Essential Calculations Workbook
ECW-1
Essential Calculations Workbook
Instructions
Complete the following workbook either individually or in small groups. There are no marks for this
workbook, but these calculations and concepts are required for lab reports and will be tested on Lab
Quizzes.
Key Concepts
1. Solving word problems
2. Significant figures
3. Precision and accuracy
4. Working with molarity
5. Dilution calculations
6. Converting between mass, moles, and molar mass
7. Converting between mass, volume, and density
8. Unit conversion
9. Estimation
A. Precision, accuracy, and significant figures
1. Exact numbers are those quantities that can be known exactly, for example the number of apples in
a basket or the number of grams in 1 kilogram. Inexact numbers are those quantities that have some
uncertainty, for example the mass of a basket of apples. In general, inexact number are the result of a
measurement. Identify each of the following values as exact numbers or inexact numbers.
a) the number of carbon atoms in a sucrose molecule
exact
inexact
b) the volume of a cup of coffee
exact
inexact
c) the number of joules in a kilojoule
exact
inexact
d) the molar mass of a hydrogen atom
exact
inexact
Fall 2025 Student Version
Essential Calculations Workbook
ECW-2
2. Determine the number of significant figures in each of the following measurements as written and
then round each to the number of significant figures indicated.
Measurement
a) 1.2367 mL to 4 significant figures
Number of significant
figures in the value
5
Rounded value
1.237 mL
b) a) 99.99 mL to 3 significant figures
c) 100.51 J to 3 significant figures
d) 0.004312 ×10−4 mol/L to 2 significant figures
e) 205.5 g/mol to 3 significant figures
f) 0.0014429 g to 2 significant figures
g) 1.0046 L to 3 significant figures
h) 3401 mg to 2 significant figures
Fall 2025 Student Version
Essential Calculations Workbook
ECW-3
3. Methane (CH4) is a more powerful greenhouse gas than carbon dioxide (CO2) and its concentration
in Earth’s atmosphere has been rising in the last decade. (The cause of this increase is still being
debated.)1
a) Use the values from your data sheet to determine the molar mass of CH4. Round your final answers
to the correct number of significant figures. Remember to include units. (ANSWER: 16.04 g/mol)
b) Atmospheric methane emissions are measured in teragrams per year (Tg/yr). How many molecules
of CH4 are in 1.00 Tg of methane? Round your answer to the correct number of significant figures. Tera
= 1012. Avogadro’s number (N) is on your data sheet. (ANSWER: 3.75 ×1034 molecules)
1
“The methane mystery” The Economist (2018) 427, 9089, 71-72.
Fall 2025 Student Version
Essential Calculations Workbook
ECW-4
4. The mass of an empty beaker is 84.631 g and the mass of a large scoop of NaCl in the same beaker is
89.631 g. How many grams of NaCl are in the beaker? Round your final answers to the correct number
of significant figures. Remember to include units. (ANSWER: 5.000 g)
5. The BC government collects air quality data at various monitoring stations around the province. The
nearest station to VIU is on Labieux Road, near Beban park (about 6 km from VIU). One metric that is
particularly important to human health is PM2.5 which counts the mass of particles with a diameter of
2.5 μm or less. It is reported in μg/m3 and the government guideline for maximum average exposure in
a 24 h period is 25 μg/m3. 2 The data for May 4th, 2018 is below. Calculate the average exposure over a
24 h period and determine whether this below the safe 24 h limit. Round your final answers to the
correct number of significant figures. Remember to include units. (ANSWER: 5 μg/m3 over 24 h)
Day
24h Time
May 4
0:00
May 4
4:00
May 4
8:00
May 4
12:00
May 4
16:00
May 4
20:00
May 5
0:00
PM2.5, μg/m3
8
5
1
6
1
4
7
https://www2.gov.bc.ca/gov/content/environment/air-land-water/air/air-quality-management/regulatoryframework/objectives-standards/pm2-5
2
Fall 2025 Student Version
Essential Calculations Workbook
ECW-5
6. A metric that we use to evaluate the accuracy of a measurement is % error. A student
experimentally determines that a 16.00 g of Werther’s Original candy contains 9.431 g of sucrose. The
nutritional label on the bag of Werther’s Original candy states that there is 10.00 g of sugar in 16 g of
candy. Assuming that all the sugar is in the form of sucrose and that the value on the label is the actual
(true) value, determine the % error of the student’s measurement. Round your final answers to the
correct number of significant figures. Remember to include units. (ANSWER: −5.7 %)
𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒 − 𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎
% 𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒 = 100 ×
𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎
7. A metric that we use to evaluate the precision of an experiment is the relative standard deviation (%
RSD).
