Skip to main content
Chemistry LibreTexts

1B: Review of the Tools of Quantitative Chemistry

  • Page ID
    214675
  • SI Prefixes 

    Exercise \(\PageIndex{1}\)

    The Si prefix for 106 is:

    a. micro

    b. milli

    c. kilo

    d. mega

    Answer

    d. mega

    Exercise \(\PageIndex{1}\)

    The Si prefix for 10-6 is:

    a. nano

    b. micro

    c. milli

    d. pico

    Answer

    b. micro

    Exercise \(\PageIndex{1}\)

    The Si prefix for 109 is:

    a. mega

    b. giga

    c. kilo

    d. deca

    Answer

    b. giga

    Exercise \(\PageIndex{1}\)

    The Si prefix for 10-1 is:

    a. mili

    b. centi

    c. deci

    d. micro

    Answer

    c. deci

    Exercise \(\PageIndex{1}\)

    The Si prefix for 10-12 is:

    a. nano

    b. fempto

    c. pico

    d. micro

    Answer

    c. pico

    Exercise \(\PageIndex{1}\)

    The Si prefix for 10-9 is:

    a. nano

    b. pico

    c. fempto

    d. micro

    Answer

    a. nano

     

    Exercise \(\PageIndex{1}\)

    The Si prefix for 101 is:

    a. deci

    b. mili

    c. deca

    d. kilo

    Answer

    c. deca

    Exercise \(\PageIndex{1}\)

    The Si prefix for 103 is:

    a. mega

    b. giga

    c. kilo

    d. deca

    Answer

    c. kilo

     

    SI Conversions

    !

    Exercise \(\PageIndex{1}\)

    2.4x103 µ g =?mg

    a. 2.4

    b. 2.4x109

    c. 2.4x10-3

    d. 2.4x108

    Answer

    &&

    !

    !

    Exercise \(\PageIndex{1}\)

    7.6x105 nL=?Micro L

    a. 7.6

    b. 7.6x106

    c. 7.6x102

    d. 7.6x107

    Answer

    c. 7.6x102

    !

    !

    Exercise \(\PageIndex{1}\)

    3.4x10-15 Mg =?ng

    a. 3.4

    b. 3.4x10-30

    c. 3.4x10-18

    d. 3.4x1012

    Answer

    a. 3.4

    !

    !

    Exercise \(\PageIndex{1}\)

    5.4x10-11Gg = ? mg

    a. 5.4

    b. 54

    c. 5.4x103

    d. 5.4x108

    Answer

    &&

    !

    !

    Exercise \(\PageIndex{1}\)

    2.8x1012fm = ?km

    a. 2.8

    b. 2.8x106

    c. 2.8x10-6

    d. 2.8x102

    Answer

    c. 2.8x10-6

    !

     

    Significant Figures

    Exercise \(\PageIndex{17}\)

    How many significant figures are in 0.00204 g?

    a. 6

    b. 5

    c. 4

    d. 3

    Answer

    d. 3

    Exercise \(\PageIndex{18}\)

    How many significant figures are in 20400 g?

    a. 5

    b. 4

    c. 3

    d. 2

    Answer

    c. 3

    Exercise \(\PageIndex{19}\)

    How many significant figures are in 20103 ml?

    a. 5

    b. 4

    c. 3

    d. 2

    Answer

    a. 5

    Exercise \(\PageIndex{20}\)

    How many significant figures are in 100 students?

    a. 3

    b. 2

    c. 1

    d. unknown

    Answer

    a. 3

    Exercise \(\PageIndex{21}\)

    How many significant figures are in 0.00001 miles?

    a. 5

    b. 3

    c. 2

    d. 1

    Answer

    d. 1

    Exercise \(\PageIndex{22}\)

    How many significant figures are in 2.00 x 104?

    a. 4

    b. 3

    c. 2

    d. 1

    Answer

    b. 3

     

    Algebra Review 

    Exercise \(\PageIndex{1}\)

