# American Intercontinential University Chemistry Worksheets

Description

Solubility
How is the quantity of solute in a saturated solution determined?
Why?
When we add salt to a pot of boiling water or sugar to a pitcher of iced tea, we expect that the added
solute will completely dissolve. It requires a large quantity of these solutes to saturate a solution. On the
other hand, water has flowed over rock riverbeds for centuries and only dissolved enough material in some
cases to provide a trace of certain minerals in the water. Different solutes, such as salt, sugar, or minerals,
dissolve to very different extents in water (and other solvents). In this activity you will learn how to quantify the amount of solute that is dissolved in a saturated solution.
Model 1 – Three Solutions
The following data refer to three experiments in which solute is added to water in a beaker at 20 ºC. The
mixtures are stirred and then allowed to sit for three hours before measuring the amount of solid that
dissolves. Ten separate trials are conducted for each experiment. The same solute is used in all three
experiments.
Experiment 1
In 10.0 g water
Experiment 2
In 20.0 g water
Experiment 3
In 50.0 g water
Trial
Mass of
(grams)
Mass of solute dissolved
(grams)
Mass of solute
Mass of solute dissolved
(grams)
Mass of solute
Mass of solute dissolved
(grams)
1
1.0
1.0
1.0
1.0
3.0
3.0
2
2.0
2.0
2.0
2.0
6.0
6.0
3
3.0
3.0
3.0
3.0
9.0
9.0
4
4.0
3.6
4.0
4.0
12.0
12.0
5
5.0
3.6
5.0
5.0
15.0
15.0
6
6.0
3.6
6.0
6.0
18.0
18.0
7
7.0
3.6
7.0
7.0
21.0
18.0
8
8.0
3.6
8.0
7.2
24.0
18.0
9
9.0
3.6
9.0
7.2
27.0
18.0
10
10.0
3.6
10.0
7.2
30.0
18.0
1. Identify the variable(s) that were controlled among all three experiments in Model 1.
2. What variable(s) were changed purposefully among the three experiments in Model 1?
Solubility
1
3. What experimental question can be answered by analyzing the data in the three experiments in
Model 1? Use the words “solvent” and “solute” in your question.
4. In each of the three experiments in Model 1, determine the point in the experiment that the
beakers became saturated. Draw a box around the entire section of data in each experiment that
represents saturated solutions.
5. Consider the data in Model 1.
a. Which experiment shows the largest mass of dissolved solute in the saturated solutions?
b. Propose an explanation for why the mass of dissolved solute changed among the three
experiments.
Solubility is a measure of the maximum amount of solute that can dissolve in a given amount of solvent
at a specific temperature. In other words, it is the ratio of solute to solvent in a saturated solution at a
specific temperature. Solubility is typically reported as grams of solute per 100 g H2O. For example, if a
maximum of 20.4 g of table sugar (sucrose) will dissolve in 10.0 g of water at 20 °C, then the solubility of
sucrose would be 204 g sucrose/100 g H2O.
6. Would it be acceptable for a student to use Trial 2 from Experiment 1 to determine the solubility
of the solute in Model 1? Explain your group’s answer in a complete sentence.
7. In Model 1 none of the experiments used 100 g of water. Use complete sentences to explain how
the ratio “grams of solute per 100 g H2O” can be calculated from the data given in Model 1.
8. Use the data in Model 1 to calculate the solubility of the solute (at 20 ºC) for all three experiments. Show your work.
Experiment 1:
2
Experiment 2:
Experiment 3:
POGIL™ Activities for High School Chemistry
9. Circle the word or phrase that best completes each of the statements below.
a. When the volume of solvent increases, the mass of solute that can dissolve in a saturated
solution (increases/decreases/stays the same).
b. When the volume of solvent increases, the solubility of a solute at a given temperature
(increases/decreases/stays the same).
10. A student claims, “In Experiment 3, Trial 9, 18.0 grams of solute dissolves, whereas in Experiment 1, Trial 9, only 3.6 grams of solute dissolves. Obviously, the solubility is greater in
Experiment 3.” With your group, devise a well-constructed response.
11. Calculate the mass of the solute used in Model 1 that is needed to make a saturated solution in
140.0 g of water without leaving any solid solute at the bottom. Show your work.
