   # A cylinder fitted with a movable piston initially contains 2.00 moles of O 2 ( g ) and an unknown amount of SO 2 ( g ). The oxygen is known to be in excess. The density of the mixture is 0.8000 g/L at some T and P. After the reaction has gone to completion, forming SO 3 ( g ), the density of the resulting gaseous mixture is 0.8471 g/L at the same T and P. Calculate the mass of SO 3 formed in the reaction. ### 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 19, Problem 105CP
Textbook Problem
1 views

## A cylinder fitted with a movable piston initially contains 2.00 moles of O2(g) and an unknown amount of SO2(g). The oxygen is known to be in excess. The density of the mixture is 0.8000 g/L at some T and P. After the reaction has gone to completion, forming SO3(g), the density of the resulting gaseous mixture is 0.8471 g/L at the same T and P. Calculate the mass of SO3 formed in the reaction.

Interpretation Introduction

Interpretation: The mass of SO3 formed in the reaction is to be calculated.

Concept introduction: Volume is calculated by the ratio of mass to density. If pressure and temperature remains constant, then volume depends upon number of moles of gas.

To determine: The mass of SO3 formed in the reaction.

### Explanation of Solution

Explanation

The reaction between O2 and SO2 is as follows,

2SO2+O22SO3

Given

Number of moles of O2 is 2 moles.

The number of moles of SO2 is assumed to be t in the container and the initial volume is assumed to be V L.

Total number of moles of gases (n1) in reactant is calculated by the formula,

n1=Number of moles of O2+Number of moles of SO2

Substitute the value of number of moles of O2 and SO2.

n1=2+t

The total mass is calculated by the formula,

Total mass=((Number of moles of O2×Molar mass of O2)+(Number of moles of SO2×Molar mass of SO2))

Molar mass of O2 is 16 g/mol and the molar mass of SO2 is 64 g/mol.

Substitute the molar mass values in the above equation,

Total mass=((2×32)+(t×64))=64+64t

Relationship between mass, density and volume (V1) is expressed as,

V1=MassDensity

The density before the reaction is 0.800 g/L.

Substitute the value of density and mass in above equation.

V1=64(1+t)0.8=20(1+t)

In the given reaction, t moles of SO2 uses t/2 moles of O2 to form t moles of SO3.

Number of moles of O2 left is calculated by the formula,

Moles of O2 left=Total moles of O2Moles of O2 reacted with SO2

Substitute the value of total moles and moles of O2 reacted in the above equation.

Moles of O2 left=2t/2

Total number of moles of gas after reaction (n2) is calculated by the formula,

n2=Number of moles of O2 left+Number of moles of SO2

Substitute the values of Number of moles of O2 left and Number of moles of SO2 in the above equation

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