Republic of the Philippines

Department of Education
REGION V - BICOL
SCHOOLS DIVISION OF MASBATE CITY
MASBATE NATIONAL COMPREHENSIVE HIGH SCHOOL
MASBATE CITY

CHEMISTRY 1
1st SEMESTER, SY. 2021-2022

Module 11
Gas Laws
2nd QUARTER WEEK – 1

I. LEARNING SKILLS/CONTENT

After going through this module, you are expected to:

1. define Pressure;
2. identify the common units of pressure;
3. identify the gas laws to explain the pressure, volume, and temperature
relationships of a gas under certain condition of change;
4. express the gas laws in equation form;
5. compute word problems involving gas laws;
6. identify the relationships among pressure, volume, temperature or
number of moles of gas using the ideal gas equation;
7. solve problems using ideal gas equation;
8. utilize Dalton’s law of partial pressure to explain mole fraction and
partial pressure of gases in mixture; and
9. compute word problems using Dalton’s law of partial pressure.

Earth is surrounded by a mixture of gases known as atmosphere. In this vast portion of

Earth, never-ending reactions take place and many of them are determined by the energy from the
sun. In this lesson, you are going to learn the underlying concept of how balloons inflate as you
blow air in it, how hot air balloon goes up, how divers able to dive in an endless water with oxygen
tank and some of the most common real-life scenario you probably encounter in your everyday
life.

Chem-rades!
Directions: Guess the word out of words. Write your answer on the space provided.
Example:
Charade Hidden term
Came Mist Three Chemistry

1. Tea you ray thee call yelled

2. Ache wall yelled
3. Pear scent age yelled
4. Ray ache taunt
5. Must ray lay shown shape
Gas Pressure
One of the most important properties of any gas is its pressure. The firmness of a balloon filled
with air indicates that the gas inside exerts pressure. This pressure is caused by gas molecules
striking the balloon’s inner surface with each collision exerting a force on the surface. The
amount of force exerted in a specific area is what we call pressure.

It is given as: Where:

P= Pressure
P= 𝐅 F= Force
𝐀 A= Area

Gas Pressure: Units and Conversions

Gas particles in the atmosphere have mass and are pulled toward the Earth by gravity where they
exert pressure on every surface it contacts. This pressure is known as the atmospheric pressure.
Atmospheric pressure can be measured with a barometer. Pressure measured with a mercury
barometer is usually reported in millimeters of mercury (mmHg), a unit that is also
called the torr after Evangelista Torricelli, who invented the mercury barometer in 1643. The
standard atmosphere (atm) is defined as

The table below shows some of the most common units and conversion factors use in
quantifying gas pressure:
Table 1. Pressure Units

SI Unit: Pascal (Pa)

1 Pa = 1 N/m2 ; 1 kPa = 103 Pa
Other Common Units
1 bar = 105 Pa = 100 kPa ; 1 millibar (mbar) = 102 Pa
1 atm = 1.01325 x105 Pa = 101.325 kPa
1 atm = 760 torr = 760 mmHg (this conversion is exact)*
1 atm = 14.7 lb/inch2 (psi) = 1.01325 bar

There are some instances in this lesson that you will be instructed to convert the units of the
variable that you are going to use in solving word problems and other related mathematical
computation.
Example 1:
1. What is the pressure (in atmospheres) of a gas that has a pressure of 600 torr?
Solution 1:
To solve this problem, you must first identify the conversion factor such as; there is 1 atm in
every 760 torr, thus

600 torr × 1 atm = 0.789 atm

760 torr

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Example 2:
2. The pressure of a gas is measured as 980 mmHg. Express this pressure in atmosphere.
Solution 2:
Conversion factor: 1 atm = 760 mmHg
980 mmHg × 1 atm = 1.29 atm
760 mmHg

Try this:

3. A sample of hydrogen gas has a pressure of 0.75 atm. Give the pressure of hydrogen in torr.
Aside from pressure, gas can also be measured and described with the other parameters (or
variables) such as volume, temperature, and amount of gas (n, mole).