    Solve the following problem for \(P\): \(\begin{equation}P V=n R T\end{equation}\)

    a. \(\begin{equation}n R T + V\end{equation}\)

    b. \(\begin{equation}n R T - V\end{equation}\)

    c. \(\begin{equation}V (n R T)\end{equation}\)

    d. \(\begin{equation}\frac{n R T}{V}\end{equation}\)

    Answer

    d. \(\begin{equation}\frac{n R T}{V}\end{equation}\)

    Exercise \(\PageIndex{2}\)

    Solve the following problem for \(T\): \(P V=n R T\)

    a. \(T=\frac{nR}{PV}\)

    b. \(T=\frac{PV}{nR}\)

    c. \(T = P V + n R\)

    d. \(T = P V -n R\)

    Answer

    b. \(\begin{equation}\mathrm{T}=\frac{\mathrm{PV}}{\mathrm{nR}}\end{equation}\)

    Exercise \(\PageIndex{3}\)

    Solve the following problem for \(T_{C}\): \(T_{F}=T_{C}\left(\frac{9}{5}\right)+32\)

    a. \(T_{C}=\left(T_{F}+32\right)\left(\frac{5}{9}\right)\)

    b. \(T_{C}=\left(T_{F}+32\right)\left(\frac{9}{5}\right)\)

    c. \(T_{C}=\left(T_{F}-32\right)\left(\frac{9}{5}\right)\)

    d. \(T_{C}=\left(T_{F}-32\right)\left(\frac{5}{9}\right)\)

    Answer

    d. \(T_{C}=\left(T_{F}-32\right)\left(\frac{5}{9}\right)\)

    Exercise \(\PageIndex{4}\)

    Solve the following problem for \(T_{f}\): \(q=m c\left(T_{f}-T_{i}\right)\)

    a. \(T_{f}=T_{i}-\frac{q}{m c}\)

    b. \(T_{f}=\frac{q}{m c}-T_{i}\)

    c. \(T_{f}=\frac{q}{m c}-T_{i}\)

    d. \(T_{f}=T_{i}+\frac{q}{m c}\)

    Answer

    d. \(T_{f}=T_{i}+\frac{q}{m c}\)

    Exercise \(\PageIndex{5}\)

    Solve the following problem for \(C_{c}\): \(m_{C} c_{C}\left(T_{F}-T_{C}\right)=-m_{H} c_{H}\left(T_{F}-T_{H}\right)\)

    a. \(c_{C}=\frac{m_{H} c_{H}\left(T_{F}-T_{H}\right)}{m_{C}\left(T_{F}-T_{C}\right)}\)

    b. \(c_{C}=\frac{-m_{H} c_{H}\left(T_{F}-T_{H}\right)}{m_{C}\left(T_{F}-T_{C}\right)}\)

    c. \(c_{C}=m_{H} c_{H}\left(T_{F}-T_{H}\right)+m_{C}\left(T_{F}-T_{C}\right)\)

    d. \(c_{C}=m_{H} c_{H}\left(T_{F}-T_{H}\right)-m_{C}\left(T_{F}-T_{C}\right)\)

    Answer

    b. \(c_{C}=\frac{-m_{H} c_{H}\left(T_{F}-T_{H}\right)}{m_{C}\left(T_{F}-T_{C}\right)}\)

    Exercise \(\PageIndex{6}\)

    Solve the following problem for \(c_{H}\): \(m_{C} c_{C}\left(T_{F}-T_{C}\right)=-m_{H} c_{H}\left(T_{F}-T_{H}\right)\)

    a. \(c_{H}=\frac{m_{C} c_{C}\left(T_{F}-T_{C}\right)}{-m_{H}\left(T_{F}-T_{H}\right)}\)

    b. \(c_{H}=\frac{m_{C} c_{C}\left(T_{F}-T_{C}\right)}{m_{H}\left(T_{F}-T_{H}\right)}\)

    c. \(c_{H}=m_{C} c_{C}\left(T_{F}-T_{C}\right)+m_{H}\left(T_{F}-T_{H}\right)\)

    d. \(c_{H}=m_{C} c_{C}\left(T_{F}-T_{C}\right)-m_{H}\left(T_{F}-T_{H}\right)\)

