Answer these questions and formulas. Ideal Gas Law Worksheet, solving problems

ideal_gas_law_worksheet.pdf

Unformatted Attachment Preview

Name______________________________________

Gas Laws Worksheet, CHEM1210, Spring 2019

Simple Gas Laws

The simple gas laws discover the relationship of pressure, temperature, volume and amount of gas. They

were derived by holding two of the gas properties constant, varying the 3rd and measuring the effect on

the 4th property. Boyle’s Law tells us that the volume of gas increases as the pressure decreases. Charles’

Law tells us that the volume of gas increases as the temperature increases. Avogadro’s Law tells us that

the volume of gas increases as the amount of gas increases. And Guy-Lassac’s Law tells us that the

pressure of gas increases as the temperature increases. The ideal gas law is the combination of the

simple gas laws.

Law Name

Law

Definition

Boyle’s Law

For a given amount of

gas at constant

temperature, the

volume of a gas varies

inversely with pressure

Constant

Properties

Law

Formula

n, T = const

” ” = % %

Charles’ Law

The volume of a fixed

amount of gas is

directly proportional

to its Kelvin

temperature if the

pressure is kept

constant.

n, P = const

Avogadro’s Law

The volume of a gas is

directly proportional

to the number of

moles of gas present

in the sample at

constant temperature

and pressure.

P, T = const

Guy-Lassac’s Law

The pressure of a

given amount of

gas is directly

proportional to the

Kelvin temperature

if the volume is

kept constant.

n, V = const

” %

=

” %

” %

=

” %

” %

=

” %

Example Problems:

Problem 1: A balloon contains 7.2 L of He. When the pressure is reduced to 2.00 atm the balloon

expands to occupy a volume of 25.1 L. What was the initial pressure exerted on the balloon?

Step 1: List the known and unknown variables: V1=7.2L, P1=?

V2=25.1L, P2=2.00atm

Step 2: Make sure that the variables are in the appropriate units.

Step 3: Identify the simple gas law that would be appropriate to solve the problem, given the

information.

Boyle’s law: ” ” = % %

Step 4: Solve:

” (7.2 ) = = (2.00 )(25.1 )

(2.00 )(25.1 )

” =

= 6.972 = 7.0

(7.2 )

Problem 2: The temperature inside my refrigerator is about 4o Celsius. If I place a balloon which is

initially at 22o C and a volume of 0.5 liters in my fridge, what will the volume of the balloon be, after

it is fully cooled by my refrigerator?

Step 1: List the known and unknown variables: T1=22o C, V1= 0.50L, T2 =4.0oC, V2=?

Step 2: Make sure that the variables are in the appropriate units

In this case, T needs to be converted to Kelvins

T1=22o C + 273.15K = 295.15K

T2 =4oC + 273.15K = 277.15K

Step 3: Identify the simple gas law that would be appropriate to solve the problem, given the

information.

Name______________________________________

7

7

Charle’s law: 98 = 9:

8

Step 4: Solve:

:

0.50

%

=

295.15 277.15

%

0.5

=

(277.15 ) = 0.47

295.15

Problem 3: A 25.5 L balloon holding 3.50 moles of carbon dioxide leaks. If we are able to determine

that 1.90 moles of carbon dioxide escaped before the container could be sealed, what is the new

volume of the container?

Step 1: List the known and unknown variables: V1=25.5L, n1=3.50 mol, n2 = 3.50mol(initially) 1.90mol(leaked)=1.60 mol (remaining in balloon), V2=?

Step 2: Make sure that the variables are in the appropriate units.

Step 3: Identify the simple gas law that would be appropriate to solve the problem, given the

information.

Avogadro’s Law:

78

=8

7

= =:

:

Step 4: Solve:

25.5

%

25.5

(1.60 ) = 11.7

=

∴ % =

3.50 1.60

3.50

Problem 4: The pressure in an automobile tire is 1.88 atm at 25.0°C. What will be the pressure, if the

temperature warms up to 37.0°C

Step 1: List the known and unknown variables: P1=1.88 atm, T1=25oC, P2=?, T2=37.0°C

Step 2: Make sure that the variables are in the appropriate units

In this case, T needs to be converted to Kelvins

T1=25.0o C + 273.15K = 298.15K

T2 =37.0oC + 273.15K = 310.15K

Step 3: Identify the simple gas law that would be appropriate to solve the problem, given the

information

Guy-Lassac’s Law∶

C8

98

=

C:

9:

Step 4: Solve:

1.88

%

1.88

(310.15 ) = 1.96

=

∴ % =

298.15 310.15

298.15

Solve the following problems

1. A rigid plastic container holds 1.00 L methane gas at 0.9 atm pressure when the temperature is

22.0°C. What pressure would the gas exert if the temperature is raised to 44.6°C ?

Name______________________________________

2. If 5.00 g of O2 gas has a volume of 7.20 L at a certain temperature and pressure, what volume

does 15.0 g of O2 have under the same conditions?

3. The gas in a 600 mL balloon has a pressure of 1.20 atm. If the temperature remains constant,

what will be the pressure of the gas in the balloon when it is compressed to 400 mL?

4. On hot days, you may have noticed that potato chip bags seem to “inflate”, even though they

have not been opened. If I have a 250 mL bag at a temperature of 19oC, and I leave it in my car

o

which has a temperature of 60 C, what will the new volume of the bag be?