Volume: the space occupied by a certain gas. It is equal to the volume of the container inasmuch
as a gas completely fills its container. The common unit for volume is the liter (L), but the SI
unit for volume is m3. The equivalence of liter in SI units is simple:

1 cubic meter (m3) = 1000 liters (L)

1 cubic decimeter (dm3) = 1 liter (L)
1 cubic centimeter (cm3) = 1 milliliter (mL)

Temperature: Determines the average kinetic energy of a body. The common unit for
temperature is degree Celsius (°C), but the SI unit is Kelvin (K). The Kelvin temperature is used
in all calculations with gases.

The relationship between the units is:

K = °C + 273.15
Amount of Gas: the quantity of the particles of gas added on a system.
In gas laws, the amount of gas in a container is usually expressed in moles (n).

Gas Laws: Pressure, Volume, Temperature and Amount of Gas Relationship

Gases have been studied for hundreds of years, and the properties that all gases display have been
summarized into gas laws that are named for their discoverers. Using the variables such as
pressure, volume, temperature and amount of gas (number of moles); we can write equations that
explain how gases behave. That behaves exactly as described by these equations is called an ideal
gas.

The Pressure-Volume Relationship: BOYLE’S LAW

Boyle’s law states that the volume (V) of an ideal gas varies inversely with the applied pressure (P)
when temperature (T) and amount of gas (n, moles) are constant. In mathematical terms, the initial
pressure P1 multiplied by the initial volume V1 of a gas gives a constant value k
P1 V1 = k
If the volume or pressure of the gas changes without changing the temperature or the amount of
the gas, the final pressure and volume will be equal to the same constant.
P2 V2 = k

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Hence, the relation of the initial and final products of the volume and pressure of a gas may be
written as:
P1 V1 = P2 V2 (at constant T and n)

Table 2. Examples of Pressure-Volume Relations and its graphical representation

Consider the situation below:

1. A sample of oxygen gas (O2) has an initial volume of 8.0 L and a pressure of 1.0 atm. What is the
new pressure if the volume is decreased to 2.0 L?

Step 1: Analyze the stem of the word problems and identify the known and the unknown variables.
Known Variables: • Some clues can be used to identify the right variable and its
V1 = 8.0 L numerical value in the problem. Words such as “initial”, “new”
P1 = 1.0 atm are some of them.
V2 = 2.0 L • Make sure that the units of the variables are scientifically
Unknown Variable: correct.
P2 = ? • Convert the units if it is needed to convert.

Step 2: Express the known and unknown variables into mathematical

equation. Remember this equation? P1 V1 = P2 V2

P1 V1 = P2 V2 • Rearrange the equation to get the correct formula to

V2 V2 compute the unknown.
Final equation:
P2 = P1 V1
V2

Step 3: Substitute the value to its corresponding variables.

P2 = (1.0 atm) (8.0 L) • Compute the problem

2.0 L • Cancel the unnecessary units to arrive with the correct one.
Final answer: 4.0 atm • Make an interpretation from the answer you computed.
***Interpretation: The
pressure is increased which
affects the volume of
the gas to occupy a smaller
volume.

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The Temperature-Volume Relationship: CHARLES’S LAW

Charles’s law states that the volume (V) of an ideal gas varies directly with absolute temperature
(T) when pressure (P) and amount of gas (n) are constant.
𝑽∝𝑻 (V= constant (k) x T) 𝑽 = k (depends on pressure
𝑻
and the amount of the gas. If the volume, V1, and temperature, T1, of a sample of gas are known,
then the volume V2, at some other temperature, T2, at the same pressure is given by unchanging
P and n)
The value of the constant
𝑉1 𝑉2
𝑇1 = 𝑇2 (P and n constant)

Graph 2. Graphical Representation of Volume-Temperature relationship

Consider the situation below:

Example 1:
1. A sample of neon gas at 760 mmHg has a volume of 10.0 L and a temperature of 34°C. Find the
new volume of the gas after the temperature has been increased to 75°C at constant pressure.
Solution:
Since the temperatures are given in degrees Celsius, you must first convert these to Kelvin.

