الجمعة، 21 مارس 2014

Chapter 1



Definitions :


Chemistry  : the study of matter and changes that it undergoes .
Matter : anything that has a mass and occupies space .
Hypothesis : an educated guess based on comprehensive observations .
scientific law : concise verbal or mathematical statement of a reliable relationship between phenomena .
Theory : a set of conceptual assumptions that explains data from accumulated experiments , called " Model ".

Classifications of matter

Substance : a form of matter that has a defined composition and distinct properties .
Condensed phase : solids and liquids to which they are collectively referred .
Fluids : gases and liquids to which they are collectively referred .
Elements : a substance that cannot be separated into smaller substances by chemical means .
Compounds : a substance composed of two or more elements , chemically united into fixed properties .
Homogeneous mixture : a mixture or two or more substances in which the compositions are uniformly distributed throughout .
Heterogeneous mixture : a mixture of tow or more substances in which the compositions are not uniformly distributed throughout .
Quantitative  properties : properties that can be determined by measurement .
Qualitative properties : properties than cannot be determined by measurement .
Weight : the force exerted by an object due to gravity .
Mass : a measure of the amount in an object .
Physical property : a property that can be measured without changing the identity of the substance .
Chemical property : a property than cannot be measured without changing the identity of the substance .
Extensive property : a property that depends on the amount of matter .
Intensive property : a property than doesn't depend on the amount of matter .
Significant figure : the meaningful digits in a reported number .
Accuracy : a way tells how close a measurement to the right true value
Precision : a way tells how multiples measurements are close to one another .
Conversion factor : a fraction in which the same quantity is expressed one way in the numerator and the other way in the denominator .
Dimension analysis : the use of conversion factor in problem solving .

Equations :

$$K= C+273.15   or K=C+273$$

$$C=(F-32) \times \frac{5}{9}$$

$$F= ( \frac{9}{5} \times C ) + 32$$

$$D=\frac{M}{V}$$ where D is the density and M , V are ,respectively,  the mass and volume

Notes :

guidelines for using significant figures :
1.  Any digit that is not zero is significant. 
2. Zeros between nonzero digits are significant. 
3. Zeros to the left of the first nonzero digit are not significant. Their purpose is to 
indicate the placement of the decimal point. 
4. For numbers that do not contain decimal points, the trailing zeros (that is, zeros 
after the last nonzero digit) may or may not be significant.

Calculation with significant figures
1. In addition and subtraction , the answer cannot have more digits to the right of the original number with the smallest number of digits to the right of the decimal number .

2. In multiplication and division , the number of digits of the answer is determined by the smallest number of significant figure of the tow multiples or dividend numbers .

Questions :

1. Bromine is a reddish-brown liquid. Calculate its density (in g/mL) if 586 g of the substance occupies 188 mL.


 $$D=\frac{M}{V}$$

Therefore :

$$M = 586 g$$
$$V=188 mL$$

Then $$D=\frac{586}{188} = 3.117 g/mL$$

2.The density of ethanol, a colorless liquid that is commonly known as grain alcohol, is 0.798 g/mL. Calculate the mass of 17.4 mL of the liquid.
$$M=D.V$$
$$D=0.798g/mL$$
$$V=17.4 mL$$
Then :
$$ M=0.798x17.4=13.89g $$

3.Convert the following temperatures to degrees Celsius or Fahrenheit: (a) 95°F, the temperature on a hot summer day; (b) 12°F, the temperature on a cold winter day; (c) a 102°F fever; (d) a furnace operating at 1852°F; (e) –273.15°C (theoretically the lowest attainable temperature).

a)
$$ C=(F-32)x\times\frac{5}{9} $$

$$ C=(95-32)\times\frac{5}{9}$$

$$ C=35 $$

b)
 $$ C=(F-32)\times\frac{5}{9} $$

$$ C=(12-32)\times\frac{5}{9} $$

$$C=-11.11$$

4.The density of water at 40°C is 0.992 g/mL. What is the volume of 2.50 g of water at this temperature?

$$V=\frac{M}{D}$$

$$M=2.50$$

$$D=0.992g/mL$$

Therefore :

$$V=\frac{2.50}{0.992}=2.52mL$$

5.Classify the following as qualitative or quantitative statements, giving your reasons. (a) The sun is approximately 93 million mi from Earth. (b) Leonardo da Vinci was a better painter than Michelangelo. (c) Ice is less dense than water. (d) Butter tastes better than margarine. (e) A stitch in time saves nine.