Name______________________________________

Ideal Gas Law

Ideal Gas Law Equation: =

The ideal gas law is an equation that relates the volume, temperature, pressure and amount of gas

particles to a constant. The ideal gas constant is abbreviated with the variable R and has the value of

0.08206 atm·L/mol·K. The ideal gas law can be used when three of the four gas variables are known.

When using this equation, it is important that the units for pressure are atmospheres (atm), volume is in

liters (L), and temperature is converted to kelvins (K). The amount of gas is measured in units called

moles (mol).

Example: The pressure exerted by 2.8 moles of argon gas at a temperature of 85oC is 420 torr. What is

the volume of this sample?

Step 1: List the known variables: n= 2.8 moles; T= 85oC; P = 420 torr.

Step 2: List the unknown variable: V=?

Step 3: Check that the known variables are expressed in the appropriate units. If not, convert them.

n= 2.8 moles ü

T= 85oC – need to convert to Kelvin. K=C+273.15=85oC+273.15=358.15K

P = 420 torr – need to convert to atmospheres using the relationship 1.00 atm = 760 torr.

” LMN

420 × OPQ MRSS = 0.553

Step 4: Substitute into the equation for volume and solve, using the units as guides and canceling them

out.

.

(2.8 ) V0.08206 . W (358.15 )

=

=

= 148.8 = 1.5 10% (2 )

0.553

Solve the following problems.

1. A scuba tank has a pressure of 190 atm at a temperature of 283K. The volume of the tank is 350

L. How many moles of air are in the tank?

Name______________________________________

2. A helium-filled balloon has a volume of 20 L and it contains 2.00 moles of gas. If the pressure of

the balloon is 1.2 atm, determine the temperature.

3. A tank of oxygen has a volume of 1500 L. The temperature of the gas inside is 35oC. If there are

9000 moles of oxygen in the tank what is the pressure in atm?

4. A canister of acetylene has a volume of 42 L. The temperature of the acetylene is 305 K and the

pressure is 780 torr. Determine the amount (moles) of gas in the canister.

Mixtures of Gases

Dalton’s law of partial pressures states that the total pressure of a mixture of gases is equal to the sum

of the individual pressures. In other words, mixtures of gases behave the same as a single gas would. In

a mixture of gases each individual gas contributes its own pressure, known as the partial pressure, to

the total pressure. The pressure of each gas is determined by the number of moles of gas, its volume

and temperature (ideal gas law). The sum of each gas pressure equals to the total pressure. The

equation for this law is MRML] = ” + % + _ …

The composition of a gas mixture can be described by the mole fractions of the gases present. The mole

fraction (X) of any component of a mixture is the ratio of the number of moles of that component to the

NR]bc Rd ”

=8

total number of moles of all the species present in the mixture (ntot): ” = MRML] NR]bc = = e= e=

e⋯

8

:

f

Name______________________________________

The mole fraction is a dimensionless quantity between 0 and 1. If X1=1.0, then the sample is pure gas 1,

not a mixture. If X1=0, then no gas 1 is present in the mixture. The sum of the mole fractions of all the

components present must equal 1.

We can use the mole fraction of a gas A in a mixture to calculate the partial pressure of gas A, given the

total pressure exerted by the gas mixture, using the following equation:

h = h MRML]

Model: A Mixture of Gases

= 0.1 mol of oxygen gas

Tank A

Row #

1

2

3

4

5

6

7

8

9

10

11

12

= 0.10 mole of nitrogen gas

Tank B

Volume (L)

Temperature (K)

Moles of O2 gas

Moles of N2 gas

Total moles of gas in tank

Pressure O2 (atm)

Pressure N2 (atm)

Total Pressure in tank (atm)

X (O2)

X (N2)

P(O2) (atm)

P(N2) (atm)

Tank C

Tank A

10.00L

298K

Tank B

10.00L

298K

–

–

Tank C

10.00L

298K

1) What do all three tanks have in common?

2) Determine the moles of O2 gas and N2 gas for each tank in the model and enter those

values in the table (rows 3,4,5)

3) Use the Ideal Gas Law to calculate the pressure of O2 (show work here) and enter the

answers in the table (row 6):

Name______________________________________

4) Use the Ideal Gas Law to calculate the pressure of N2 (show work here) and enter the

answers in the table (row 7):

5) What is the total pressure in each tank? Show work here. Enter your answers in the table (row

8).

6) Determine the mole fractions (X) of O2 gas and N2 gas for each tank. Show work here. Enter the

values in the table (row 9, 10).

7) Calculate the partial pressures of O2 gas (P(O2)) and N2 gas (P(N2)) for tank C using the mole

fraction and the total pressure of each gas. Show work here. Enter the values in the table (rows

11,12).

8) What do you notice when comparing rows 11 and 12 with rows 6 and 7? Why?

Solve the following problems:

1. Three gases are originally present in three separate 1.00 L containers. The pressure of the CO2

container is 0.32atm, the N2 container is at 0.49atm, and the He container measures at

0.16atm. The three gasses are then transferred to a single 1.00 L container.

i.

What is the pressure of this mixture of gases?

ii.

What are the mole fractions of the gases in the above mixture?

2. A mixture containing 0.226 mol He, 0.342 mol Ne, and 0.128 mol Ar is confined in a 4.00- L

vessel at 25 °C.

i.

What is the total pressure of the gas mixture?

ii.

What are the mole fractions of all the gases in the mixture?

iii.

What is the partial pressure of each gas in the mixture?

3. A mixture of 2 mol H2 and 3 mol He exerts a total pressure of 3 atm. What is the partial pressure

of He?

…

Purchase answer to see full

attachment