Chapter 10, Problem 74GQ

### 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

# A miniature volcano can be made in the laboratory with ammonium dichromate. When ignited, it decomposes in a fiery display.(NH4)2Cr2O7(s) → N2(g) + 4 H2O(g) + Cr2O3(s)If 0.95 g of ammonium dichromate is used and the gases from this reaction are trapped in a 15.0-L flask at 23 °C, what is the total pressure of the gas in the flask? What are the partial pressures of N2 and H2O?

Interpretation Introduction

Interpretation: For the given reaction under given reaction conditions the total pressure of gas in the flask and the partial pressures of the given gases 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,

â€‚Â MassÂ of(NH4)2Cr2O7â€Šâ€Š=â€Šâ€Š0.95gVolumeâ€Šâ€Š=â€Šâ€Š15LTemperatureâ€Šâ€Š=â€Šâ€Š23oC

The given balanced equation for the combustion of given compound in order to obtain the given set of gas is as follows,

â€‚Â (NH4)2Cr2O7â†’N2(g)+4H2O(g)+Cr2O3(s)

â€‚Â Molesâ€Šâ€Šofâ€Šâ€Š(NH4)2Cr2O7=massmolarâ€Šâ€Šmassâ€Šâ€Šofâ€Šâ€Š(NH4)2Cr2O7â€Šâ€Šâ€Š=0.95g252.07g/molâ€Šâ€Šâ€Šâ€Šâ€Š=â€Šâ€Š0.0037688mol

Now using ideal gas equation the partial pressure of the given gases can be determined.

From the equation it clear that one mole of (NH4)2Cr2O7 gives 1 mole of N2(g).

â€‚Â Â PVÂ =Â nRTmolesÂ ofÂ N2Â =Â 0.0037688Â mol,Pâ€Šâ€Š=â€Šâ€ŠnRTVâ€Šâ€Š=â€Šâ€Š0.0037688Ã—0.08206Ã—273.1515â€Šâ€Šâ€Šâ€Šâ€Šâ€Šâ€Šâ€Šâ€Š=â€Šâ€Š6.11Ã—10âˆ’3atm

â€‚Â Â PVÂ =â€‰Â nRTmolesÂ ofÂ H2OÂ isÂ asÂ follows,â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰=â€‰â€‰4Ã—0

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