Chapter 10, Problem 62GQ

### 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

# A bicycle tire has an internal volume of 1.52 L and contains 0.406 mol of air. The tire will burst if its internal pressure reaches 7.25 atm. To what temperature, in degrees Celsius, does the air in the tire need to be heated to cause a blowout?

Interpretation Introduction

Interpretation: The temperature at which the tire will blowout should be determined by using the given conditions that volume of tire is 1.52L that contains 0.406mol of air which will burst at pressure of about 7.25atm.

Concept introduction:

Ideal gas Equation:

Any gas can be 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 Volume,Â Vâ€Šâ€Šâ€Šâ€Šâ€Šâ€Šâ€Šâ€Šâ€Šâ€Šâ€Šâ€Šâ€Šâ€Šâ€Šâ€Šâ€Šâ€Šâ€Šâ€ŠÂ =Â 1.52Â LmoleÂ ofÂ air,Â nÂ â€Šâ€Šâ€Šâ€Šâ€Šâ€Šâ€Šâ€Šâ€Š=Â 0.406Pressure,Â Pâ€Šâ€Šâ€Šâ€Šâ€Šâ€Šâ€Šâ€Šâ€Šâ€Šâ€Šâ€Šâ€Šâ€Šâ€Šâ€Šâ€Šâ€Šâ€Šâ€Šâ€ŠÂ =Â 7.25Â atmGasÂ constant,Â RÂ =Â 0.0821Â LÂ atmÂ mol-1K-1Temperature,Â TÂ =Â ?

In order to find the temperature at which 0.406 mole of air inside the given 1.52Â L volume of tire heated to blowout the tire we need to use the ideal gas equation.

The calculation for determination of temperature is described as follows,

â€‚Â PVÂ =Â nRTT=PVnRâ€Šâ€Šâ€Šâ€Šâ€Šâ€Šâ€Šâ€Šâ€Š=7

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