Download EXPERIMENT 1 - DIMENSIONAL ANALYSIS

Experiment 1
CHEM 5 – Chemistry for Nurses
EXPERIMENT 1 - DIMENSIONAL ANALYSIS
I. LEARNING OBJECTIVES
In this exercise, you will:
• Learn the standard units used in three systems of measurement encountered in nursing
calculations (metric, apothecary, and household)
• Become proficient in converting between the three systems of measurement using
dimensional analysis
• Become proficient at using dimensional analysis in a variety of common nursing
calculations
II. PRELAB ASSIGNMENT
The pre-lab assignment must be completed before the lab.
1. Read Chapter 1 of your text and work two chapter problems each in sections 1.3, 1.4, 1.5 and
1.6
2. Read the Background section for this lab (Section III).
3. Complete the following problems before lab. You must SHOW ALL WORK to receive
credit and to be allowed to complete the lab.
a. A nurse tells a patient that she must lose at least 16 kg of body weight to no longer be
considered obese. How many pounds is this?
b. A nurse measures the height of a 13 year old girl to be 54 inches. How many meters is
this?
c. A patient is prescribed 25 mg of Benadryl. The dose on hand is 0.05 g in each capsule.
How many capsules should the patient take?
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CHEM 5 – Chemistry for Nurses
III. BACKGROUND
A. Systems of Measurement
Measurement is at the foundation of providing good medical care. This is manifested in two
ways. First, helping a sick individual requires documenting symptoms, very often through some
type of measurement. Second, medications are administered in measured doses. Mistakes in
measurement can have grave consequences, therefore it is very important for nurses to have
complete confidence in reading and making measurements. Nurses typically encounter three
different systems of measurement: metric, apothecary, and household.
1. The metric system.
The metric system is the most commonly used system of measurement in science and
medicine. It consists of the following basic units:
Physical
property
Mass
Length
Volume
Basic
unit
gram, g
meter, m
Liter, L
Many times, substances are measured in amounts smaller or larger than conveniently
indicated by the basic units. Therefore, it is often necessary to convert between smaller and
larger versions of the basic units using prefixes as follows:
Prefix,
abbreviation
kilo, k_
deci, d_
centi, c_
milli, m_
micro, μ_ or
mc_
Relationship to basic unit
Example
1000 or 103
0.1 or 10-1
0.01 or 10-2
0.001 or 10-3
(note: 1 mL = 1 cm3 = 1 cc)
0.000001 or 10-6
kilograms, kg
deciliter, dL
centimeter, cm
milliliter, mL
microgram, μg or mcg
2. Apothecary units of measurement
Apothecary units are still in use in many hospitals and other health care settings. Common
apothecary units include the dram (dr), grain (gr), and drop (gtt). The metric equivalencies are as
follows:
Experiment 1
CHEM 5 – Chemistry for Nurses
Unit
dram (dr)
grain (gr)
drop (gtt)
Metric equivalence
1 dr = 60 grains, or 3.887 g
1 gr = 0.067 g; 1g = 15 gr
Two sizes, micro and macro.
1 mL = 10-20 macrogtts (mggts)
1 mL = 60 microgtts (μggts)
3. English (household) units of measurement.
English, or household, units of measurement are also common in clinical and hospital
settings. The metric equivalencies are as follows:
Unit
teaspoon (tsp)
tablespoon (tbs)
ounce (ou or oz)
cup (C) = 8 ou
quart (qt) = 1/4 gallon = 2 pts =
4 cups
pound (lb)
inch (in)
1 mile (mi)
Metric equivalence
5 mL
15 mL
30 mL
240 mL
0.946 L
453.54 g
2.54 cm
1.61 km
4. Temperature measurements
There are two types of temperature scales that nurses encounter, Fahrenheit and centigrade
(or Celsius). These scales differ from each other in two respects: 1. the size of the degree (the
Fahrenheit degree is 1.8, or 9/5, bigger than the Celsius degree), 2. the position used to denote
the temperature at which water freezes. Water freezes at 0 oC or 32 oF, so these two scales are
offset from each other by 32. These differences are reflected in the equations used to convert
between Fahrenheit and centigrade scales, shown below. Note that the conversion equations can
include the correction factor for degree size either as a decimal number or a fraction.
o
F = (1.8 x oC) + 32
o
C = (oF – 32)
1.8
or
o
C = 5 (oF-32)
9
or
o
F = 9 (oC) + 32
5
B. Dimensional analysis
Experiment 1
CHEM 5 – Chemistry for Nurses
Conversions within and between systems of measurement can be accomplished through
dimensional analysis. Dimensional analysis is a critical skill for nurses. It allows nurses to
convert between different sizes of units (e.g. kilograms vs grams), different systems of
measurement (e.g. apothecary vs metric), and to solve other kinds of problems encountered
during routine nursing care by keeping track of the units. In this experiment, you will use
dimensional analysis as applied to common nursing situations.
