideal Gas Law at STP simplifies the calculation of the volume of an ideal gas. For instance, 1 mole of an ideal gas is known to occupy 22.4 liters at STP.
volume of ideal gas
The volume of an ideal gas depends on the conditions under which the gas is measured. The Ideal Gas Law equation, \(PV = nRT\), allows us to calculate this volume by using the pressure (\(P\)), number of moles (\(n\)), the gas constant (\(R\)), and temperature (\(T\)).
  • P: Pressure of the gas
  • V: Volume of the gas
  • n: Moles of the gas
  • R: Gas constant (0.0821 L路atm路mol-1路碍-1)
  • T: Temperature in Kelvin
At STP, the volume occupied by 1 mole of any ideal gas is approximately 22.4 liters. This is not just an arbitrary number but a result derived from the Ideal Gas Law applied under these specific standard conditions.
pressure conversions
Pressure conversions are crucial in chemistry, especially when working with gases from different environments. Pressure is often measured in units of atmospheres (atm), but it can also be expressed in other units such as Pascals (Pa) or mmHg. Converting between these units helps scientists work with the pressure in terms that make the most sense for their particular application.

Converting Between Units

When conducting experiments on Venus, the pressure is considered as 1 Venusian-atmosphere, equivalent to 92 Earth-atmospheres. Therefore, understanding how to convert between these units is important.
  • 1 Venusian-atmosphere = 92 Earth-atmospheres
This conversion allows for applying the same formulas, such as the Ideal Gas Law, accurately regardless of the given planetary conditions.
Venusian-atmosphere
The Venusian-atmosphere serves as a fascinating departure from Earth's atmospheric conditions. On Venus, the pressure is significantly higher; 1 Venusian-atmosphere is equal to 92 Earth-atmospheres. This means that the pressure experienced on the surface of Venus is much greater than what we experience on Earth.

Implications for Gas Volume

Because of this high pressure, using the Ideal Gas Law with Venusian conditions provides interesting results. For instance, when calculating the volume of a gas on Venus at STP, the same 1 mole of ideal gas that occupies 22.4 liters on Earth will occupy a much smaller volume, about 0.244 liters, due to the increased pressure.
  • Pressure Effect: Higher pressure reduces gas volume
This is a clear demonstration of how changing one variable in the Ideal Gas Law affects the others, showcasing the adaptability of gases to different environmental conditions.

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Most popular questions from this chapter

(a) Calculate the specific heat capacity at constant volume of water vapor, assuming the nonlinear triatomic molecule has three translational and three rotational degrees of freedom and that vibrational motion does not contribute. The molar mass of water is 18.0 g/mol. (b) The actual specific heat capacity of water vapor at low pressures is about 2000 \(\mathrm{J} / \mathrm{kg} \cdot \mathrm{K}\) . Compare this with your calculation and comment on the actual role of vibrational motion.

A canister of 1.20 mol of nitrogen gas \((28.0 \mathrm{g} / \mathrm{mol})\) at \(25.0^{\circ} \mathrm{C}\) is left on Jupiter's satellite after completion of a future space mission. Europa has no appreciable atmosphere, and the acceleration due to gravity at its surface is 1.30 \(\mathrm{m} / \mathrm{s}^{2}\) . After some time, the canister springs a small leak, allowing molecules to escape through a small hole. What is the maximum height (in \(\mathrm{km}\) ) above Europa's surface that a \(\mathrm{N}_{2}\) molecule having speed equal to the rms speed will reach if it is shot straight up out of the hole in the canister? Ignore the variation in \(g\) with altitude,

A cylinder 1.00 \(\mathrm{m}\) tall with inside diameter 0.120 \(\mathrm{m}\) is used to hold propane gas (molar mass 44.1 \(\mathrm{g} / \mathrm{mol}\) ) for use in a barbecue. It is initially filled with gas until the gauge pressure is \(1.30 \times 10^{6} \mathrm{Pa}\) and the temperature is \(22.0^{\circ} \mathrm{C} .\) The temperature of the gas remains constant as it is partially emptied out of the tank, until the gauge pressure is \(2.50 \times 10^{5}\) Pa. Calculate the mass of propane that has been used.

We have two equal-size boxes, \(A\) and \(B\) . Each box contains gas that behaves as an ideal gas. We insert a thermometer into each box and find that the gas in box \(A\) is at a temperature of \(50^{\circ} \mathrm{C}\) while the gas in box \(B\) is at \(10^{\circ} \mathrm{C}\) . This is all we know about the gas in the boxes. Which of the following statements must be true? Which could be true? (a) The pressure in \(A\) is higher than in \(B\) . There are more molecules in \(A\) than in \(B .(\mathrm{c}) A\) and \(B\) cannot contain the same type of gas. (d) The molecules in \(A\) have more average kinetic energy per molecule than those in \(B\) . (e) The molecules in \(A\) are moving faster than those in \(B\) . Explain the reasoning behind your answers.

Puffy cumulus clouds, which are made of water droplets, occur at lower altitudes in the atmosphere. Wispy cirrus clouds, which are made of ice crystals, occur only at higher altitudes. Find the altitude \(y\) (measured from sea level) above which only cirrus clouds can occur. On a typical day and at altitudes less than 11 \(\mathrm{km}\), the temperature at an altitude \(y\) is given by \(T=T_{0}-\alpha y,\) where \(T_{0}=15.0^{\circ} \mathrm{C}\) and \(\alpha=6.0 \mathrm{C}^{\circ} / 1000 \mathrm{m} .\)
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