Chapter 10, Problem 112SCQ

### Chemistry & Chemical Reactivity

10th Edition
John C. Kotz + 3 others
ISBN: 9781337399074

Chapter
Section

### Chemistry & Chemical Reactivity

10th Edition
John C. Kotz + 3 others
ISBN: 9781337399074
Textbook Problem

# Each of four flasks is filled with a different gas. Each flask has the same volume, and each is filled to the same pressure, 3.0 atm, at 25 °C. Flask A contains 116 g of air, flask B has 80.7 g of neon, flask C has 16.0 g of helium, and flask C has 160. g of an unknown gas. (a) Do all four flasks contain the same number of gas molecules? If not, which one has the greatest number of molecules? (b) How many times heavier is a molecule of the unknown gas than an atom of helium? (c) In which flask do the molecules have the largest kinetic energy? The highest rms speed?

(a)

Interpretation Introduction

Interpretation:

It is given that four flasks contain four different gas with each has the same volume and filled at temperature of 25oC and pressure of 3 atm the flask with that contains gas with greatest number of molecules, the unknown gas should be compared with that of helium and the flask that have largest kinetic energy and with the highest rms speed should be determined.

Concept introduction:

Ideal gas Equation:

Any gas can be described by using four terms namely pressure, volume, temperature and the amount of gas.  Thus combining three laws namely Boyle’s, Charles’s Law and Avogadro’s Hypothesis the following equation could be obtained.

It is referred as ideal gas equation.

nTPV = RnTPPV = nRTwhere,n = moles of gasP = pressureT = temperatureR = gas constant

Under some conditions gases don not behave like ideal gas that is they deviate from their ideal gas properties.  At lower temperature and at high pressures the gas tends to deviate and behave like real gases.

Boyle’s Law:

At given constant temperature conditions the mass of given ideal gas in inversely proportional to its volume.

Charles’s Law:

At given constant pressure conditions the volume of ideal gas is directly proportional to the absolute temperature.

Two equal volumes of gases with same temperature and pressure conditions tend to have same number of molecules with it.

Molar mass: The molar mass of a substance is determined by dividing the given mass of substance by the amount of the substance.

Partial pressure: The partial pressure for any gas can be obtained by multiplication of total pressure of the gas with the mole fraction of the gas present in that total mixture.

Mole fraction: It defines the amount of particular species present in the mixture. It is obtained by dividing the mole of gas by the total mole of gas present in the mixture.

The root mean square velocity μ is defined as the measure of velocity of particle in gas. It is the method to determine the single velocity value for particles.

Root mean square velocity can be determined,

μrms=(3RTM)1/2 (1)

(gas constant)R=8.314JKmolM=Molarmass

Molar mass: The molar mass of a substance is determined by dividing the given mass of substance by the amount of the substance.

Explanation

According to the Avogadro hypothesis gases with equal volume subjected under same temperature and the pressure conditions tend to have same molecules.

All the gases in given four flasks ...

(b)

Interpretation Introduction

Interpretation:

It is given that four flasks contain four different gas with each has the same volume and filled at temperature of 25oC and pressure of 3 atm the flask with that contains gas with greatest number of molecules, the unknown gas should be compared with that of helium and the flask that have largest kinetic energy and with the highest rms speed should be determined.

Concept introduction:

Ideal gas Equation:

Any gas can be described by using four terms namely pressure, volume, temperature and the amount of gas. Thus combining three laws namely Boyle’s, Charles’s Law and Avogadro’s Hypothesis the following equation could be obtained. It is referred as ideal gas equation.

nTPV = RnTPPV = nRTwhere,n = moles of gasP = pressureT = temperatureR = gas constant

Under some conditions gases don not behave like ideal gas that is they deviate from their ideal gas properties.  At lower temperature and at high pressures the gas tends to deviate and behave like real gases.

Boyle’s Law:

At given constant temperature conditions the mass of given ideal gas in inversely proportional to its volume.

Charles’s Law:

At given constant pressure conditions the volume of ideal gas is directly proportional to the absolute temperature.

Two equal volumes of gases with same temperature and pressure conditions tend to have same number of molecules with it.

Molar mass: The molar mass of a substance is determined by dividing the given mass of substance by the amount of the substance.

Partial pressure: The partial pressure for any gas can be obtained by multiplication of total pressure of the gas with the mole fraction of the gas present in that total mixture.

Mole fraction: It defines the amount of particular species present in the mixture. It is obtained by dividing the mole of gas by the total mole of gas present in the mixture.

The root mean square velocity μ is defined as the measure of velocity of particle in gas. It is the method to determine the single velocity value for particles.

Root mean square velocity can be determined,

μrms=(3RTM)1/2 (1)

(gas constant)R=8.314JKmolM=Molarmass

Molar mass: The molar mass of a substance is determined by dividing the given mass of substance by the amount of the substance.

(c)

Interpretation Introduction

Interpretation:

It is given that four flasks contain four different gas with each has the same volume and filled at temperature of 25oC and pressure of 3 atm the flask with that contains gas with greatest number of molecules, the unknown gas should be compared with that of helium and the flask that have largest kinetic energy and with the highest rms speed should be determined.

Concept introduction:

Ideal gas Equation:

Any gas can be described by using four terms namely pressure, volume, temperature and the amount of gas.  Thus combining three laws namely Boyle’s, Charles’s Law and Avogadro’s Hypothesis the following equation could be obtained.  It is referred as ideal gas equation.

nTPV = RnTPPV = nRTwhere,n = moles of gasP = pressureT = temperatureR = gas constant

Under some conditions gases don not behave like ideal gas that is they deviate from their ideal gas properties.  At lower temperature and at high pressures the gas tends to deviate and behave like real gases.

Boyle’s Law:

At given constant temperature conditions the mass of given ideal gas in inversely proportional to its volume.

Charles’s Law:

At given constant pressure conditions the volume of ideal gas is directly proportional to the absolute temperature.

Two equal volumes of gases with same temperature and pressure conditions tend to have same number of molecules with it.

Molar mass: The molar mass of a substance is determined by dividing the given mass of substance by the amount of the substance.

Partial pressure: The partial pressure for any gas can be obtained by multiplication of total pressure of the gas with the mole fraction of the gas present in that total mixture.

Mole fraction: It defines the amount of particular species present in the mixture. It is obtained by dividing the mole of gas by the total mole of gas present in the mixture.

The root mean square velocity μ is defined as the measure of velocity of particle in gas. It is the method to determine the single velocity value for particles.

Root mean square velocity can be determined,

μrms=(3RTM)1/2 (1)

(gas constant)R=8.314JKmolM=Molarmass

Molar mass: The molar mass of a substance is determined by dividing the given mass of substance by the amount of the substance.

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