Solubility
3
Extension Questions
Model 2 – Solubility Curves
Solubility (g solute/100 g water)
100
90
80
70
Substance A
60
50
40
30
Substance B
20
10
0
0
10
20
30
40
50
60
Temperature (°C)
12. According to the graph in Model 2, what is the solubility of Substance A at 30 oC?
13. Describe the trend in solubility for Substances A and B in Model 2 as temperature increases.
14. If a saturated solution of Substance A in 100.0 g of water is cooled from 30 oC to 10 oC, what
mass of solid solute would crystallize out? Show your work.
15. If a saturated solution of Substance B in 50.0 g of water at 30 oC is warmed to 50 oC, what mass
of solute would need to be added to make the solution saturated again?
4
POGIL™ Activities for High School Chemistry
Mole Ratios
How can the coefficients in a chemical equation be interpreted?
Why?
A balanced chemical equation can tell us the number of reactant and product particles (ions, atoms,
molecules or formula units) that are necessary to conserve mass during a chemical reaction. Typically
when we balance the chemical equation we think in terms of individual particles. However, in real life
the reaction represented by an equation occurs an unimaginable number of times. Short of writing very
large numbers (1023 or larger) in front of each chemical in the equation, how can we interpret chemical
equations so that they more realistically represent what is happening in real life? In this activity you will
explore the different ways a chemical reaction can be interpreted.
Model 1 – A Chemical Reaction
N2(g) + 3H2(g) → 2NH3(g)
1. Consider the reaction in Model 1.
a. What are the coefficients for each of the following substances in the reaction?
N2
H2
NH3
b. Draw particle models below to illustrate the reaction in Model 1.
2. Consider each situation below as it relates to the reaction in Model 1.
a. Calculate the amount of reactants consumed and products made.
b. Record the ratio of N2 to H2 to NH3. Reduce the ratio to the lowest whole numbers possible.
N2
Consumed
H2
Consumed
NH3
Produced
Ratio N2:H2:NH3
(reduced)
For a single reaction, how many
molecules of each substance would
be consumed or produced?
If the reaction occurred one hun­
dred times, how many molecules
would be consumed or produced?
If the reaction occurred 538 times,
how many molecules would be
consumed or produced?
Mole Ratios
1
3. Refer to the data table in Question 2.
a. How do the reduced ratios in the last column compare to the coefficients in the reaction
shown in Model 1?
b. Use mathematical concepts to explain how your answer in part a is possible.
4. Even 538 is a small number of molecules to use in a reaction. Typically chemists use much larger
numbers of molecules. (Recall that one mole is equal to 6.02 x 1023 particles.) Consider each
situation below as it relates to the reaction in Model 1: N2(g) + 3H2(g) → 2NH3(g).
a. Calculate the amount of reactants consumed and products made.
b. Record the ratio of N2 to H2 to NH3. Reduce the ratio to the lowest whole number possible.
N2
Consumed
H2
Consumed
NH3
Produced
Ratio
N2:H2:NH3
If the reaction occurred 6.02 ×
1023 times, how many molecules
would be consumed or pro­
duced?
How many moles of each sub­
stance would be consumed or
produced in the previous situa­
tion?
5. Refer to the data table in Question 4.
a. How do the reduced ratios in the last column compare to the coefficients in the reaction in
Model 1?
b. Use mathematical concepts to explain how your answer in part a is possible.
6. The ratio obtained from the coefficients in a balanced chemical equation is called the mole ratio.
a. What is the mole ratio for the reaction in Model 1?
b. Explain why this ratio is called the mole ratio?
2
POGIL™ Activities for High School Chemistry
7. Use the mole ratio from the balanced chemical equation in Model 1, N2(g) + 3H2(g) →
2NH3(g), to solve the following problems. Hint: Set up proportions.
a. How many moles of nitrogen would be needed to make 10.0 moles of ammonia?
b. How many moles of ammonia could be made by completely reacting 9.00 moles of
hydrogen?
c. How many moles of hydrogen would be needed to react completely with 7.41 moles of
nitrogen?
8. Consider this situation as it relates to the reaction in Model 1, N2(g) + 3H2(g) → 2 NH3(g).
a. Calculate the amounts of reactants consumed and the amount of product made.
b. Record the mass ratio of N2 to H2 to NH3. Reduce the ratio to the lowest whole numbers
possible.