Dimensional analysis is carried out using the following steps:
1.
2.
3.
4.
Identify the units you need
Identify the units you have
Identify the conversion factors you need to convert units you have to units you need.
Write an equation using the conversion factors that will convert the units you have into
those you need, starting with the units you have and working your way over to the units
you need.
Conversion factors are equivalencies that are written as fractions. Each conversion factor has a
numerator and a denominator. The quantities in the numerator and the denominator are equal to
each other thus a conversion factor is always equal to one. Examples of conversion factors
include the following:
1000 mL
1L
453.54 g
1 lb
_1 m_
103 mm
15 gr
1g
106 μg
1g
Example 1. A nurse needs to measure 0.25 L of saline solution to add to a patient's IV bag. The
graduated cylinder she has for measuring this amount uses units of mL. How many mL of saline
is equivalent to 0.25 L?
Answer
Step 1: identify the units you need.
Units needed = mL
Step 2: identify the units you have.
Units you have = L
Step 3: identify the conversion factor(s) needed to convert from units you have to units you
need.
Conversion factors needed: 1 L = 1000 mL = 103 mL; 1 mL = 0.001 L = 10-3 L
Experiment 1
CHEM 5 – Chemistry for Nurses
Note that there are multiple conversion factors that could be used. It is frequently the case that
dimensional analysis problems can be solved using different conversion factors, as long as the
equivalencies used are correct.
Step 4: write an equation using the conversion factors that will convert the units you have
into those you need, starting with the units you have and working your way over to the units
you need. Cancel units to obtain units needed.
Units you have x conversion factor(s) = units you need
0.25 L x 1000 mL = 250 mL
1L
The nurse should pour saline into the graduated cylinder until the 250 mL mark is reached.
Example 2.
A nurse needs to convert a doctor's order for 2 mg of the pain reliever darvocet to the unit
indicated in the tablets, which is grains. How many grains of darvocet should the patient
receive?
Answer
Step 1: identify the units you need.
Units needed = grains
Step 2: identify the units you have.
Units you have = mg
Step 3: identify the conversion factor(s) needed to convert from units you have to units you
need.
Conversion factors needed: 103 mg = 1 g (or 1 mg = 10-3 g) and 1 g = 15 gr (or 1 gr =
0.067 g)
Note that two conversion factors are needed in this problem.
Step 4: write an equation using the conversion factors that will convert the units you have
into those you need, starting with the units you have and working your way over to the units
you need. Cancel units to obtain units needed.
Units you have x conversion factor 1 x conversion factor 2 = Units you need
2 mg darvocet x 10-3 g x 15 gr = 0.03 gr
1 mg
1g
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CHEM 5 – Chemistry for Nurses
Note that all of the units cancel, except the ones you need.
Example 3:
A 6 month old baby girl is brought into the emergency room. The baby weighs 4 kg and has a
head circumference of 32 cm. The admitting nurse is very alarmed by these measurements.
Why? (normal weight for a 6 month old baby girl is 14-18 lbs, normal head circumference is
16.5 in).
Answer
To answer this problem, you need to convert the baby's metric measurements to the English
(household) system.
Step 1: identify the units you need.
Units needed = lbs and in.
Step 2: identify the units you have.
Units you have = kg and cm.
Step 3: identify the conversion factor(s) needed to convert from units you have to units you
need.
Conversion factors needed: 1 kg = 2.2 lbs; 1 in = 2.54 cm
Step 4: write an equation using the conversion factors that will convert the units you have
into those you need, starting with the units you have and working your way over to the units
you need. Cancel units to obtain units needed..
4 kg x 2.2 lb = 8.8 lb
1 kg
32 cm x 1 in = 12.6 in
2.54 cm
The nurse is concerned because the baby is seriously underweight and has an abnormally
small head circumference.
C. Scientific Notation
Scientific notation is a shorthand method for expressing very large or small numbers by
keeping track of the decimal place using an exponent. Many times the quantities used in
medicine are too small to be expressed in the basic units of grams, meters, or liters. We can
convert to the units we need using dimensional analysis. Alternatively, we can express a value
using scientific notation. It is important to become proficient at these kinds of calculations since
knowing and recognizing correct dosages and their units may save a person's life.