    Answer

    a. \(c_{H}=\frac{m_{C} c_{C}\left(T_{F}-T_{C}\right)}{-m_{H}\left(T_{F}-T_{H}\right)}\)

    Exercise \(\PageIndex{7}\)

    Solve the following problem for \(T_{C}\): \(m_{C} c_{C}\left(T_{F}-T_{C}\right)=-m_{H} c_{H}\left(T_{F}-T_{H}\right)\)

    a. \(T_{C}=T_{F}-\frac{m_{H} c_{H}\left(T_{F}-T_{H}\right)}{m_{C} c_{C}}\)

    b. \(T_{C}=T_{F}-\left(\frac{m_{C} c_{C}}{m_{H} c_{H}\left(T_{F}-T_{H}\right)}\right)\)

    c. \(T_{C}=T_{F}+\left(\frac{m_{C} c_{C}}{m_{H} c_{H}\left(T_{F}-T_{H}\right)}\right)\)

    d. \(T_{C}=T_{F}+\frac{m_{H} c_{H}\left(T_{F}-T_{H}\right)}{m_{C} c_{C}}\)

    Answer

    d. \(T_{C}=T_{F}+\frac{m_{H} c_{H}\left(T_{F}-T_{H}\right)}{m_{C} c_{C}}\)

    Exercise \(\PageIndex{8}\)

    Solve the following problem for \(T_{F}\): \(m_{C} c_{C}\left(T_{F}-T_{C}\right)=-m_{H} c_{H}\left(T_{F}-T_{H}\right)\)

    a. \(T_{F}=\frac{m_{C} c_{C} T_{C}-m_{H} C_{H} T_{C}}{\left(m_{C} c_{C}+m_{H} c_{H}\right)}\)

    b. \(T_{F}=\frac{m_{C} c_{C} T_{C}+m_{H} C_{H} T_{H}}{\left(m_{C} C_{C}+m_{H} C_{H}\right)}\)

    c. \(T_{F}=\frac{m_{C} c_{C} T_{C}-m_{H} c_{H} T_{C}}{\left(m_{C} c_{C}-m_{H} C_{H}\right)}\)

    d. \(T_{F}=\frac{m_{C} c_{C} T_{C}+m_{H} C_{H} T_{C}}{\left(m_{C} c_{C}-m_{H} C_{H}\right)}\)

    Answer

    b. \(T_{F}=\frac{m_{C} c_{C} T_{C}+m_{H} C_{H} T_{H}}{\left(m_{C} C_{C}+m_{H} C_{H}\right)}\)

     

    Mathematics Review

    Exercise \(\PageIndex{9}\)

    12.56 + 2.4 = 

    a. 15

    b. 14.96

    c. 15.0

    d. 14.9

    Answer

    c. 15.0

    Exercise \(\PageIndex{10}\)

    98.3 - 89.4 = 

    a. 8.90

    b. 9

    c. 8.9

    d. 9.00

    Answer

    c. 8.9

    Exercise \(\PageIndex{11}\)

    82.0 + 34.4 = 

    a. 116.4

    b. 116

    c. 117

    d. 120

    Answer

    a. 116.4

    Exercise \(\PageIndex{12}\)

    12.56 x 2.4 = 

    a. 30.144

    b. 30.14

    c. 30.1

    d. 30.

    Answer

    d. 30.