To convert Celsius to Kelvin, this conversion is used

K = °C + 273.15
so,
T1 = 34°C + 273.15 = 307.15 K
T2 = 75°C + 273.15 = 348 K

Placing the information for the gas in a table gives the following:

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According to the temperature-volume relationship,

• Manipulate the equation by crossed-multiplying

𝑉1 = 𝑉2 the variables to arrive in this equation:
𝑇1 𝑇2
𝑽𝟐 = 𝑽𝟏𝑻𝟐
𝑻𝟏

Substituting the given with the variable in your equation will give you,

V2 = (10.0 L)(348 K) • The final volume of 11.3 L is larger than the

307 K initial volume of 10.0 L as a result of the
= 11.3 L temperature increase.

The Amount - Volume Relationship: AVOGADRO’S LAW

Avogadro’s law states that the volume (V) of an ideal gas varies directly with amount (n) when
temperature (T) and pressure (P) are constant.

𝑽∝𝒏 (V= constant (k) x n) 𝑽 = k ( unchanging T and P)

𝒏

The value of the constant depends on the temperature and them pressure. Avogadro’s law means,
for example, that at constant temperature and pressure, the number of moles of gas doubles, the
volume doubles. It also means that at the same temperature and pressure, the volumes of two
different amounts of gases are related as follows:

𝑉1 = 𝑉2
𝑛1 𝑛2 (T and P constant)

The table below shows the comparison of three gases namely: helium (He), methane (CH 4), and
oxygen gas (O2) in terms of volume and amount of gases illustrating Avogadro’s hypothesis.

Table 3. Avogadro’s hypothesis and its graphical representation

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Experiments show that at 0°C and 1 atm pressure, 22.4 L of any gas will contain 1 mol of the gas
(6.02 x 1023 gas molecules).
Example 1:
1. A balloon containing 2.00 moles of helium has a volume of 880 mL. What is the new volume
after 6.00 moles of helium are added to the balloon at the same temperature and pressure?
Solution:
• List the known and the unknown values.

• Rearrange the equation for Avogadro’s law to isolate V 2.

• Substitute the given to the variables in the equation/formula.

*** The final volume of 2640 mL is larger than the initial volume of 880 mL as a result of the
addition of number of moles.

The Combination of Three Gas Laws: IDEAL GAS LAW

The three gas laws just discussed focus on the effects of changes in P, T, or n on a gas volume.
These three gas laws can be combined to give the ideal gas law, which summarizes the
relationships among volume, temperature, pressure, and amount of gas.

To make this proportionality into an equation, a proportionality constant, R, named the ideal gas
constant, is used. The equation becomes

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And, on rearranging, gives the equation called the ideal gas law.

The constant R can be calculated from the experimental fact that 0°C and 1 atm the volume of 1
mol of gas is 22.414-L. This temperature and pressure are called standard temperature and
pressure or STP, and the volume is called the standard molar volume.
Solving the ideal gas law for R, and substituting, gives

The ideal gas constant has different numerical values in different units, as
shown in the table below.

Let’s take a look at this situation:

Example 1:
1. Calculate the pressure exerted by 0.300 mole of gas contained in an 8.00 L vessel at 18°C

Solution:
• Identify the known and the unknown variables.

Known variables Unknown variable

V = 8.00 L P=?
n = 0.300 mol
T = 18°C + 273.15 = 291.15 K

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• Rearrange the equation for ideal gas law to isolate the variable P.
From: Final equation:
PV = nRT P = nRT
Divide V to both side of the V
equation to isolate P
PV = nRT
V V

• Substitute the given to its corresponding variable in the equation.

