EBK CHEMICAL PRINCIPLES
EBK CHEMICAL PRINCIPLES
8th Edition
ISBN: 9781305856745
Author: DECOSTE
Publisher: CENGAGE LEARNING - CONSIGNMENT
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Chapter 16, Problem 148CP
Interpretation Introduction

Interpretation:

The minimum volume of the container needs to be determined.

Concept introduction:

The density is calculated as follows:

  d=mV

Here, m is mass and V is volume.

The ideal gas equation is given below:

  PV = nRT

Here,

P = pressure

V = volume

n = number of moles

R = gas constant

T = Temperature

Expert Solution & Answer
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Answer to Problem 148CP

Minimum volume of the container = 5779 feet3

The cube dimensions are as follows:

a = 17.95 feet

b = 17.95 feet

c = 17.95 feet

Explanation of Solution

The volume of water can be converted into gallons as follows:

  Volume of water = 1 gallon × ( 3785 c m 3 1 gallon) = 3785 cm3

Density of water = 0.998 g/cm3

Temperature of water = 25ºC

Now, calculate the moles of water in 1 gallon as:

  Density =  mass volume  mass of water = density × volume  = 0.998 g/c m 3 × 3785 c m 3 = 3777.4 g of water  moles of water =  mass of water molar mass of water    =  3777.4 g 18.02 g/ mol    = 209.62 mol of water 

Next step is to determine the minimum volume of the container.

The volume of the water vapour is equal to the volume of the container

  PV = nRT

P = vapour pressure of water at 25ºC

n = 209.62 mol of water

R = 0.082 atm L/K mol

T = 25ºC + 273 = 298 K

  vapour pressure of water at 25ºC = 23.8 torr × ( 1 atm 760torr ) = 0.0313 atm

Now rearrange the above equation to get,

  V = nRT / P = ( 209.62 mol)( 0.082 atm L/K mol)( 298 K)0.0313 atm  = 163651 L × ( 1 fee t 3 28.3168 L) = 5779 feet3

Now we determine the cube dimensions.

Volume of the cube = a x b x c

Since each side of a cube is the same: volume of the cube = a × a ×a = a3

  a =( volume of the cube)3 =( 5779 fee t 3 )3 = 17.95 feet

Cube dimensions are as follows:

a = 17.95 feet

b = 17.95 feet

c = 17.95 feet

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Chapter 16 Solutions

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