    Exercise \(\PageIndex{13}\)

    Solve the following to the correct number of significant figures:

    \(\frac{198.1}{12.1+198.1}\)

    a. 0.9424

    b. 0.942

    c. 0.94

    d. 0.9

    Answer

    a. 0.9424

    Exercise \(\PageIndex{14}\)

    Solve the following to the correct number of significant figures:

    \(\frac{12.1}{12.1+198.1}\)

    a. 0.05756

    b. 0.0575

    c. 0.0576

    d. 0.058

    Answer

    c. 0.0576

    Exercise \(\PageIndex{15}\)

    4.12 / 384 = 

    a. 0.0107

    b. 0.011

    c. 0.01

    d. 0.0

    Answer

    a. 0.0107

    Exercise \(\PageIndex{16}\)

    412 - 0.4 = 

    a. 411.6

    b. 412

    c. 410

    d. 400

    Answer

    b. 412

     

    Scientific Notation

    Exercise \(\PageIndex{23}\)

    Express 234.00 in scientific notation. 

    a. 2.34 x 102

    b. 234 x 102

    c. 2.34 x 104

    d. Can't be done

    Answer

    c. 2.34 x 104

    Exercise \(\PageIndex{24}\)

    Express 0.000100 in scientific notation. 

    a. 1.000 x 104

    b. 1.00 x 10-4

    c. 1.00 x 10-3

    d. Can't be done

    Answer

    b. 1.00 x 10-4

    Exercise \(\PageIndex{25}\)

    Express 200 to 2 significant figures.

    a. 2.0 x 103

    b. 2.0 x 102

    c. 2 x 102

    d. Can't be done

    Answer

    b. 2.0 x 102

    Exercise \(\PageIndex{26}\)

    Express 23470.34 in scientific notation. 

    a.  2.347034 x 104

    b. 2.347034 x 10-4

    c.  2.347034 x 106

    d. Can't be done

    Answer

    a.  2.347034 x 104

    Exercise \(\PageIndex{27}\)

    Express 0.0374600 in scientific notation. 

    a.  3.746 x 105

    b.  3.746000 x 10-3

    c.   3.74600 x 10-2

    d. Can't be done

    Answer

    && c.   3.74600 x 10-2

     

    Scientific Notation and Arithmetic Operations

    Exercise \(\PageIndex{1}\)

    5.548x10-6+6.165x10-4

    a. -6.220x10-4

    b. 6.220x10-4

    c. 6,220x10-5

    Answer

    b. 6.220x10-4

    Exercise \(\PageIndex{1}\)

    (65.68+45.08)x(58.26+37.9)

    a. 10700

    b. 10600

    c. 1070

    d. 1060

    Answer

    a. 10700

    Exercise \(\PageIndex{1}\)

    (0.0546-0.0265)+(1.629x10-3-5.688x10-4)

    a. 2.91x10-2

    b. 2.92x10-1

    c. 2.916x10-2

    d. 2.92x10-2

    Answer

    d. 2.92x10-2

    Exercise \(\PageIndex{1}\)

    (0.0546-0.0265)+(1.629x10-3-5.688x10-4)

    a. 2.91x10-2

    b. 2.92x10-1

    c. 2.916x10-2

    d. 2.92x10-2

    Answer

    d. 2.92x10-2

     

     

    Mathematics 

    Exercise \(\PageIndex{28}\)

    (44.5 + 12.1) X (116 - 104) = 

    a. 679.2

    b. 680

    c. 6.80 x 102

    d. 700

    Answer

    b. 680

    Exercise \(\PageIndex{29}\)

    (32.4 - 41) X (4.867 + 2.295) = 

    a. -61.5932

    b. -61.6

    c. -62

    d. -60

    Answer

    d. -60

    Exercise \(\PageIndex{30}\)

    (0.086 + 0.034) X (1.283 + 0.137) = 

    a. 0.1704

    b. 0.170

    c. 0.17

    d. 0.2

    Answer

    b. 0.170

    Exercise \(\PageIndex{31}\)

    (2 X 102) X (4 X 103) = 

    a. 8 X 105

    b. 8 X 104

    c. 8 X 106

    d. 8.0 X 105

    Answer

    a. 8 X 105

    Exercise \(\PageIndex{32}\)

