   Chapter 10, Problem 69GQ

Chapter
Section
Textbook Problem

You have four gas samples: 1. 1.0 L of H2 at STP 2. 1.0 L of Ar at STP 3. 1.0 L of H2 at 27 °C and 760 mm Hg 4. 1.0 L of He at 0 °C and 900 mm Hg (a) Which sample has the largest number of gas panicles (atoms or molecules)? (b) Which sample contains the smallest number of panicles? (c) Which sample represents the largest mass?

(a)

Interpretation Introduction

Interpretation:

Considering the four different given gases the gas with largest number of molecules, the gas with smallest number of molecules and the gas with largest mass should be determined.

Concept Introduction:

Ideal gas Equation:

Any gas is 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.

Explanation

For the four given set of samples calculate the number of moles present in the each given sample as follows,

1L of H2 at 273.15K and at 760 mmHg pressure that is at STP.

PV=nRTn=PVRT=1atm×1L0.0821×273.15=0.0446moles

Mass = Moles × Molar mass=0.0446 ×2=0.0892g

1. 2 1L of Ar at 273.15K and at 760 mmHg pressure that is at STP.

PV=nRTn=PVRT=1atm×1L0.0821×273.15=0.0446moles

Mass = Moles × Molar mass=0.0446 ×40=1.784g

1. 3 1L of H2 at 27oC and at 760 mmHg pressure

(b)

Interpretation Introduction

Interpretation:

The smallest number of particle has to be identified.

Concept Introduction:

Ideal gas Equation:

Any gas is 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.

(c)

Interpretation Introduction

Interpretation:

The largest mass of the sample has to be identified.

Concept Introduction:

Ideal gas Equation:

Any gas is 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.

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