Gas Mixtures and Partial Pressures: DALTON’S LAW OF PARTIAL PRESSURE

John Dalton was the first to observe that the total pressure exerted by a mixture of gases is the sum
of the partial pressures of the individual gases in the mixture. The pressure of one gas in a mixture
of gases is what we call as the partial pressure. Dalton’s law of partial pressures is a consequence of
the fact that gas molecules behave independently of one another. Let’s consider the main
components of our atmosphere to demonstrate Dalton’s law of partial pressures for which the
total number of moles is approximately:
𝒏𝒕𝒐𝒕𝒂𝒍 = 𝒏𝑵𝟐 + 𝒏𝑶𝟐 + 𝒏𝑨𝒓
If we replace n in the ideal gas law with ntotal, the summation of the individual numbers of moles
of gases, the equation becomes
Ptotal V = ntotal RT

Expanding the right side of the equation and rearranging gives:

The quantities𝑃𝑁2,𝑃𝑂2, 𝑃𝐴𝑟 are the partial pressures of the three major components of the
atmosphere. Dalton’s law means that the pressure exerted by the atmosphere is the sum of the
pressures due to nitrogen gas, oxygen gas, and argon, and other much less abundant components.
We can also write a ratio of the partial pressure of one of the components, A, of a gas mixture over
the total pressure,

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On cancelling terms on the right-hand side of this equation, we get

The ratio of the pressures is the same as the ratio of the number of moles of gas A to the total
number of moles. This ratio ( 𝒏𝑨 ) is called the mole fraction of A and is given the symbol XA.
𝒏𝒕𝒐𝒕𝒂𝒍
Hence, rearranging the equation gives
PA = XA Ptotal
Consider the following examples:
Example 1: Simple partial pressures
1. If we have a flask containing Nitrogen gas, whose partial pressure is 0.78 atm and oxygen gas,
whose partial pressure is 0.20 atm, what is the total pressure in the flask?

Solution:
• Identify the known and the unknown variables.
Known variables Unknown variable
𝑷𝑵𝟐= 0.78 atm Ptotal = ?
𝑷𝑶𝟐= 0.20 atm

• Use the correct formula to carry out the computation.

Ptotal = 𝑷𝑵𝟐+ 𝑷𝑶𝟐

• Use the correct formula to carry out the computation.

Ptotal = 𝑷𝑵𝟐+ 𝑷𝑶𝟐
Ptotal = (0.78 atm) + ( 0.20 atm) = 0.98 atm

Example 2: Mole fraction

2. What is the partial pressure of carbon dioxide in container that holds 5.0 moles of carbon
dioxide, 3.0 moles of nitrogen gas, and 1.0 mole of helium gas and has a total pressure of 1.05
atm helium gas and has a total pressure of 1.05 atm
Solution:
• Find the mole fraction of CO2.
nCO2/ ntotal = 5.0 moles/9.0 moles = 0.56
• Multiply the mole fraction by the total pressure.
PCO2 = XCO2 Ptotal = (0.56) (1.05 atm) = 0.58 atm

Example 3: Application of other gas laws

3. Two flasks are connected by a stopcock. When the stopcock is closed, flask A contains 3.5 L of
nitrogen gas at 2.55 atm and flask B contains 1.5 L of carbon monoxide gas at 0.85 atm. What is
the total pressure when the stopcock is open and the gases are allowed to mix?

Solution:
• Determine the final volume for the
gases. It’s easy! Add the 2 volumes
together.

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Vtotal = VA + VB = 3.5-L + 1.5-L
Vtotal = 5-L

• Use Boyle's law (P1V1 = P2V2) to find the final partial pressure for both N2 and CO2 individually.
Remember Boyle’s law: (P1V1 = P2V2)
a. Find the final pressure (P2) of N2:
P2 = P1V1/V2 = (2.55-atm)(3.5-L)/5.0-L = 1.785-atm
b. Find the final pressure (P2) of CO2:
P2 = P1V1/V2 = (0.85-atm)(1.5-L)/5.0-L = 0.255-atm
*** You might be confused why 5.0-L is used as the final volume of the two gases. It is because in this
situation, the initial pressures and volumes of both gases is the value before the mixture happens.
On the other hand, the final pressures and volumes of the two will be when the two gases already
mixed that’s why the final volume of the two is the same. It is equal to the combination of their
initial volumes.
• Use Dalton's law of partial pressures to find the total final pressure.
Ptotal = PN2 + PCO2 = 1.785-atm + 0.255-atm
Ptotal = 2.0-atm

II. LEARNING ACTIVITIES

ACTIVITY 1: Conceptual Check!

