   # An ideal gas is contained in a cylinder with a volume of 5.0 × 10 2 mL at a temperature of 30.°C and a pressure of 710. torr. The gas is then compressed to a volume of 25 mL, and the temperature is raised to 820.°C. What is the new pressure of the gas? ### Chemistry: An Atoms First Approach

2nd Edition
Steven S. Zumdahl + 1 other
Publisher: Cengage Learning
ISBN: 9781305079243

#### Solutions

Chapter
Section ### Chemistry: An Atoms First Approach

2nd Edition
Steven S. Zumdahl + 1 other
Publisher: Cengage Learning
ISBN: 9781305079243
Chapter 8, Problem 61E
Textbook Problem
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## An ideal gas is contained in a cylinder with a volume of 5.0 × 102 mL at a temperature of 30.°C and a pressure of 710. torr. The gas is then compressed to a volume of 25 mL, and the temperature is raised to 820.°C. What is the new pressure of the gas?

Interpretation Introduction

Interpretation: For the given data, the pressure inside the cylinder should be determined.

Concept introduction:

By combining the three gaseous laws namely Boyle’s law, Charles’s law and Avogadro’s law a combined gaseous equation is obtained. This combined gaseous equation is called Ideal gas law.

According to ideal gas law,

PV=nRT

Where,

P = pressure in atmospheres

V= volumes in liters

n = number of moles

R =universal gas constant ( 0.08206L×atm/K×mol )

T = temperature in kelvins

By knowing any three of these properties, the state of a gas can be simply identified with applying the ideal gas equation. For a gas at two conditions, the unknown variable can be determined by knowing the variables that change and remain constant and can be generated an equation for unknown variable from ideal gas equation.

### Explanation of Solution

Explanation

From the ideal gas equation the equation for final pressure for a gas at two conditions can be derived by knowing initial pressure ( P1 ), temperature ( T1 ) and volume ( V1 ) and final volume

( V2 ), temperature ( T2 ). It is the ratio of product of initial volume, pressure and final temperature to the product of initial temperature and final volume.

According to ideal gas equation,

PV=nRT

By rearranging the above equation,

PVT=nR

Here for the given data n is constant and R is a gas constant, for a gas at two conditions the equation can be written as:

P1V1T1=nR=P2V2T2orP1V1T1=P2V2T2

For the given data, for a constant number of moles the equation for final pressure should be

P2=P1V1T2V2T1 (1)

To find out the final pressure of gas , it is needed to take and write the given data and substitute their values in the equation (1). For two conditions problem, units for P and V just needed to be the same units and it is not needed to convert the standard units. But in the case of pressure, it must be converted to the Kelvin.

P1=710

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