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CHEM 5 – Chemistry for Nurses
Example 4.
A standard dose of the bronchodilator Atrovent™ (ipratropium bromide) is 0.000018 g per puff.
Express this value a. in micrograms and b. in grams using scientific notation
Answer
a. To convert this value to micrograms, we need to use a conversion factor for grams to
micrograms. Using the information from the prefixes table above (section A.1):
0.000018 g
x
1 mcg
10-6 g
=
18 mcg
b. To convert this value to scientific notation, we need to obtain a coefficient, which is a
number between 1 and 10, by moving the decimal to the right five places and then multiplying
by the corresponding power of 10, in this case 10-5. When a decimal is moved to the right, the
power of 10 is negative, when it is moved to the left, the power of 10 is positive.
0.000018 g
=
1.8 x 10-5 g
Example 5.
Viral load is a term that gives the number of virus particles per unit volume in an infected
sample. It can be expressed using different units such as particles/mL. If 1 mL of a person's
blood sample shows 65,000,000 copies of a virus, how is this number expressed in scientific
notation?
Answer
Here, we are not changing units. We are just moving the decimal place, in this case to the left.
Then we multiply by the correct power of 10.
65,000,000 copies/mL =
6.5 x 107 copies/mL
D. Concentration and Dilution
When administering drugs to a patient, it is of the utmost importance that nurses understand
the relationships between mass (or weight), volume, and concentration. Mass refers to the
quantity of matter (e.g. grams or pounds) and volume refers to the space a given amount of
matter occupies (e.g. cubic centimeters or gallons). Concentration is the ratio of mass (or
number of particles) to volume (e.g. mg/mL, g/cc, mol/L) and is a property most commonly
applied to gases and liquids. When we talk about liquids, we usually are talking about a
solution, which has particles of a given substance (the solute) dissolved in a solvent (usually
water). We will usually deal with homogeneous solutions in which the particles are uniformly
distributed in the water. A solution can be dilute (relatively few particles per unit volume of
solution) or concentrated (relatively more particles per unit volume of solution). It is very
Experiment 1
CHEM 5 – Chemistry for Nurses
important for nurses to understand how changing masses or volumes effect concentration. For
example, a fatal accident occurred recently when a young woman drank too much water as part
of a radio show contest. She died partly due to the increased blood volume that resulted from
drinking so much water. One consequence of the increased volume was dilution of her
electrolytes, which are charged particles in the blood that help control heart and kidney function.
Adding water without changing the number of electrolyte particles resulted in a concentration of
electrolytes that was too low for normal function (less mass or particles per unit volume).
Consequently, the young woman died.
Because it is so important for nurses to understand concentration and dilution, you will
practice using those concepts in this experiment. Although at this point you will use mass in
calculations involving concentration, it is useful to think about concentration as some number of
particles in a given volume. Later in the semester, you will encounter a new unit, the mole (or,
more simply, the mol), which is more appropriate for expressing number of particles. For now,
however, we will use particles and mass interchangeably. Some example calculations follow.
Example 6.
You decide to heat up a 1 cup portion of soup for lunch. To cool it down after it boils so you can
eat it comfortably, you add an additional half cup of water. Is the soup more concentrated or
more dilute than before? Explain both in words and mathematically by discussing the ratio of
mass to volume in this situation.
Answer
The soup is more dilute because water has been added which increased the volume without
changing the mass of soup we started with. Mathematically,
Before adding water: mass of soup
1 cup
After adding water:
mass of soup
1.5 cups
The ratio of mass to volume after heating is a smaller quantity than before because the number in
the denominator is larger. This is illustrated by a simple picture. The two beakers contain the
same number of particles but the beaker on the right has a greater volume, meaning the mass to
volume ratio is smaller and the solution is more dilute.
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CHEM 5 – Chemistry for Nurses
Weight/volume percent
One of the most common units of concentration in nursing is weight/volume percent which is
defined as the grams of solute per 100 mL of solution. For example, a 1% (w/v) solution means
it is a solution that contains 1 g of solute in 100 mL of solution. A 10% (w/v) solution means the
solution contains 10 g of solute in 100 mL of solution.
Example 7.
Normal saline is often administered by IV to treat dehydration. Normal saline for humans is
0.9% (w/v) sodium chloride, meaning that every 100 mL of solution contains 0.9 g of sodium
chloride. A nurse adds 250 mL of water to 500 mL of 0.9% (w/v) saline solution. Use this
information to answer the questions below.
a. How many grams of sodium chloride are in the original 500 mL solution (before the addition
of water)?
