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Chapter 6 The States of Matter

6.8 The Combined Gas Law and Ideal Gas Law

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The combined gas law uses Boyle’s Law, Charles’ Law, and Gay-Lussac’s Law (n is constant).

P1 V1 = P2 V2

T1 T2

Combined Gas Law

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A sample of helium gas has a volume of 0.180 L, a pressure of 0.800 atm and a temperature of 29°C. At what temperature (°C) will the helium have a volume of 90.0 mL and a pressure of 3.20 atm (n is constant)?1. Set up Data TableConditions 1 Conditions 2

P1 = 0.800 atm P2 = 3.20 atm

V1 = 0.180 L (180 mL) V2 = 90.0 mL

T1 = 29°C + 273 = 302 K T2 = ??

Combined Gas Law Calculation

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Combined Gas Law Calculation (continued)

2. Solve for T2 P1 V1 = P2 V2

T1 T2

T2 = T1 x P2 x V2

P1 V1

T2 = 302 K x 3.20 atm x 90.0 mL = 604 K 0.800 atm 180.0 mL

T2 = 604 K - 273 = 331 °C

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A gas has a volume of 675 mL at 35°C and 0.850 atm pressure. What is the volume(mL) of the gas at -95°C and a pressure of 802 mm Hg (n constant)?

Learning Check

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Solution

Data TableConditions 1 Conditions 2

T1 = 308 K T2 = -95°C + 273 = 178K

V1 = 675 mL V2 = ???

P1 = 646 mm Hg P2 = 802 mm Hg

Solve for V2

V2 = V1 x P1 x T2

P2 T1

V2 = 675 mL x 646 mm Hg x 178K = 314 mL 802 mm Hg x 308K

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The ideal gas law uses Boyle’s Law, Charles’ Law, and Gay-Lussac’s Law, and Avogadro’s Law in a gas sample.

PV = nRT

R is the universal gas constant that relates pressure, volume, temperature, and number of moles of gas in the ideal gas law.

R (gas constant) = 0.0821 L atm mol K

Ideal Gas Law

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Learning Check

A gas system has pressure, volume and temperature of 1.93 atm, 4.31L and 692.0oC, respectively. How many moles of gas are present?

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Solution

First, organize the data converting the temperature and volume, if needed:P=1.93atmV=4.31Ln=?(in moles)T=692.0C=>965KRearrange the ideal gas equation to solve for the missing quantity

PV=nRT=>n=PV/RTSubstitute in the given quantities and solve, using the appropriate ideal gas constant and converting the initial result to the desired dimension, as necessary:(1.93*4.31)/(0.0821*965)=0.105moles

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Learning Check

A gas system has pressure, moles and temperature of 1.77 atm,0.183 moles and 62.00oC, respectively. What is the volume in mL?

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Solution

First, organize the data converting the temperature and volume, if needed:P=1.77atmV=?(in mL)n=0.183molesT=62.00C=>335KRearrange the ideal gas equation to solve for the missing quantity

PV=nRT=>V=nRT/PSubstitute in the given quantities and solve, using the appropriate ideal gas constant and converting the initial result to the desired dimension, as necessary: (0.183*0.0821*335)/1.77=2.84L=>2840mL