# 1.6 Mathematical treatment of measurement results  (Page 5/9)

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## Key concepts and summary

Measurements are made using a variety of units. It is often useful or necessary to convert a measured quantity from one unit into another. These conversions are accomplished using unit conversion factors, which are derived by simple applications of a mathematical approach called the factor-label method or dimensional analysis. This strategy is also employed to calculate sought quantities using measured quantities and appropriate mathematical relations.

## Key equations

• ${T}_{\text{°C}}=\phantom{\rule{0.2em}{0ex}}\frac{5}{9}\phantom{\rule{0.2em}{0ex}}×\phantom{\rule{0.2em}{0ex}}{T}_{\text{°F}}-32$
• ${T}_{\text{°F}}=\phantom{\rule{0.2em}{0ex}}\frac{9}{5}\phantom{\rule{0.2em}{0ex}}×\phantom{\rule{0.2em}{0ex}}{T}_{\text{°C}}+32$
• ${T}_{\text{K}}=\text{°C}+273.15$
• ${T}_{\text{°C}}=\text{K}-273.15$

## Chemistry end of chapter exercises

Write conversion factors (as ratios) for the number of:

(a) yards in 1 meter

(b) liters in 1 liquid quart

(c) pounds in 1 kilogram

(a) $\frac{\text{1.0936 yd}}{\text{1 m}}$ ; (b) $\frac{\text{0.94635 L}}{\text{1 qt}}$ ; (c) $\frac{\text{2.2046 lb}}{\text{1 kg}}$

Write conversion factors (as ratios) for the number of:

(a) kilometers in 1 mile

(b) liters in 1 cubic foot

(c) grams in 1 ounce

The label on a soft drink bottle gives the volume in two units: 2.0 L and 67.6 fl oz. Use this information to derive a conversion factor between the English and metric units. How many significant figures can you justify in your conversion factor?

$\begin{array}{c}\frac{\text{2.0 L}}{\text{67.6 fl oz}}\phantom{\rule{0.2em}{0ex}}=\phantom{\rule{0.2em}{0ex}}\frac{\text{0.030 L}}{\text{1 fl oz}}\end{array}$
Only two significant figures are justified.

The label on a box of cereal gives the mass of cereal in two units: 978 grams and 34.5 oz. Use this information to find a conversion factor between the English and metric units. How many significant figures can you justify in your conversion factor?

Soccer is played with a round ball having a circumference between 27 and 28 in. and a weight between 14 and 16 oz. What are these specifications in units of centimeters and grams?

68–71 cm; 400–450 g

A woman's basketball has a circumference between 28.5 and 29.0 inches and a maximum weight of 20 ounces (two significant figures). What are these specifications in units of centimeters and grams?

How many milliliters of a soft drink are contained in a 12.0-oz can?

355 mL

A barrel of oil is exactly 42 gal. How many liters of oil are in a barrel?

The diameter of a red blood cell is about 3 $×$ 10 −4 in. What is its diameter in centimeters?

8 $×$ 10 −4 cm

The distance between the centers of the two oxygen atoms in an oxygen molecule is 1.21 $×$ 10 −8 cm. What is this distance in inches?

Is a 197-lb weight lifter light enough to compete in a class limited to those weighing 90 kg or less?

yes; weight = 89.4 kg

A very good 197-lb weight lifter lifted 192 kg in a move called the clean and jerk. What was the mass of the weight lifted in pounds?

Many medical laboratory tests are run using 5.0 μL blood serum. What is this volume in milliliters?

5.0 $×$ 10 −3 mL

If an aspirin tablet contains 325 mg aspirin, how many grams of aspirin does it contain?

Use scientific (exponential) notation to express the following quantities in terms of the SI base units in [link] :

(a) 0.13 g

(b) 232 Gg

(c) 5.23 pm

(d) 86.3 mg

(e) 37.6 cm

(f) 54 μm

(g) 1 Ts

(h) 27 ps

(i) 0.15 mK

(a) 1.3 $×$ 10 −4 kg; (b) 2.32 $×$ 10 8 kg; (c) 5.23 $×$ 10 −12 m; (d) 8.63 $×$ 10 −5 kg; (e) 3.76 $×$ 10 −1 m; (f) 5.4 $×$ 10 −5 m; (g) 1 $×$ 10 12 s; (h) 2.7 $×$ 10 −11 s; (i) 1.5 $×$ 10 −4 K

definition of isomerism
Compounds that have the same molecular formula, but different structural formula. Sent from Egypt
Abdelkarim
who is the father of chemistry
what is hybridization and bonding
please who is the father of chemistry
Naomi
Antoine Lavoisier
Abdelkarim
Abdelkarim
Also, god has created everything
Abdelkarim
(Allah, the creator)
Abdelkarim
how to determine the empirical formula
what is neutralisation reaction
It is a reaction where an acid (aq) reacts with an alkali (aq) to form salt AND water.
Abdelkarim
What is the ratio of the average kinetic energy of a SO 2 molecule to that of an O 2 molecule in a mixture of two gases? What is the ratio of the root mean square speeds, u rms , of the two gases?
what is methyl orange
its an indicator
Abigail
It is an organic molecule that reacts with acid/base medium and shows change in colour (due to formed products). It can be used to test for alcohols which are prohibited to drink in Islam as it is bad for brain and liver and immunity.
Abdelkarim
it is an indicator used to determine the end point in an acid-base titration
xMah_Bx
Abdelkarim
covalent bond explanation
God has lictured these rules that the electrons move with them and the space time curve. So we prwy to God in Islam or we suffer. Please learn about Islam and science and mention God and thank him.
Abdelkarim
yes, it is very true. God is the one who inspires science. Then we, as his children, have the privilege to learn about what he has created. I'm still a novis at chemistry. I still have a lot to learn.
Eric
Beautiful, however, what I learned from the Quran is that god has created human and has a mission like managing the ecology, building, learning, mentioning god (saying glory to Almighty for instance few times and periodic). And the moat important prayer lile prophet Muhammed the last meassenger.
Abdelkarim
Also God forgives all sins except assossiating any one with him like sons and daughters or stone sculpture. Beautifully, if some one stops from saying this God can switch their sins to virtueness. And God all merciful doesnt get bored forgiving people who ask for forgiveness.
Abdelkarim
Also, there is a versw in the Quran that sates: { corruption has appeared in the land and the sea he will taste them from what their hands have gained} this reminds me of covid from stupid politicians who will be throne to hell.
Abdelkarim
nature of bond in N2 molecule is
Triple covalent bond, and that is why it is hardly reactive because in order to react you must break three strong covalent bonds.
Abdelkarim
what is electromagnetic energy
in a school of 120 students, 41studied mathematics, 48studied chemistry and 42 studied physics, 16 studied both chemistry and mathematics, 14 studied mathematics and physics, 18 studied chemistry and physics and 9 studied all the three subjects. how many of them studied exactly one subject?
Does Chromium oxidize?
yes
Alaa
@Alaa It doesn't.
Jag
yes. it's a very strong oxidizing agent
xMah_Bx
what is compound
what are the types of hydrocarbon
homologous series is under what
Dolapo
Jag
OK Aliphatic and Aromatic.
Jag