± Introduction to the Ideal Gas Law Learning Goal: To apply the ideal gas law to

Question

± Introduction to the Ideal Gas Law

Learning Goal:

To apply the ideal gas law to problems involving temperature, pressure, volume, and moles of a gas.

PV=nRT

Part A

A balloon is floating around outside your window. The temperature outside is -3 C , and the air pressure is 0.800 atm . Your neighbor, who released the balloon, tells you that he filled it with 3.40 moles of gas. What is the volume of gas inside this balloon?

Express your answer to three significant figures and include the appropriate units.

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Part B

A 10.0 L gas cylinder is filled with 8.80 moles of gas. The tank is stored at 31 C . What is the pressure in the tank?

Express your answer to three significant figures and include the appropriate units.

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Part C

A 280. L kiln is used for vitrifying ceramics. It is currently operating at 1295 C , and the pressure is 1.025 atm . How many moles of air molecules are within the confines of the kiln?

Express your answer to three significant figures and include the appropriate units.

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Part D

A 20.0 L gas cylinder has been filled with 6.00 moles of gas. You measure the pressure to be 4.00 atm . What is the temperature inside the tank?

Express your answer to three significant figures and include the appropriate units.

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± Introduction to the Ideal Gas Law

Learning Goal:

To apply the ideal gas law to problems involving temperature, pressure, volume, and moles of a gas.

The four properties of gases (pressure P, volume V, temperature T, and moles of gas n) are related by a single expression known as the ideal gas law:

PV=nRT

The variable R is known as the universal gas constant and has the value R=0.0821 Latm/(moleK). The units of Rdictate the units for all other quantities, so when using this value of R, use units of atmospheres for pressure, liters for volume, and kelvins for temperature.

Part A

A balloon is floating around outside your window. The temperature outside is -3 C , and the air pressure is 0.800 atm . Your neighbor, who released the balloon, tells you that he filled it with 3.40 moles of gas. What is the volume of gas inside this balloon?

Express your answer to three significant figures and include the appropriate units.

Vballoon =

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Part B

A 10.0 L gas cylinder is filled with 8.80 moles of gas. The tank is stored at 31 C . What is the pressure in the tank?

Express your answer to three significant figures and include the appropriate units.

Ptank =

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Part C

A 280. L kiln is used for vitrifying ceramics. It is currently operating at 1295 C , and the pressure is 1.025 atm . How many moles of air molecules are within the confines of the kiln?

Express your answer to three significant figures and include the appropriate units.

nair =

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Part D

A 20.0 L gas cylinder has been filled with 6.00 moles of gas. You measure the pressure to be 4.00 atm . What is the temperature inside the tank?

Express your answer to three significant figures and include the appropriate units.

Ttank =

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Explanation / Answer

Part A

P = atmospheric pressure = 0.8 atm

T = -3 c = 270 k

n = 3.4 mol

V = nRT/P = 3.4*0.0821*270/0.8 = 94.2 L

part B

V = 10 L

n = 8.8 mol

T = 31 C = 304 k

R = 0.0821 l.at.k-1.mol-1

Ptank = 8.8*0.0821*304/10 = 22.0 atm

part C

V = 280 L

n = ? mol

T = 1295 C = 1568 k

P = 1.025 atm

R = 0.0821 l.at.k-1.mol-1

n = PV/RT = 1.025*280/(0.0821*1568) = 2.23 mol

part D

V = 20 L

n = 6 mol

T = ? k

P = 4 atm

R = 0.0821 l.at.k-1.mol-1

T = PV/nR = 4*20/(0.0821*6)

   = 162 K

   = -111 C

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