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An automobile tire with a maximum rating of 34.0 psi (gauge pressure) is inflated (while cold) to a volume of 9.8 L and a pressure of 33.0 psi at a temperature of 9 .0°C . While the car is being driven on the highway on a hot day, the tire warms to 70 .0°C , and its volume expands to 10.1 L. Does the pressure in the tire exceed its maximum rating under these conditions? (Note: The gauge pressure is the difference between the total pressure and atmospheric pressure. Find the total pressure by assuming that atmospheric pressure is 14.7 psi.)

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Chemistry In Focus

7th Edition
Tro + 1 other
Publisher: Cengage Learning,
ISBN: 9781337399692

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Chapter
Section
BuyFindarrow_forward

Chemistry In Focus

7th Edition
Tro + 1 other
Publisher: Cengage Learning,
ISBN: 9781337399692
Chapter 11, Problem 51E
Textbook Problem
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An automobile tire with a maximum rating of 34.0 psi (gauge pressure) is inflated (while cold) to a volume of 9.8 L and a pressure of 33.0 psi at a temperature of 9 .0°C . While the car is being driven on the highway on a hot day, the tire warms to 70 .0°C , and its volume expands to 10.1 L. Does the pressure in the tire exceed its maximum rating under these conditions? (Note: The gauge pressure is the difference between the total pressure and atmospheric pressure. Find the total pressure by assuming that atmospheric pressure is 14.7 psi.)

Interpretation Introduction

Interpretation:

The pressure of an automobile tire at 70

C, having volume 10.1 L, is to be calculated.

Concept Introduction:

Combined gas law, also called general gas equation, combines Boyle’s Law and Charles’s Law. It states that the ratio of the pressure-volume product and the absolute temperature of a gas is equal to a constant.

P1V1T1=P2V2T2

Here, P1 and P2 are the initial and final pressures of the ideal gas, V1 and V2 are the initial and the final volumes of the gas and T1, T2 are the initial and final temperatures of the ideal gas.

Converting degree Celsius to Kelvin by adding 273K, the conversion factor is as:

T=°C+ 273K

Explanation of Solution

Given information:

Initial Pressure in the tire is 33.0psi.

Initial Temperature in the tire is 9°C.

Final Temperature of the tire is 70°C.

Initial Volume of the tire is 9.8L.

Final Volume of the tire is 10.1L.

Maximum pressure (gauge pressure) of the tire is 34psi.

According to combinedgas law,

P1V1T1=P2V2T2

Now, converting the temperature from degree Celsius to Kelvin by using a conversion factor as:

T1=9°C=9+273K=282K

T2=70°C=70+273K=343K

The pressure in the tire is the sum of the actual pressure in the tire and atmospheric pressure.

Totalpressure=33.0psi+14.7psi=47

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Chemistry In Focus
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