Answer
This is a simple conversion problem and should be answered as demonstrated in the previous
section (find the units you have, the units you need, the conversion factors you need, and write
an equation to accomplish the conversion). In this case, the unit we have is mL, the unit we need
is grams, and our conversion factor is 0.9 g/100 mL.
500 mL
x
0.9 g =
100 mL
4.5 g
b. How many grams of sodium chloride are in the solution after the water was added?
Answer
Since no additional sodium chloride was added, the amount is the same, or 4.5 g
c. Is the saline solution more concentrated or more dilute after the addition of water?
Explain.
Answer
The solution is more dilute because more volume was added as plain water (the solvent) without
changing the mass (or number of particles) of sodium chloride (the solute). Therefore, since the
volume increased with no change in mass, the ratio of mass to volume is smaller and the solution
is more dilute.
d. What is the new concentration (in weight percent) of the solution?
Answer
Experiment 1
CHEM 5 – Chemistry for Nurses
The new concentration is the mass divided by the new volume multiplied by 100 (to account
for the fact that the concentration is given as weight percent):
4.5 g x
750 mL
100
=
0.60 %
You could also answer this problem by realizing that the product of the old (undiluted)
concentration and volume is the same as the product of the new (diluted) concentration and
volume. A simple equation illustrating this is:
C1V1 = C2V2
where C1 and V1 = concentration and volume before dilution and C2 and V2 = concentration and
volume after dilution.
Using this equation:
0.9% x 500 mL = X% x 750 mL
Solving for X, we obtain the same answer, 0.60 %.
Experiment 1
CHEM 5 – Chemistry for Nurses
IV. PROCEDURE
Complete the following problems during the lab period; they cannot be turned it later for credit.
SHOW ALL WORK, clearly indicating all steps needed to reach your answer. Points will be
taken off for any work not shown. Obtain your lab instructor's initials for each exercise in the
box provided below.
1. A 52 yo female has a breast tumor surgically removed. The surgeon hands the tumor to the
surgical nurse and asks her to weigh it. She determines the weight to be 0.27 lb. How many
kilograms is this?
Units you need
Units you have
Conversion factor(s)
___________
___________
______________________
Equation
______________________________________________
Answer
_____________
2. A pediatric nurse needs to administer 40 mg of prednisone, a steroid used in transplant
related immunosuppression, to a 5-year old child. The pharmacist has provided the steroid in
a liquid solution containing 1 drams/L.
a. Express the prednisone concentration in drams/mL, using scientific notation.
Units you need
Units you have
Conversion factor(s)
___________
___________
______________________
Equation
______________________________________________
Answer
_____________
Conversion to scientific
notation
________________
b. How many mL of liquid should the nurse administer?
Units you need
___________
Units you have (list all) ___________
Conversion factors (you need 3) ______________________
Experiment 1
CHEM 5 – Chemistry for Nurses
Equation
______________________________________________
Answer
_____________
c. The child needs to be given this medication daily at home. The nurse believes it will be
easier for the mother to give it in teaspoon, rather than syringe, form. How many tsps should
the mother give?
Units you need
Units you have
Conversion factor(s)
___________
___________
______________________
Equation
______________________________________________
Answer
_____________
3. A person’s core body temperature, best measured using a rectal thermometer, is usually at or
near 98.2 oF. A young woman involved in a boating accident is brought into the ER
shivering and semi-conscious. Her core body temperature was measured and found to be 34
o
C. How many degrees F has her core body temperature been lowered by exposure to the
water?
4. A 210 lb, 46 yo male in cardiac arrest needs the drug milrinone, which helps the heart pump
more strongly. The correct initial loading dose is 50 mcg/kg body weight. Milrinone is
available in solution at a concentration of 0.2 mg/mL. Note: use the problem-solving
format as shown in problems 1 and 2.
a. What mass of the drug is needed in the initial dose?
b. What volume of Milrinone (in mL) is needed in the initial dose?
Experiment 1
CHEM 5 – Chemistry for Nurses
c. Express the volume you obtained in L using scientific notation.
