Chapter 10, Problem 63GQ

### Chemistry & Chemical Reactivity

10th Edition
John C. Kotz + 3 others
ISBN: 9781337399074

Chapter
Section

### Chemistry & Chemical Reactivity

10th Edition
John C. Kotz + 3 others
ISBN: 9781337399074
Textbook Problem

# The temperature of the atmosphere on Mars can be as high as 27 °C at the equator at noon, and the atmospheric pressure is about 8 mm Hg. If a spacecraft could collect 10. m3 of this atmosphere, compress it to a small volume, and send it back to Earth, how many moles would the sample contain?

Interpretation Introduction

Interpretation: The number of moles of sample collected from mars at given temperature pressure and given volume should be determined.

Concept introduction:

Ideal gas Equation:

Any gas is described by using four terms namely pressure, volume, temperature and the amount of gas.  Thus combining three laws namely Boyle’s, Charles’s Law and Avogadro’s Hypothesis the following equation could be obtained.  It is referred as ideal gas equation.

nTPV = RnTPPV = nRTwhere,n = molesofgasP = pressureT = temperatureR = gas constant

Under some conditions gases don not behave like ideal gas that is they deviate from their ideal gas properties.  At lower temperature and at high pressures the gas tends to deviate and behave like real gases.

Boyle’s Law:

At given constant temperature conditions the mass of given ideal gas in inversely proportional to its volume.

Charles’s Law:

At given constant pressure conditions the volume of ideal gas is directly proportional to the absolute temperature.

Two equal volumes of gases with same temperature and pressure conditions tend to have same number of molecules with it.

Explanation

Given,

â€‚Â VÂ =Â 10Â m3TÂ â€Šâ€Šâ€Šâ€Š=Â 27âˆ˜Câ€Šâ€ŠPâ€Šâ€ŠÂ =Â 8Â mmHgÂ

In order to calculate the moles of sample collected the given data should be incorporated into the ideal gas equation which is achieved as follows,

â€‚Â RÂ =Â 0.0821Â L.atm.K-1.mol-1PÂ =Â 8Â mmÂ HgÂ â€Šâ€Š=â€Šâ€Š0.0105Â atmÂ Â TÂ =Â â€Šâ€Š27âˆ˜Câ€Šâ€Š=â€Šâ€Š300

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