a) It is a quantitative statement because it uses a measurement 
b) It is a qualitative statement because it doesn't use a measurement 
c) It is a qualitative statement because it doesn't use a measurement
d) It is a quantitative statement because it uses a measurement 
e) it is  a qualitative statement because it doesn't use a measurement 

6.Determine whether the following statements describe chemical or physical properties: (a) Oxygen gas supports combustion. (b) Fertilizers help to increase agricultural production. (c) Water boils below 100°C on top of a mountain. (d) Lead is denser than aluminum. (e) Uranium is a radioactive element.

Remembering that physical properties involve no change in the chemical composition of materials while chemical properties do involve chemical change .
a) Chemical property "something burns in oxygen to create an oxide"
b) Chemical property 'The biochemical processes of plants are chemical "
c) Physical property "Still is water, just the boiling point is reduced at reduced pressure"
d) Physical property "Density is a physical property"
e) Chemical property "Radioactivity involves changes in the composition of the materials"

7.
Determine whether each of the following describes a physical change or a chemical change: (a) The helium gas inside a balloon tends to leak out after a few hours. (b) A flashlight beam slowly gets dimmer and finally goes out. (c) Frozen orange juice is reconstituted by adding water to it. (d) The growth of plants depends on the sun's energy in a process called photosynthesis. (e) A spoonful of salt dissolves in a bowl of soup.

a) Physical property
b) Chemical property
c) Physical property
d) Chemical property
c) Physical property

8.Express the following numbers in scientific notation: (a) 0.000000027, (b) 356, (c) 47,764, (d) 0.096.

a) $$ 2.7\times10^{-8}$$

b) $$ 3.56 \times10^2$$

c) $$ 4.7764 \times10^1$$

d) $$ 9.6  \times10^{-2}$$

9.Determine the number of significant figures in each of the following measurements: (a) 4867 mi, (b) 56 mL, (c) 60,104 tons, (d) 2900 g, (e) 40.2 g/cm3, (f) 0.0000003 cm, (g) 0.7 min, (h) 4.6 × 1019 atoms.\

a) 4
b) 2
c) 5
d) 2 or 3 or 4
e) 3
f) 1
g) 1
h) 2

10. Three students (A, B, and C) are asked to determine the volume of a sample of ethanol. Each student measures the volume three times with a graduated cylinder. The results in milliliters are: A (87.1, 88.2, 87.6); B (86.9, 87.1, 87.2); C (87.6, 87.8, 87.9). The true volume is 87.0 mL. Comment on the precision and the accuracy of each student's results.

The first student's "A" results are not precious not accurate .
The second student's "B" results are precious and accurate .
The third student's "C" results are precious but they are accurate 

11. The average speed of helium at 25°C is 1255 m/s. Convert this speed to miles per hour (mph).

$$1255m/s\, . \frac{1mile}{1609m} . \frac{3600s}{1h}\,=2.807\times10^{3}$$

12.A slow jogger runs a mile in 13 min. Calculate the speed in (a) in/s, (b) m/min, (c) km/h (1 mi = 1609 m; 1 in = 2.54 cm).

a) $$\frac{1}{13} mi/min.\,\frac{1609m}{1mi} . \frac{2.54in}{1m} . \frac{1min}{60s}=5.24 in/s$$

b) $$\frac{1}{13} mi/min . \,\frac{1609m}{mi}=123.77m/min$$
c) $$\frac{1}{13} mi/min . \,\frac{1.609km}{1mi} .\frac{3600s}{1h}=445.57km/h$$

13. A 6.0-ft person weighs 168 lb. Express this person's height in meters and weight in kilograms (1 lb = 453.6 g; 1 m = 3.28 ft).

$$ Hight : 6ft\, .\frac{1m}{3.28ft}=1.83m$$
$$ Weight : 168Ib\, .\frac{453.6g}{1Ib}\, . \frac{1kg}{1000}=76.20kg$$

14. The average time it takes for a molecule to diffuse a distance of x cm is given by
where t is the time in seconds and D is the diffusion coefficient. Given that the diffusion coefficient of glucose is 5.7 × 10−7 cm2/s, calculate the time it would take for a glucose molecule to diffuse 10 µ m, which is roughly the size of a cell.

