   # A gas sample containing 1.50 moles at 25°C exerts a pressure of 400. torr. Some gas is added to the same container and the temperature is increased to 50.°C. If the pressure increases to 800. torr, how many moles of gas were added to the container? Assume a constant-volume container. ### 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 55E
Textbook Problem
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## A gas sample containing 1.50 moles at 25°C exerts a pressure of 400. torr. Some gas is added to the same container and the temperature is increased to 50.°C. If the pressure increases to 800. torr, how many moles of gas were added to the container? Assume a constant-volume container.

Interpretation Introduction

Interpretation: For the given data, the number of moles of gas added to the container 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

Derive the equation for final number of moles of gas from ideal gas equation for a gas at two conditions.

According to ideal gas equation,

PV=nRT

By rearranging the above equation,

PVnT=R

Since R is a gas constant, for a gas at two conditions the equation can be written as:

P1V1n1T1=R=P2V2n2T2orP1V1n1T1=P2V2n2T2 (1)

For the given data, for a constant volume the above equation (1) becomes,

P1n1T1=P2n2T2 (2)

From equation (2) the final number of moles of gas ( n2 ) can be determined as follows,

n2=n1P2T1P1T2 (3)

From the ideal gas equation the equation for number of moles of gas for a gas at two conditions can be derived by knowing initial pressure ( P1 ), temperature ( T1 ) and number of moles of gas( n1 ) and final pressure( P2 ), temperature( T2 ). It is the ratio of product of initial temperature, number of moles and final pressure to the product of initial pressure and final temperature,.

The given data and its values.

P1=400torrP2=800torrT1=25°C=298Ksince,1K=°C+273=25°C+273

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