% 𝑅𝑅𝑅𝑅𝑅𝑅 = 100 ×
𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑
𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚 𝑜𝑜𝑜𝑜 𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚 𝑣𝑣𝑣𝑣𝑣𝑣𝑣𝑣𝑣𝑣
A diabetic measures concentration of glucose in her blood (mmol/L) three times in a row using the
same handheld blood glucose monitor. She gets the following results: 4.8, 4.4, 4.3 mmol/L. The
standard deviation for these concentrations is 0.3 mmol/L. Determine the % RSD. Round your final
answers to the correct number of significant figures. Remember to include units. (ANSWER: 7%)
Fall 2025 Student Version
Essential Calculations Workbook
ECW-6
B. Solutions, Concentrations, and Dilution
One common unit for concentration is molarity (moles/L). This unit is important because it allows us to
express the number of molecules (or any other chemical species such as atoms or ions) in units of
moles per litre. Molarity is defined as:
𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀 (𝑀𝑀) =
𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚 𝑜𝑜𝑜𝑜 𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠
𝐿𝐿 𝑜𝑜𝑜𝑜 𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠
8. Erythrosine (C20H6I4Na2O5; MM = 879.86 g/mol) is a red food dye used to visualize plaque on teeth.
Calculate the molarity of erythrosine solution prepared by dissolving 2.00 g of the solid in 5.00 ×102 g
of water. Assume that the density of the solution and water are 0.997 g/mL and that adding the dye to
the water doesn’t change the volume. (ANSWER: 0.00453 M)
Fall 2025 Student Version
Essential Calculations Workbook
ECW-7
9. A student prepares some simulated sea water for a weathering experiment by making a 600 mM
NaCl solution. They need 2.00 L of simulated sea water, how many grams of NaCl should they weigh
out to make the solution? Assume that the volume of NaCl is negligible when dissolved in solution.
(ANSWER: 70 g of NaCl)
10. Review the video on volumetric glassware so you understand how volumetric pipets and flasks are
used. The drawing below shows the preparation of a diluted solution from a stock solution using
volumetric glassware. The diluted solution is prepared by measuring 25.00 mL of the stock solution
using a volumetric pipet and then transferring contents of the volumetric pipet into the 50 mL
volumetric flask and diluting so that the total volume is 50.00 mL. Each circle in the stock solution
represents 1.0 mmol of solute.
a) If 25.00 mL of the stock solution is measured out, how many circles
should be in the volumetric pipet?
b) How many circles should be in the diluted solution?
c) Calculate the concentration of solute (in mol/L) in the diluted solution.
(ANSWER: 0.040 mol/L)
Fall 2025 Student Version
Essential Calculations Workbook
ECW-8
11. The drawing below shows the preparation of a diluted solution from a stock solution. The
concentration of the stock solution is unknown. The diluted solution is prepared by measuring 10.00
mL of the stock solution using a volumetric pipet and then transferring contents of the volumetric pipet
into the 1L volumetric flask. The diluted solution is analyzed and the concentration was determined to
be 3.0 mmol/L. Each circle represents 1.0 mmol of solute.
a) How many circles were in the volumetric pipet before transferring the
solution to the 1 L volumetric flask?
b) Calculate the concentration of the stock solution in mol/L.
Fall 2025 Student Version
Essential Calculations Workbook
ECW-9
12. When learning about solutions, students are often taught to do dilutions calculations using the
formula C1V1 = C2V2 where, C1 is the concentration of the more concentrated solution, C2 is the
concentration of the diluted solution, V1 is the volume of the concentrated solution, and V2 is the
volume of the diluted solution. (This equation also appears in other forms such as M1V1 = M2V2.).