Directions: Complete the information in each matrix about the relationship of temperature,
volume, pressure, and amount of gas. Write your answer on a separate answer sheet.

Matrix 1: At constant temperature and amount of gas

Volume Pressure
Increases _______________
_______________ Increases

Matrix 2: At constant pressure and amount of gas

Volume Temperature
_______________ Decreases
Increases _______________

Matrix 3: At constant pressure and temperature

Volume Amount of gas

Increases ______________
_______________ Decreases

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 ACTIVITY 2: Complete Me!

Directions: Complete the sentences below by guessing the right term represented by the image
in the statement. Write your answer on the separate answer sheet.

Statement 1:

Statement 2:

ACTIVITY 3: Let’s Match!

Directions: Fill-in the matrix with the correct information asked. Write your answer on a separate
answer sheet. (*** in graphical illustration, you are tasked to draw the relationship of two variables.
Draw it on your answer sheet.)

Gas Law Equation Graphical

Representation

_______________________ ________________________

Charles’s law ________________________ _____________________________

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 _____________________
𝑉1 = 𝑉2 ________________________________
𝑛1 𝑛2

ACTIVITY 4: Apply Me!

Directions: Given below are real-life situations which involve the application of gas laws. Match
the gas law involve for each situation. Write your answer on a separate answer sheet.

Situations Gas law Involved

1. When a basketball is left in a cold garage or
outside during cold months, its volume
decreases.
2. Air bubbles expand as they ascend in water.

3. When ascending or descending in a plane,

or taking a subway or train under a deep
waterway, your ears “pop,” or feel
uncomfortable because of a change of
pressure in your head.
4. As you dive deeper, the pressure increases
on your body and decreases the volume in
your lungs.
5. A flat tire takes up less space than an
inflated tire, because it contains less air.

ACTIVITY 5: ASSESSMENT

Directions: Choose the letter of the best answer. Write the chosen letter on a separate sheet of
paper.

1. The amount of force exerted by an object on a certain area is known

as____.
a. acceleration b. pressure c. velocity d. newton
2. The following are the most common units use in quantifying pressure
EXCEPT _________.
a. torr b. pascal c. atmospheric pressure d. Weber
3. Increasing the number of air molecules contained in a basketball will
likely increase its volume. This is according to __________.
a. Boyle’s law b. Charles’ law c. Avogadro’s law d. Lavoisier’s law
4. According to Charles’ law, the volume of gases at constant pressure is directly proportional to
the temperature in which the gas is exposed. This statement is represented by which of the
following mathematical equation?
a. VT= k b. T/V =k c. V/T= k d. PV= k