N2
Consumed
H2
Consumed
NH3
Produced
Mass Ratio
N2:H2:NH3
How many grams of each
substance would be consumed
or produced in the situation in
Question 4?
9. Refer to the data table in Question 8.
a. Can the mole ratio from a balanced chemical equation be interpreted as a ratio of masses?
b. Use mathematical concepts to explain how your answer in part a is possible.
10. As a group, develop a plan to solve the following problem. Remember that the mole ratio cannot
be used directly in this situation. Note: You do not need to do the actual calculation here.
“What mass of nitrogen is needed to produce 30.0 g of ammonia?”
Mole Ratios
3
Model 2 – Proposed Calculations for Mass of NH3 to Mass of N2
Toby’s Method
x grams
1 mole N2
———— = —————
➞   x = ______ g N2
30.0 g
2 moles NH3
Rachel’s Method
1 mole NH
30.0 g NH3 × —————3 = ______ moles NH3
17.0 g NH3
x mole N2
1 mole N2
—–————–
= —————

_____ mole NH3 2 moles NH3
x = ______ moles N2
28.0 g N
______ mole N2 × ————2 = ______ g N2
1 mole N2
Jerry’s Method
1 mole NH
1 mole N2
28.0 g N
30.0 g NH3 × —————3 × —————
× ————2 = ______ g N2
17.0 g NH3
2 moles NH3 1 mole N2
11. Model 2 shows three proposed calculations to solve the problem in Question 10. Complete the
calculations in Model 2 by filling in the underlined values.
12. Which method does not use the mole ratio in an appropriate manner? Explain.
13. Two of the methods in Model 2 give the same answer. Show that they are mathematically
equivalent methods.
14. Use either Rachel or Jerry’s method from Model 2 to calculate the mass of hydrogen needed to
make 30.0 g of ammonia. N2(g) + 3H2(g) → 2NH3(g)
4
POGIL™ Activities for High School Chemistry
Extension Questions
15. One mole of any gas will occupy 22.4 L of volume at standard temperature and pressure (STP).
Consider this situation as it relates to the reaction in Model 1: N2(g) + 3H2(g) → 2NH3(g)
a. Calculate the volumes of reactants consumed and the volume of product made.
b. Record the ratio of N2 to H2 to NH3. Reduce the ratio to the lowest whole numbers possible.
N2
Consumed
H2
Consumed
NH3
Produced
Volume Ratio
N2:H2:NH3
How many liters of each sub­
stance would be consumed or
produced if the reaction occurred
6.02 × 1023 times at STP?
16. Refer to the data table in Question 15.
a. Can the mole ratio from a balanced chemical equation be interpreted as a ratio of volumes for
gases?
b. Use mathematical concepts to explain how your answer in part a is possible.
17. Explain why the ratio of volumes is NOT followed in the following reactions.
2H2(g)
44.8 L
+
O2(g) → 2H2O(l)
22.4 L
NH3(g)
0.036 L 22.4 L
+
HCl(g) → NH4Cl(s)
22.4 L
0.035 L
18. Which of the following quantities are conserved (total amount in reactants = total amount in
products) in a chemical reaction? Find an example or counter example from this activity to sup­
a. Molecules
c. Mass
b. Moles
d. Volume
e. Atoms of an element
Mole Ratios
5
Limiting and Excess Reactants
Is there enough of each chemical reactant to make a desired amount of product?
Why?
If a factory runs out of tires while manufacturing cars, production stops. No more cars can be fully built
without ordering more tires. A similar thing happens in a chemical reaction. If there are fixed amounts of
reactants to work with in a chemical reaction, one of the reactants may be used up first. This prevents the
production of more products. In this activity, you will look at several situations where the process or reaction is stopped because one of the required components has been used up.
Model 1 – Assembling a Race Car
Race Car Part List
Body (B)
Cylinder (Cy)
Engine (E)
Tire (Tr)
Race Car
1. How many of each part are needed to construct 1 complete race car?
Body (B)
Cylinder (Cy)
Engine (E)
Tire (Tr)
2. How many of each part would be needed to construct 3 complete race cars? Show your work.
Body (B)
Cylinder (Cy)
Engine (E)
Tire (Tr)
3. Assuming that you have 15 cylinders and an unlimited supply of the remaining parts:
a. How many complete race cars can you make? Show your work.
b. How many of each remaining part would be needed to make this number of cars? Show your
work.
