Chapter 10, Problem 105IL

### 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

# You have a gas, one of the three known phosphorus-fluorine compounds (PF3, PF3, and P2F4). To find out which, you have decided to measure its molar mass. (a) First, yon determine that the density of the gas is 5.60 g/L at a pressure of 0.971 atm and a temperature of 18.2 °C. Calculate the molar mass and identify the compound. (b) To check the results from part (a), you decide to measure the molar mass based on the relative rales of effusion of the unknown gas and CO2. You find that CO2 effuses at a rate of 0.050 mol/min, whereas the unknown phosphorus fluoride effuses at a rate of 0.028 mol/min. Calculate the molar mass of the unknown gas based on these results.

(a)

Interpretation Introduction

Interpretation:

From the given set of gases the gas that matches with the molar mass obtained from the calculation using given set of conditions 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.

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.

Average Kinetic energy: The kinetic energy for the gas is directly proportional to the kelvin temperature. The kinetic energy is equal to half of the multiplied value obtained by multiplication of mass of gas with rms velocity of the gas.

Explanation

Given:

â€‚Â Density,Â Dâ€Šâ€Šâ€Šâ€Š=5.60Â g/LPressure,Â Pâ€Šâ€Šâ€Š=â€Šâ€Š0.971Â atmTemperature,â€Šâ€ŠTÂ =Â 18.2oCÂ =Â 273.15+18.2Â =Â 291.35K

Using ideal gas equation the molar mass for the unknown gas is determined as follows,

â€‚Â PV=Â nRTâ€Šâ€Šâ€Šâ€Šâ€Šâ€Šâ€ŠPÂ =Â nRTVâ€Šâ€Šâ€Šâ€Šâ€Šâ€Šâ€Šâ€Šâ€ŠPÂ =Â MassMolarâ€Šâ€ŠmassÃ—RTVâ€ŠMolarâ€Šâ€ŠmassÂ =Â MassVÃ—RTPâ€Šâ€Šâ€Šâ€Šâ€Šâ€Šâ€Šâ€Šâ€Šâ€Šâ€Šâ€Šâ€Šâ€Šâ€Šâ€Šâ€Šâ€Šâ€Šâ€Šâ€Šâ€Šâ€Šâ€Šâ€Šâ€Šâ€Šâ€Šâ€Šâ€Šâ€Šâ€Šâ€Šâ€Šâ€Šâ€Šâ€Šâ€Šâ€Šâ€Šâ€Šâ€Šâ€Šâ€Šâ€Šâ€Šâ€Šâ€Šâ€Šâ€Šâ€Šâ€Šâ€Šâ€Šâ€Šâ€Šâ€Š=5.60Â g/LÃ—0.0821Ã—291.35â€Šâ€Š0

(b)

Interpretation Introduction

Interpretation:

From the given set of gases the gas that matches with the molar mass obtained from the calculation using given set of conditions 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.

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.

Average Kinetic energy: The kinetic energy for the gas is directly proportional to the kelvin temperature. The kinetic energy is equal to half of the multiplied value obtained by multiplication of mass of gas with rms velocity of the gas.

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