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5. You observed that as the bubble goes up from the bottom of the sea to the surface of the water,
its size changes and grow bigger. What would be the BEST conclusion about the relationship of
pressure and volume based on the situation given?
a. Pressure and volume is inversely proportional at constant temperature.
b. Pressure and volume is directly proportional at constant temperature.
c. Volume of the bubble is not affected by the pressure under the sea.
d. Pressure under the sea is lesser compare to the surface which allows the bubble to expand.
6. If the volume available to an ideal gas is increased, the pressures exerted by one mole of gas
molecules will _____________.
a. Increase b. Decrease c. Decrease then increase d. Remains the same
7. Calculate the pressure exerted by 0.300 mole of gas contained in an 8.00 liters vessel at 18°C.
(***R=0.0821 Latm/molK)
a. 0.986 atm b. 1.001 atm c. 0.896 atm d. 0.789 atm
8. The total pressure of a mixture of non-reacting gases is equal to the sum of the partial
pressures of the individual gases. This is according to _____________.
a. Gay-Lussac’s law b. Boyle’s law c. Avogadro’s law d. Dalton’s law of partial pressure
9. What is the partial pressure of nitrogen gas in container that holds 8.0 moles of CO2, 5.0 moles
of N2, and 2.0 mole of H2 and has a total pressure of 3.00 atm?
a. 1.60 atm b. 1.00 atm c. 2.49 atm d. 1.57 atm
10. At 30°C, the volume of a sample of air was 5.8-L what would be the volume of the air sample
if it is heated to 60°C at the same pressure?
a. 6.37-L b. 7.22-L c. 100-L d. 2.71-L
11. A barometric reading of 950 mmHg is recorded in a barometer at the top of the mountain.
Convert this value to standard atmospheric pressure (atm) unit. (*** 1 atm=760 mmHg)
a. 1.25 atm b. 1.25 mmHg c. 722, 000 atm d. 722, 000 mmHg
12. A balloon with an initial volume of 1.1 liters at room temperature (25°C) is placed in a tub
full of cold water with a temperature of -10°C. What will happen to the volume of the balloon as
it is placed inside the tub? What is its volume?
a. Increase in volume: 2.2 liters b. Increase in volume: 1.9 liters
c. Decrease in volume: 0.75 liters d. Decrease in volume: 0.97 liters
13. A plastic balloon containing 2.00 moles of helium has a volume of 0.88 liters. What is the new
volume after 6.00 moles of helium are added to the balloon at the same temperature and
pressure?
a. 880 liters b. 2640 liters c. 2.640 liters d. 5,280 liters
14. The pressure of an ideal gas in a sealed container of volume V is increased from P to 3P. What
will happen to the volume, V of this gas?
a. There is no change. b. decreases to V/3.
c. increases from V to 3V. d. increases from V to 2V.
15. The temperature of a fixed mass of gas increases from 100K to 400K. What will happen to its
volume? It will ________.
a. stay the same.
b. double.
c. increase by a factor of four (four times its original volume).
d. decrease to a quarter of its original volume.

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ACTIVITY 6: PERFORMANCE TASK

A. Word-Problem Challenge!

Directions: Analyze the word-problems below and answer it by showing your step-by-step
computations.

1. A steel cylinder with a volume of 15.0-L is filled with 40.0-g of nitrogen gas (N2) at 24°C.
What is the pressure, in Pa, of the nitrogen gas in cylinder? (5PTS.)

2. Calculate the volume that will be occupied by 20-g carbon dioxide at 25°C and at 1.25-
atm. (5PTS.)

B. I Can Apply Further!

Directions: Fill-in the matrix below the necessary information asked. This activity is based on
your experiences in everyday life, be it in school, at home or any place where the concept that have
been discussed are involved.

Activities/situation involving Gas laws involved in the

gases activity/situation
Ex: Inflating tricycle tires Boyle’s law/Avogadro’s law
1.
2.
3.
4.
5.

C. A Message to Conserve!

Directions: Write a short paragraph with no more than 5 sentences about the topic given below.
(The goal of this activity is to motivate you to be concern in the status of our air/atmosphere)
(5PTS.)

“AIR POLLUTION”
_________________________________________________________________________________________________________

_________________________________________________________________________________________________________

_________________________________________________________________________________________________________

_________________________________________________________________________________________________________

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 III. REFLECTION

Complete the following statements

I discovered that_______________________________________________.

I realized that _______________________________________________.

I can apply to my life _________________________________________.

IV. REFERENCE

Baynosa, Ranlee John. (2020). Module 11. Gas Laws. Department of Education
– MIMAROPA Region – Division of Palawan

V. KEY ANSWER

ASSESSMENT CONCEPTUAL COMPLETE ME!

1. B CHECK! Laws, Combined,
2. D 1. Decreases Relationship,
3. C 2. Decreases Volume,
4. C 3. Decreases Temperature,
5. A 4. Increases Pressure
6. B 5. Increases 2. Pressure,
7. C 6. Increases Mixture, Gases,
B. Conceptual 3. Summation,
8. D
Individual,
9. B Mixture
10. A
11. A Let’s Match
12. D 1. Boyle’s law
13. C 2. P1V1 = P2V2
14. B 3. V1/T1 = V2/T2
15. C 4. A directly
proportional
graph (V and T)
5. Avogadro’s law
6. A directly
proportional
graph (V and n)

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