Limiting and Excess Reactants
1
Model 2 – Manufacturing Race Cars
Race Car Part List
Race Car
Parts
Body (B)
Cylinder (Cy)
Engine (E)
Tire (Tr)
Container A
4. Count the number of each Race Car Part present in Container A of Model 2.
Body (B)
Cylinder (Cy)
Engine (E)
Tire (Tr)
5. Complete Model 2 by drawing the maximum number of cars that can be made from the parts in
Container A. Show any excess parts remaining also.
6. A student says “I can see that we have three car bodies in Container A, so we should be able to
build three complete race cars.” Explain why this student is incorrect in this case.
7. Suppose you have a very large number (dozens or hundreds) of tires and bodies, but you only
have 5 engines and 12 cylinders.
a. How many complete cars can you build? Show your work.
b. Which part (engines or cylinders) limits the number of cars that you can make?
2
POGIL™ Activities for High School Chemistry
8. Fill in the table below with the maximum number of complete race cars that can be built from
each container of parts (A–E), and indicate which part limits the number of cars that can be
built. Divide the work evenly among group members. Space is provided below the table for each
group member to show their work. Have each group member describe to the group how they
determined the maximum number of complete cars for their container. Container A from Model
2 is already completed as an example.
1 B + 3 Cy + 4 Tr + 1 E = 1 car
Container
Bodies
Cylinders
Tires
Engines
A
B
C
D
E
3
50
16
4
20
10
12
16
9
36
9
50
16
16
40
2
5
16
6
24
Max.
Number of
Completed
Cars
2
Limiting
Part
Engines
9. The Zippy Race Car Company builds toy race cars by the thousands. They do not count individual car parts. Instead they measure their parts in “oodles” (a large number of things).
a. Assuming the inventory in their warehouse below, how many race cars could the Zippy Race
Car Company build? Show your work.
Body (B)
Cylinder (Cy)
Engine (E)
Tire (Tr)
4 oodles
5 oodles
8 oodles
8 oodles
b. Explain why it is not necessary to know the number of parts in an “oodle” to solve the problem in part a.
10. Look back at the answers to Questions 8 and 9. Is the component with the smallest number of
parts always the one that limits production? Explain your group’s reasoning.
Limiting and Excess Reactants
3
Model 3 – Assembling Water Molecules
Represents 1 mole of H2
Chemical
Reactants
Chemical
Products
Container Q
Before Reaction
Container Q
After Reaction
Represents 1 mole of O2
Chemical Reaction
2H2
+
O2

2H2O
11. Refer to the chemical reaction in Model 3.
a. How many moles of water molecules are produced if one mole of oxygen molecules
completely reacts?
b. How many moles of hydrogen molecules are needed to react with one mole of oxygen
molecules?
12. Complete Model 3 by drawing the maximum moles of water molecules that could be produced
from the reactants shown, and draw any remaining moles of reactants in the container after
reaction as well.
a. Which reactant (oxygen or hydrogen) limited the production of water in Container Q?
b. Which reactant (oxygen or hydrogen) was present in excess and remained after the production of water was complete?
4
POGIL™ Activities for High School Chemistry
13. Fill in the table below with the maximum moles of water that can be produced in each container
(Q–U). Indicate which reactant limits the quantity of water produced—this is the limiting
reactant. Also show how much of the other reactant—the reactant in excess—will be left over.
Divide the work evenly among group members. Space is provided below the table for each group
member to show their work. Have each group member describe to the group how they determined the maximum number of moles of water produced and the moles of reactant in excess.
Container Q from Model 3 is already completed as an example.
2H2 + O2 → 2H2O
Container
Moles of
Hydrogen
Moles of
Oxygen
Max. Moles
of Water
Produced
Limiting
Reactant
Reactant
in Excess
Q
7
3
6
O2
1 mole H2
R
8
3
S
10
5
T
5
5
U
8
6
14. Look back at Questions 12 and 13. Is the reactant with the smaller number of moles always the
limiting reactant? Explain your group’s reasoning.
Limiting and Excess Reactants
5
15. Below are two examples of mathematical calculations that could be performed to find the limiting reactant for Container U in Question 13.
