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Chapter 17: Problem 72

You're on a team planning a mission to Venus to collect atmospheric samples for analysis. The design specs call for a \(1-\mathrm{L}\) sample container, while the scientists want at least 1 mol of gas. Venus's atmospheric pressure is 90 times that of Earth, and its average temperature is \(730 \mathrm{K}\). Will the design work?

Short Answer

Expert verified
The volume of 1 mol of gas in Venusian conditions, calculated using the ideal gas law, will determine the design's effectiveness. If the calculated volume exceeds 1 L, the design will be ineffective; if it's less than or equal to 1 L, the design will work.

Step by step solution

01

Understand the Problem

The goal is to calculate the volume of one mole of gas under given conditions on Venus. The volume is to be compared with the volume of container, i.e, 1 L to verify if the design works.
02

Apply ideal gas law

Rearrange the Ideal gas law \(PV = nRT\) to isolate \(V\), to get \(V = \frac{{nRT}}{P}\). In this equation \(P\) is the pressure, \(V\) is the volume, \(n\) is the number of moles, \(R\) is the gas constant and \(T\) is the absolute temperature.
03

Substitute the values

Substitute the given values: \(n = 1\) mol, \(R = 0.0821 \, \mathrm{L} \cdot \mathrm{atm}/\mathrm{K} \cdot \mathrm{mol}\), \(T = 730 \, \mathrm{K}\), and \(P = 90 \times 1 \, \mathrm{atm}\) into the rearranged ideal gas law equation.
04

Calculate the volume

Calculating it will give the volume of the gas collected in the container on Venus. If the volume is less than or equal to 1 L then the design is effective, otherwise it fails.

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Most popular questions from this chapter

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