5. Heparin is an anti-drug clotting agent often used following implantation of arterial stents. Its
misuse in newborns leading to several critical illnesses and deaths has recently been widely
reported in the news. Heparin is typically prepared in IV form at a concentration of 25,000
units/250 mL. Note: use the problem-solving format as shown in problems 1 and 2.
a. If an adult needs to have heparin administered by IV at a rate of 1000 units per hour, how
many mL of heparin IV solution should be administered per hour?
b. Assume the IV solution available is 5,000 units/5 mL. Is this a more or less concentrated
solution? Your answer should include a calculation. (Hint: reduce the concentration
value to one number in U/mL and compare).
c. What volume of this solution will provide the same dose per hour as the solution with a
concentration of 25,000 units/250 mL? (Hint: this is the same question as asked in part a.
but calculated with the new solution of 5000 U/mL).
Experiment 1
CHEM 5 – Chemistry for Nurses
NOTE: TURN IN THIS PAGE WITH YOUR POST-LAB!!! You must include lab
instructor initials on this page and work completed for question 5 along with your post-lab to
receive credit for the lab.
Lab instructor initials:
Exercise 1
_____
Exercise 2
_____
Exercise 3
_____
Exercise 4
_____
Exercise 5
_____
Experiment 1
CHEM 5 – Chemistry for Nurses
V. POST-LAB REPORT
NOTE: TURN IN THESE PROBLEMS AND THE INITIALS PAGE AT THE START OF
NEXT WEEK'S LAB PERIOD
SHOW ALL WORK to receive credit using the format shown in the procedure. Make sure
you also include units. A grade of zero will be assigned to problems involving numbers with no
units shown.
1. A very young child's temperature may be taken in three ways: by ear, under the arm, or
rectally. A mother takes her baby’s temperature using each method with the following
results:
Ear thermometer:
Underarm thermometer:
Rectal thermometer:
102.5 o Fahrenheit
101.7 o Fahrenheit
100.1 o Fahrenheit
______ centigrade
______ centigrade
______ centigrade
Convert each of these temperatures to degrees Fahrenheit and record the results in the space
provided. SHOW ALL WORK below.
2. A 70 yo male with a large pressure sore is brought to the emergency room for treatment. The
wound measures 5.2 x 2.1 cm.
a. What are these values in inches?
b. What is the area of the wound in in2? (Assume the wound shape is a rectangle).
c. Express the area in in2 using scientific notation.
Experiment 1
CHEM 5 – Chemistry for Nurses
3. Dehydration in infants can be a serious problem. The daily fluid requirement for infants
between 0 and 10 kg is 100 mL per kg.
a. If an infant weighs 14.3 pounds, what is his daily fluid requirement in mL?
b. Formula and breast milk are normally measured in ounces. What is the child's daily fluid
requirement in ounces?
4. Cubicin is an antibiotic used to treat serious, recalcitrant streptococcus infections, including
methicillin-resistant strains (MRSA bacteria). The dosage is 4 mg/kg administered once a
day over a 30 minute period by IV. Cubicin is usually sold in solid form and reconstituted in
0.9% normal saline.
a. What mass, in grams, of cubicin should be given to a patient weighing 116 pounds?
b. Express your answer from part a. in μg (mcg) using scientific notation.
c. What volume, in mL, of 0.9% saline is needed to prepare an IV solution of cubicin for
this patient that has a concentration of 0.2 mg/mL? Note that you do not need to worry
about the concentration of the 0.9% saline solution here as it is the diluent.
Experiment 1
CHEM 5 – Chemistry for Nurses
5. Claravis is a commonly prescribed drug for the treatment of severe, suppurating acne. The
recommended dose is 0.5-1.0 mg/kg/day, which must be administered in two doses with
food. It is supplied as soft capsules in 30 mg quantities.
a. Claravis is not recommended for one specific group of individuals. What is this group,
and why is the drug not recommended? (Full citation of your source required; eg
www.wikipedia.org is not an acceptable citation).
b. Draw the chemical structure of Claravis (isotetrinoin). (Full citation required)
c. How many 30 mg capsules should a 19-year old male weighing 160 pounds take each
day?
Experiment 1
CHEM 5 – Chemistry for Nurses
6. A nurse opens a package containing a 10% (w/v) dextrose IV bag and sees that the bag
contains mostly liquid but also some solids. The bag should contain only liquid.
a. Is the liquid in the bag more or less concentrated than the expected 10% solution?
Explain.
b. Assume the solid portion is dextrose with a mass of 21.7 g. What mass of dextrose
remains in the liquid? (Assume a 1 L bag).
c. What is the concentration of dextrose in the liquid?
d. Should the nurse use this IV bag? Why or why not?
7. A nurse prepares a solution by mixing 50 mL of 5% dextrose with 450 mL of water. What is
the new concentration of dextrose?