8 mol H2
6 mol O2
(
(
)
)
(
)
2 mol H2O
————–
= 8 mol H2O
2 mol H2
8 mol H2
2 mol H2O
————–
= 12 mol H2O
1 mol O2
There are 6 moles of O2 present, which is
more than enough, so H2 must be the
limiting reactant.
Hydrogen makes the lesser amount of
product, so it is the limiting reactant.
1 mol O2
————–
= 4 mol O2 needed
2 mol H2
a. Do both calculations give the same answer to the problem?
b. Which method was used most by your group members in Question 13?
c. Which method seems “easier,” and why?
d. Did your group use any other method(s) of solving this problem that were scientifically and
mathematically correct? If so, explain the method.
6
POGIL™ Activities for High School Chemistry
Extension Questions
16. Consider the synthesis of water as shown in Model 3. A container is filled with 10.0 g of H2 and
5.0 g of O2.
a. Which reactant (hydrogen or oxygen) is the limiting reactant in this case? Show your work.
Hint: Notice that you are given reactant quantities in mass units here, not moles.
b. What mass of water can be produced? Show your work.
c. Which reactant is present in excess, and what mass of that reactant remains after the reaction
Limiting and Excess Reactants
7
Gas Variables
How are the variables that describe a gas related?
Why?
Imagine buying a balloon bouquet at a party store. How will the helium gas in the bouquet behave if you
carry it outside on a hot summer day? How will it behave if you carry it outside during a snowstorm?
What happens if the balloons are made of latex, which can stretch? What happens if the balloons are made
of Mylar®, which cannot stretch? What if you add just a small amount of gas to each balloon? What if you
add a lot of gas? In this activity, you will explore four variables that quantify gases—pressure (P), volume
(V), temperature (T), and moles (n) of gas. These four variables can be related mathematically so that
Model 1 – Gases in a Nonflexible Container

A1
A2
A3
Volume = 1 unit
Volume = 1 unit
Volume = 1 unit
External pressure = 1 atm External pressure = 1 atm External pressure = 1 atm
Internal pressure = 1 atm Internal pressure = 2 atm Internal pressure = 3 atm
Temperature = 200 K
Temperature = 200 K
Temperature = 200 K
Experiment B (Heating the gas)

B1
B2
B3
Volume = 1 unit
Volume = 1 unit
Volume = 1 unit
External pressure = 1 atm External pressure = 1 atm External pressure = 1 atm
Internal pressure = 1 atm Internal pressure = 2 atm Internal pressure = 3 atm
Temperature = 200 K
Temperature = 400 K
Temperature = 600 K
*Note: Volume in this model is recorded in units rather than liters because 4 molecules of gas at the conditions given would occupy a very small space (~1 × 10–22 μL). The particles shown here are much larger compared to the space between them
than actual gas particles.
Gas Variables
1
1. In Model 1, what does a dot represent?
2. Name two materials that the containers in Model 1 could be made from that would ensure that
they were “nonflexible?”
3. In Model 1, the length of the arrows represents the average kinetic energy of the molecules in
that sample. Which gas variable (Pinternal, V, T or n) is most closely related to the length of the
arrows in Model 1?
4. Complete the following table for the two experiments in Model 1.
Experiment A
Experiment B
Independent Variable
Dependent Variable
Controlled Variable(s)
5. Of the variables that were controlled in both Experiment A and Experiment B in Model 1, one
requires a nonflexible container. Name this variable, and explain why a nonflexible container is
necessary. In your answer, consider the external and internal pressure data given in Model 1.
Pressure is caused by molecules hitting the sides of a container or other objects. The pressure changes
when the molecules change how often or how hard they hit. A nonflexible container is needed if the gas
sample is going to have an internal pressure that is different from the external pressure. If a flexible container is used, the internal pressure and external pressure will always be the same because they are both
pushing on the sides of the container equally. If either the internal or external pressure changes, the flexible container walls will adjust in size until the pressures are equal again.
2
POGIL™ Activities for High School Chemistry
6. Name the two factors related to molecular movement that influence the pressure of a gas.
7. Provide a molecular-level explanation for the increase in pressure observed among the flasks of
Experiment A.
8. Provide a molecular-level explanation for the increase in pressure observed among the flasks of
Experiment B.
9. Predict what would happen to the volume and internal pressure in Experiment A of Model 1 if a
flexible container were used.
