   Chapter 10, Problem 110SCQ

Chapter
Section
Textbook Problem

Two flasks, each with a volume of 1.00 L, contain O2 gas with a pressure of 380 mm Hg. Flask A is at 25 °C, and flask B is at 0 °C. Which flask contains the greater number of O2 molecules?

Interpretation Introduction

Interpretation: For the given O2 gas in two flasks under same volume and pressure conditions with different temperature condition such that flask A is at 25oC and flask B at 0oC, the gas in flask with greater number of O2 molecules 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.

Explanation

Given:

According to the ideal gas equation pressure is generally expressed as follows,

PV = nRTn =PVRTwhere, n = molesForgasinflask B,n =1atm×380mmHg760mmHg×1L0.0821Latm mol-1K-1×(0+273K)=0.022molesForgasinflask A,n =1atm×380mmHg760mmHg×1L0.0821Latm mol-1K-1×(25+273K)=0.020moles

Hence,No. of molecules  = moles × 6.023×1023moleculesNo

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