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Chapter 6 The States of Matter. 6.8 The Combined Gas Law and Ideal Gas Law. Combined Gas Law. The combined gas law uses Boyle’s Law, Charles’ Law, and Gay-Lussac’s Law (n is constant). P 1 V 1 = P 2 V 2 T 1 T 2. Combined Gas Law Calculation.

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chapter 6 the states of matter
Chapter 6 The States of Matter

6.8

The Combined Gas Law and Ideal Gas Law

combined gas law
Combined Gas Law

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 calculation
Combined Gas Law Calculation

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 Table

Conditions 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 continued
Combined Gas Law Calculation (continued)

2. Solve for T2P1 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

learning check
Learning Check

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)?

solution
Solution

Data Table

Conditions 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 = V1xP1 x T2

P2 T1

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

802 mm Hg x 308K

ideal gas law
Ideal Gas Law

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

learning check1
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?

solution1
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 quantityPV=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

learning check2
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?

solution2
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 quantityPV=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