10. Predict what would happen to the volume and internal pressure in Experiment B of Model 1 if a
flexible container were used.
11. For each experiment in Model 1, determine the relationship between the independent and dependent variables, and write an algebraic expression for the relationship using variables that relate to
the experiment (Pinternal, V, T or n). Use k as a proportionality constant in each equation.
Experiment A
Experiment B
Direct or Inverse Proportion?
Algebraic Expression
Gas Variables
3
Model 2 – Gases in a Flexible Container
Experiment C
C1
C2
C3
Volume = 1 unit
Volume = 2 units
Volume = 3 units
External pressure = 1 atm External pressure = 1 atm External pressure = 1 atm
Internal pressure = 1 atm Internal pressure = 1 atm Internal pressure = 1 atm
Temperature = 200 K
Temperature = 200 K
Temperature = 200 K
Experiment D
(Heating the gas)

D1
D2
D3
Volume = 1 unit
Volume = 2 units
Volume = 3 units
External pressure = 1 atm External pressure = 1 atm External pressure = 1 atm
Internal pressure = 1 atm Internal pressure = 1 atm Internal pressure = 1 atm
Temperature = 200 K
Temperature = 400 K
Temperature = 600 K
Experiment E
(Reducing the
external pressure
on the gas)

E1
Volume = 1 unit
External pressure = 1 atm
Internal pressure = 1 atm
Temperature = 200 K
E2
E3
Volume = 2 units
Volume = 3 units
External pressure = 0.50 atm External pressure = 0.33 atm
Internal pressure = 0.50 atm Internal pressure = 0.33 atm
Temperature = 200 K
Temperature = 200 K
12. Consider the gas samples in Model 2.
a. Name two materials that the containers in Model 2 could be made from that would ensure
that they were “flexible”?
b. What is always true for the external and internal pressures of a gas in a flexible container?
4
POGIL™ Activities for High School Chemistry
13. Complete the following table for the three experiments in Model 2.
Experiment C
Experiment D
Experiment E
Independent Variable
Dependent Variable
Controlled Variable(s)
14. Provide a molecular level explanation for the increase in volume among the balloons in Experiment C. (How often and/or how hard are the molecules hitting the sides of the container?)
15. Provide a molecular level explanation for the increase in volume among the balloons in
Experiment D.
16. Provide a molecular level explanation for the increase in volume among the balloons in
Experiment E.
17. Compare Experiment A of Model 1 with Experiment C of Model 2. How are these two
experiments similar and how are they different in terms of variables?
18. Compare Experiment B of Model 1 with Experiment D of Model 2. How are these two
experiments similar and how are they different in terms of variables?
19. If Experiment E of Model 2 were done in a nonflexible container, would there be any change to
the internal pressure of the flask when the external pressure was reduced? Explain.
Gas Variables
5
20. For each experiment in Model 2, determine the relationship between the independent and
dependent variables, and write an algebraic expression for the relationship using variables
that relate to those in the experiment (Pinternal, V, T or n). Use k as a proportionality constant
in each equation.
Constant Pressure
Experiment C
Experiment D
Experiment E
Direct or Inverse Proportion?
Algebraic Expression
21. The three samples of identical gas molecules below all have the same internal pressure. Rank the
samples from lowest temperature to highest temperature, and add arrows of appropriate size to
illustrate the average kinetic energy of the molecules in the samples.
6
POGIL™ Activities for High School Chemistry
Extension Questions
22. Draw a sample of gas that is colder than all three of the samples in Question 21. Explain why
you are sure that it is colder.
23. Four of the relationships you investigated in Models 1 and 2 are named after scientists who
discovered the relationships. Use the Internet or your textbook to match each of the scientists
below with the appropriate law. Write the algebraic expression that describes the law in the box
below each name.
Robert Boyle
Jacques Charles
Guillaume Amontons
Chemists combine all of the relationships seen in Models 1 and 2 into one law—the Ideal Gas Law. It is
one equation that describes gas behavior and the relationship among all four variables, P, V, T, and n. In
the Ideal Gas Law the proportionality constant is represented by the letter R (rather than the generic k).
24. Circle the algebraic equation below that best combines all of the relationships you identified
among P, V, T, and n in this activity.
P = RTnV
Gas Variables
PT = RnV
PV = nRT
PTV = Rn
7