Chapter The Gaseous State, Question Problem 9QE

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Interpretation:

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An equation for density of a gas has to be derived from the ideal gas law.

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Concept Introduction:

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The mathematical relation between volume and pressure that holds true as per the Boyle’s law for volume and pressure is as follows:

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  V=(constant)×1P

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Here,

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V denotes the volume.

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P denotes the volume.

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Similarly, the mathematical relation between volume and temperature as per the Charles law are as follows:

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  V=(constant)×T

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Here,

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V denotes the volume.

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T denotes the temperature.

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The mathematical relation between volume and amount at constant pressure as per the Avogadro’s law is as follows:

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  V=(constant)×n

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Here,

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V denotes the volume.

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n denotes the number of moles.

\r\n", 'sectionSequence': 0, 'computed': {'sectionNameWithHtmlRemoved': 'Interpretation Introduction', 'sectionTextWithHtmlRemoved': 'Interpretation: An equation for density of a gas has to be derived from the ideal gas law . Concept Introduction: The mathematical relation between volume and pressure that holds true as per the Boyle’s law for volume and pressure is as follows: V = ( constant ) × 1 P Here, V denotes the volume. P denotes the volume. Similarly, the mathematical relation between volume and temperature as per the Charles law are as follows: V = ( constant ) × T Here, V denotes the volume. T denotes the temperature. The mathematical relation between volume and amount at constant pressure as per the Avogadro’s law is as follows: V = ( constant ) × n Here, V denotes the volume. n denotes the number of moles.'}}, {'sectionName': 'Explanation', 'sectionText': "\r\n

The combination of all the gas laws namely Boyle’s law, Charles law and Avogadro’s leads to the ideal gas law equation as given below:

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\u2002PV=nRT(1)

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The relation between number of moles and mass is as follows:

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\u2002n=mM(2)

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Here,

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n is the number of moles.

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m is the given mass.

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M is the molecular mass.

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Substitute the expression of the number of moles from equation (2) in equation (1).

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\u2002PV=(mM)RT

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Rearrange to write the expression of Pressure

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