# 1B: Review of the Tools of Quantitative Chemistry

## SI Prefixes

Exercise $$\PageIndex{1}$$

The Si prefix for 106 is:

a. micro

b. milli

c. kilo

d. mega

d. mega

Exercise $$\PageIndex{1}$$

The Si prefix for 10-6 is:

a. nano

b. micro

c. milli

d. pico

b. micro

Exercise $$\PageIndex{1}$$

The Si prefix for 109 is:

a. mega

b. giga

c. kilo

d. deca

b. giga

Exercise $$\PageIndex{1}$$

The Si prefix for 10-1 is:

a. mili

b. centi

c. deci

d. micro

c. deci

Exercise $$\PageIndex{1}$$

The Si prefix for 10-12 is:

a. nano

b. fempto

c. pico

d. micro

c. pico

Exercise $$\PageIndex{1}$$

The Si prefix for 10-9 is:

a. nano

b. pico

c. fempto

d. micro

a. nano

Exercise $$\PageIndex{1}$$

The Si prefix for 101 is:

a. deci

b. mili

c. deca

d. kilo

c. deca

Exercise $$\PageIndex{1}$$

The Si prefix for 103 is:

a. mega

b. giga

c. kilo

d. deca

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

&&

!

!

Exercise $$\PageIndex{1}$$

7.6x105 nL=?Micro L

a. 7.6

b. 7.6x106

c. 7.6x102

d. 7.6x107

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

a. 3.4

!

!

Exercise $$\PageIndex{1}$$

5.4x10-11Gg = ? mg

a. 5.4

b. 54

c. 5.4x103

d. 5.4x108

&&

!

!

Exercise $$\PageIndex{1}$$

2.8x1012fm = ?km

a. 2.8

b. 2.8x106

c. 2.8x10-6

d. 2.8x102

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

d. 3

Exercise $$\PageIndex{18}$$

How many significant figures are in 20400 g?

a. 5

b. 4

c. 3

d. 2

c. 3

Exercise $$\PageIndex{19}$$

How many significant figures are in 20103 ml?

a. 5

b. 4

c. 3

d. 2

a. 5

Exercise $$\PageIndex{20}$$

How many significant figures are in 100 students?

a. 3

b. 2

c. 1

d. unknown

a. 3

Exercise $$\PageIndex{21}$$

How many significant figures are in 0.00001 miles?

a. 5

b. 3

c. 2

d. 1

d. 1

Exercise $$\PageIndex{22}$$

How many significant figures are in 2.00 x 104?

a. 4

b. 3

c. 2

d. 1

b. 3

## Algebra Review

Exercise $$\PageIndex{1}$$

Solve the following problem for $$P$$: $$$$P V=n R T$$$$

a. $$$$n R T + V$$$$

b. $$$$n R T - V$$$$

c. $$$$V (n R T)$$$$

d. $$$$\frac{n R T}{V}$$$$

d. $$$$\frac{n R T}{V}$$$$

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. $$T = P V -n R$$

b. $$$$\mathrm{T}=\frac{\mathrm{PV}}{\mathrm{nR}}$$$$

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

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. $$T_{f}=T_{i}+\frac{q}{m c}$$

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

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

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

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

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

c. 15.0

Exercise $$\PageIndex{10}$$

98.3 - 89.4 =

a. 8.90

b. 9

c. 8.9

d. 9.00

c. 8.9

Exercise $$\PageIndex{11}$$

82.0 + 34.4 =

a. 116.4

b. 116

c. 117

d. 120

a. 116.4

Exercise $$\PageIndex{12}$$

12.56 x 2.4 =

a. 30.144

b. 30.14

c. 30.1

d. 30.

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

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

c. 0.0576

Exercise $$\PageIndex{15}$$

4.12 / 384 =

a. 0.0107

b. 0.011

c. 0.01

d. 0.0

a. 0.0107

Exercise $$\PageIndex{16}$$

412 - 0.4 =

a. 411.6

b. 412

c. 410

d. 400

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

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

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

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

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

&& 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

b. 6.220x10-4

Exercise $$\PageIndex{1}$$

(65.68+45.08)x(58.26+37.9)

a. 10700

b. 10600

c. 1070

d. 1060

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

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

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

b. 680

Exercise $$\PageIndex{29}$$

(32.4 - 41) X (4.867 + 2.295) =

a. -61.5932

b. -61.6

c. -62

d. -60

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

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

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

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

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

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%

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%

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

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

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

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

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

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

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

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