Explain why this equation works. (Hint: Think about the previous two questions.)
13. A Starbucks Venti® Caramel Frappuccino® is 709 mL contains 130. mg of caffeine (C8H10N4O2; MM =
194.19 g/mol). You give 400. mL of your drink to your friend who adds 250. mL of milk to their portion.
a) How much caffeine is in your friend’s drink? (ANSWER: 73.3 mg caffeine)
b) What is the concentration of caffeine in your friend’s drink in mg/L and mol/L? (ASNWER: 113 mg
caffeine/L of drink, 5.82 × 10−4 mol caffeine/L of drink)
Fall 2025 Student Version
Essential Calculations Workbook
ECW-10
14. Fluorescein (C20H12O5; MM = 332.3 g/mol) is a fluorescent dye that can be observed visually when
the concentration is greater than 1.50 ×10−7 mol/L, which makes it useful in many fields including sea—
air search and rescue, and ophthalmology. One important use for fluorescein is as a tracer dye in
mapping ground water flow. In this case, fluorescein is added to the source of the water and then
observed downstream. If a hydrologist wants to be able to see the fluorescein in a pond that is
approximated as half sphere with a radius of 2.0 m, what is the minimum amount of fluorescein, in
grams, that needs to be added in order to be observed visually? (ANSWER: 0.84 g of fluorescein)
4
Volume of a sphere: 𝑉𝑉 = 3 𝜋𝜋𝑟𝑟 3
1 m3 = 1,000 L
Fall 2025 Student Version
Essential Calculations Workbook
ECW-11
C. Estimation
In many situations we may not have all the information necessary to make a highly accurate calculation
− indeed some information cannot be known! Despite the inaccuracy, having idea of what to expect
allows one to make a quick judgement on the validity of a statement or method of solving a problem.
In some cases, it can uncover flaws in the solution – whether they are your own or someone else’s. 3
Some things to consider when estimating:
• You will have to make some numbers up.
• Estimated values will have correct units. If not, then there may be a logical flaw.
• Keep track of your assumptions and best guess values used so that you can refine your estimate
with more accurate values later.
15. Estimate the amount of energy in Joules that a person requires for growth and survival over their
lifetime. How many jellybeans would you need to provide that amount of energy? Compare your
answer to your neighbours’ and discuss who has the better estimate. The nutritional label from a
package of Jelly Belly jellybeans is given below. Note that nutritional Calories (with a capital C) is equal
to 1000 science calories (with a lower-case c) and 1 calorie = 4.184 J.
List the assumptions you made to make your estimate.
Nobel Laurate in Physics Enrico Fermi was famous for using estimation. He worked on the Manhattan Project
and was present at the first nuclear explosion. In his notes he describes estimating the blast force by “dropping
from about six feet small pieces of paper before, during and after the passage of the blast wave”. His estimate
was to within a factor of 2 of the measured value. Ref: Nuclear Weapons Journal, Issue 2, 2005 pg. 45.
3
Fall 2025 Student Version
Essential Calculations Workbook
ECW-12
Additional Practice
17. You make a refreshing summer drink by diluting 100 mL of orange juice with 300 mL of sparkling
water. If the orange juice has a sugar concentration of 84 g/L, what is the sugar concentration (in g/L)
in your drink? (ANSWER: 21 g of sugar/L of juice)
18. Hard water contains high concentrations calcium (Ca2+) and magnesium (Mg2+) ions, which leads to
the formation of scale in kettles. After moving into a new house, a student notices that scale was
forming in their kettle and decides to determine the calcium concentration in their water. They dilute a
10.00 mL sample of well water to a total volume of 100.00 mL with deionized water. The calcium
concentration in the 100.00 mL sample was determined to be 1.45 x 10-4 mol/L when analyzed by
flame atomic absorption spectroscopy. What is the calcium concentration in the well water from the
student’s house? (ANSWER: 1.45 ×10−3 M)
19. How many pencils would it take to trace the equator?
20. Lithium is an essential metal used in batteries for electric vehicles. How many grams of lithium
would you need to replace all the gas-powered cars in Nanaimo to electric cars?
Fall 2025 Student Version