    3.18 X 10-3 + 4.6 X 10-4

    a. 3.64 X 10-4

    b. 3.6 X 10-4

    c. 3.64 X 10-3

    d. 3.6 X 10-3

    Answer

    c. 3.64 X 10-3

    Exercise \(\PageIndex{32}\)

    8.4 X 10-8 + 3.2x10-3

    a. 11.6x10-8

    b. 8.4 X 10-8

    c. 3.2x10-3

    d. 3.200084x10-3

    Answer

    c. 3.2x10-3

    Exercise \(\PageIndex{33}\)

    Solve the following: 

    \(\frac{\left(6.0221367 \times 10^{23}\right)\left(6.62608 \times 10^{-34}\right)}{\left(2.99792458 \times 10^{8}\right)\left(9.6485309 \times 10^{4}\right)}\)

    a. 1.3795x10-23

    b. 1.3795x10-24

    c. 1.3795x10-25

    d. 1.3795x1023

    Answer

    a. 1.3795x10-23

     

    Percent

    Exercise \(\PageIndex{34}\)

    What is the mass percent water in a solution made by mixing 41.48 g salt with 972 g water?

    a. 0.95907%

    b. 95.91%

    c. 95.9%

    d. 4.09%

    Answer

    c. 95.9%

    Exercise \(\PageIndex{35}\)

    What is the mass percent salt in a solution made by mixing 41.48 g salt with 972 g water?

    a. .040928%

    b. 4.0928%

    c. 4.093%

    d. 4.09%

    Answer

    c. 4.093%

    Exercise \(\PageIndex{36}\)

    An ore sample is 1.67% gold. How much pure gold is in 23.4 g of the ore?

    a. 0.39078g

    b. 0.3908g

    c. 0.391g

    d. 0.398g

    Answer

    a. 0.39078g

    Exercise \(\PageIndex{37}\)

    Modern copper deposits tend to be low grade sulfide ores. What quantity of 0.874% copper ore is required to produce 1.00 lb of copper?

    a. 114.4 lb

    b. 97.4 lb

    c. 23.4 lb

    d. 114 lb

    Answer

    d. 114 lb

    Exercise \(\PageIndex{37}\)

    What mass of sulfur is released upon combustion of 50.0 lbs of low grade coal containing 12.4% sulfur?

    a. 6.2 lb

    b. 6.20 lb

    c. 3.4lb

    d. 3.40 lb

    Answer

    b. 6.20 lb

     

    Temperature Conversions 

    Exercise \(\PageIndex{1}\)

    Ethanol is the active ingredient in alcoholic beverages and boils at 173.3oF. What is its boiling point in degrees Celsius?

    a. 140 oC

    b. 67.3 oC

    c. 78.5 oC

    d. -78.5 oC

    Answer

    c. 78.5 oC

    Exercise \(\PageIndex{1}\)

    What is the boiling point of ethanol in degrees Kelvin, use result of question 1.

    a. -194.7 K

    b. 351.65 K

    c. 351.7 K

    d. 351 K

    Answer

    c. 351.7 K

    Exercise \(\PageIndex{1}\)

    0 K is called abolute zero and is the coldest temperature matter can theoretical reach. What is absolute zero in degrees Fahrenheit?

    a. 523 oF

    b. -523 oF

    c. -170 oF

    d. -460 oF

    Answer

    d. -460 oF

    Exercise \(\PageIndex{1}\)

    Acetic acid is the active ingredient in vinegar. Pure acetic acid is called glacial acetic acid because it is often frozen at room temperature. What is the freezing point of acetic acid in degrees Fahrenheit if it is 16.6oC?

    a. 57.9oF

    b. 61.9oF

    c. 32.0oF

    d. 88.6oF

    Answer

    b. 61.9oF

    Exercise \(\PageIndex{1}\)

    If you add salt to water you lower its freezing point. OoF is the lowest temperature liquid water can be lowered to by adding salt. What is this temperature in degrees Kelvin?

    a. 0 K

    b. 255 K

    c. 46 K

    d. 212 K

    Answer

    b. 255 K