1.12: End of Chapter Problems I
- Page ID
- 436077
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\(\newcommand{\avec}{\mathbf a}\) \(\newcommand{\bvec}{\mathbf b}\) \(\newcommand{\cvec}{\mathbf c}\) \(\newcommand{\dvec}{\mathbf d}\) \(\newcommand{\dtil}{\widetilde{\mathbf d}}\) \(\newcommand{\evec}{\mathbf e}\) \(\newcommand{\fvec}{\mathbf f}\) \(\newcommand{\nvec}{\mathbf n}\) \(\newcommand{\pvec}{\mathbf p}\) \(\newcommand{\qvec}{\mathbf q}\) \(\newcommand{\svec}{\mathbf s}\) \(\newcommand{\tvec}{\mathbf t}\) \(\newcommand{\uvec}{\mathbf u}\) \(\newcommand{\vvec}{\mathbf v}\) \(\newcommand{\wvec}{\mathbf w}\) \(\newcommand{\xvec}{\mathbf x}\) \(\newcommand{\yvec}{\mathbf y}\) \(\newcommand{\zvec}{\mathbf z}\) \(\newcommand{\rvec}{\mathbf r}\) \(\newcommand{\mvec}{\mathbf m}\) \(\newcommand{\zerovec}{\mathbf 0}\) \(\newcommand{\onevec}{\mathbf 1}\) \(\newcommand{\real}{\mathbb R}\) \(\newcommand{\twovec}[2]{\left[\begin{array}{r}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\ctwovec}[2]{\left[\begin{array}{c}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\threevec}[3]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\cthreevec}[3]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\fourvec}[4]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\cfourvec}[4]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\fivevec}[5]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\cfivevec}[5]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\mattwo}[4]{\left[\begin{array}{rr}#1 \amp #2 \\ #3 \amp #4 \\ \end{array}\right]}\) \(\newcommand{\laspan}[1]{\text{Span}\{#1\}}\) \(\newcommand{\bcal}{\cal B}\) \(\newcommand{\ccal}{\cal C}\) \(\newcommand{\scal}{\cal S}\) \(\newcommand{\wcal}{\cal W}\) \(\newcommand{\ecal}{\cal E}\) \(\newcommand{\coords}[2]{\left\{#1\right\}_{#2}}\) \(\newcommand{\gray}[1]{\color{gray}{#1}}\) \(\newcommand{\lgray}[1]{\color{lightgray}{#1}}\) \(\newcommand{\rank}{\operatorname{rank}}\) \(\newcommand{\row}{\text{Row}}\) \(\newcommand{\col}{\text{Col}}\) \(\renewcommand{\row}{\text{Row}}\) \(\newcommand{\nul}{\text{Nul}}\) \(\newcommand{\var}{\text{Var}}\) \(\newcommand{\corr}{\text{corr}}\) \(\newcommand{\len}[1]{\left|#1\right|}\) \(\newcommand{\bbar}{\overline{\bvec}}\) \(\newcommand{\bhat}{\widehat{\bvec}}\) \(\newcommand{\bperp}{\bvec^\perp}\) \(\newcommand{\xhat}{\widehat{\xvec}}\) \(\newcommand{\vhat}{\widehat{\vvec}}\) \(\newcommand{\uhat}{\widehat{\uvec}}\) \(\newcommand{\what}{\widehat{\wvec}}\) \(\newcommand{\Sighat}{\widehat{\Sigma}}\) \(\newcommand{\lt}{<}\) \(\newcommand{\gt}{>}\) \(\newcommand{\amp}{&}\) \(\definecolor{fillinmathshade}{gray}{0.9}\)Significant Figures
1. How many significant figures does each number have?
6,798,000 6,000,798 6,000,798.00 0.0006798
2.1828 0.005505 55,050 5 500
2. Solve and write the answer with the appropriate number of significant figures.
23.096 × 90.300 125 × 9.000 1,027 + 610.0 + 363.06
217 ÷ 903 13.77 + 908.226 + 515 255.0 − 99 0.00666 x 321
3. Explain why the concept of significant figures is important in scientific measurements.
4. State the rules for determining the significant figures in a measurement.
5. When do you round a number up, and when do you not round a number up?
Scientific Notation and Decimal Form
1. Express each number in scientific notation.
67,000,000,000 1,689
12.6 1,492
102,000,000 101,325
0.000006567 −0.0004004
0.000000000000123 0.000355
0.314159 −0.051204
2. Change the number in scientific notation to standard form.
5.27 × 104 1.0008 × 106
6.98×108 1.005×102
6.22 × 10−2 9.9 × 10−9
9.98 × 10−5 5.109 × 10−8
3. Why it is easier to use scientific notation to express very large or very small numbers?
Converting Units
1. The average volume of blood in an adult male is 4.7 L. What is this volume in milliliters? [1L =1000 mL]
2. A hummingbird can flap its wings once in 18 ms. How many seconds are in 18 ms? [1 s = 1000 ms]
3. Perform the conversion 32.08 kg to grams. [1 kg = 1000 g]
States of Matter
1. What state or states of matter does each statement, describe?
- This state has a definite volume, but no definite shape.
- This state has no definite volume.
- This state allows the individual particles to move about while remaining in contact.
- This state has individual particles in a fixed position with regard to each other.
- This state has individual particles far apart from each other in space.
- This state has a definite shape.
Energy
1. Classify each of the following energies as kinetic energy or potential energy:
The energy in a chocolate bar.
The energy of rushing water used to turn a turbine or a water wheel.
The energy of a skater gliding on the ice.
The energy in a stretched rubber band.
2. You mix two chemicals in a beaker and notice that as the chemicals react, the beaker becomes noticeably colder. Which chemicals have more chemical potential energy, those present at the start of the reaction or those present at the end of the reaction?
Measurements
1. Identify the number and the unit in each quantity.
- one dozen eggs
- 2.54 centimeters
- a box of pencils
- 88 meters per second
Temperature
1. Convert each temperature to °C.
- the temperature of the surface of the sun (5800. K)
- the boiling point of gold (3080. K)
- the boiling point of liquid nitrogen (77.36 K)
2. Convert each temperature to K.
98.6 oC 25.0 oC 0.0 oC -40.0 oC
Density and Specific Gravity
For the following problems assume room temperature of 20oC.
1. Calculate the density of a 30.2 mL sample of ethyl alcohol with a mass of 23.7102 g. What is the specific gravity of ethyl alcohol?
2. If you have a 2.130 mL sample of acetic acid with mass 0.002234 kg, what is the density in kg/L? What is the specific gravity of acetic acid?
3. A mercury thermometer for measuring a patient’s temperature contains 0.750 g of mercury. What is the volume of this mass of mercury? The density of Hg is 13.6 g/mL. What is the specific gravity of Hg?
4. You have a sample of aluminum that has a volume of 7.88 mL. What is the mass of Al if the density is 2.70 g/mL. What is the specific gravity of Al?