1B: Review of the Tools of Quantitative Chemistry

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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 173.3^oF. 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 16.6^oC?

a. 57.9^oF

b. 61.9^oF

c. 32.0^oF

d. 88.6^oF

Answer: b. 61.9^oF

Exercise \(\PageIndex{1}\)

If you add salt to water you lower its freezing point. O^oF 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