$$t=\frac{x^2}{2d}\rightarrow t=\frac{(10\times10^{-4})^2}{2\times5.7\times10^{-7}}=\frac{1}{11400}=0.877s$$

15.(a) Carbon monoxide (CO) is a poisonous gas because it binds very strongly to the oxygen carrier hemoglobin in blood. A concentration of 8.00 × 102 ppm by volume of carbon monoxide is considered lethal to humans. Calculate the volume in liters occupied by carbon monoxide in a room that measures 17.6 m long, 8.80 m wide, and 2.64 m high at this concentration. (b) Prolonged exposure to mercury (Hg) vapor can cause neurological disorder and respiratory problems. For safe air quality control, the concentration of mercury vapor must be under 0.050 mg/m3. Convert this number to g/L. (c) The general test for type II diabetes is that the blood sugar (glucose) level should be below 120 mg per deciliter (mg/dL). Convert this number to micrograms per milliliter (μg/mL).

a) start by converting the room dimensions to L

$$17.6 long\, \times 8.80 wide\, \times 2.64 high\, \frac{(10)^3}{1m^3}=4.089\times10^{5}$$

'ppm' means part per million part .

then :

$$\frac{8.00\times 10^2}{1.00\times10^6}=8\times10^{-4}$$

multiplying this percent by volume of the carbon monoxide into the volume of the room

$$4.089\times 10^{5} \times 8\times 10^{-4}=327.12\, L$$

b) 
$$0.05mg/m^3 \, \frac{1g}{1000mg} \, \times{1m}{10^3L}=5\times10^{-8}$$

c)
$$120mg/dL\,\times \frac{10^{3}\mu g}{1mg}\,\times\frac{10dL}{1L}\,\times\frac{1L}{1000ml}=1200\mu /mL$$


16.A piece of metal with a mass of 13.2 g was dropped into a graduated cylinder containing 17.00 mL of water. The graduated cylinder after the addition of the metal is shown. Determine the density of the metal to the appropriate number of significant figures.





$$D=\frac{M}{V}\,\rightarrow$$
$$M=13.2g$$
$$V=18.5-17.0=1.5mL$$
$$D=\frac{13.2}{1.5}\,=8.8g/mL$$

17.Which of the following statements describe physical properties and which describe chemical properties? (a) Iron has a tendency to rust. (b) Rainwater in industrialized regions tends to be acidic. (c) Hemoglobin molecules have a red color. (d) When a glass of water is left out in the sun, the water gradually disappears. (e) Carbon dioxide in air is converted to more complex molecules by plants during photosynthesis.

a) Chemical property
b) Chemical property
c) Physical property
d) Physical property
e) Chemical property

18. In determining the density of a rectangular metal bar, a student made the following measurements: length, 8.53 cm; width, 2.4 cm; height, 1.0 cm; mass, 52.7064 g. Calculate the density of the metal to the correct number of significant figures.

$$D=\frac{M}{V}\rightarrow M=52.7064 \, V=(8.53\times2.4\times1)cm^3\,\rightarrow\,D=\frac{52.7064}{20.472}\,=\,2.575g/cm^3$$

19.Calculate the mass of each of the following: (a) a sphere of gold with a radius of 10.0 cm (volume of a sphere with a radius r is $$V= \frac{4}{3} \times \Pi r^3$$ density of gold = 19.3 g/cm3), (b) a cube of platinum of edge length 0.040 mm (density = 21.4 g/cm3), (c) 50.0 mL of ethanol (density = 0.798 g/mL)

a) $$M=D\times V \rightarrow D=19.3g/cm^3\,V=(\frac{4}{3}\times\Pi\times10^3) \rightarrow M=19.3\times 418.88=8\times 10^4$$

b) $$M=D\times V $$
$$ D=21.4g/cm^3 \, V= (0.0040)^3$$
$$M=21.4 \times 6.4 \times 10^{-8}\,=1.4\times10^{-6}$$

c) $$M=D\times V \rightarrow D=0.798g/mL \, V= 50.0mL$$
$$M=0.399 g$$

20.A cylindrical glass tube 12.7 cm in length is filled with mercury (density = 13.6 g/mL). The mass of mercury needed to fill the tube is 105.5 g. Calculate the inner diameter of the tube (volume of a cylinder of radius r and length h is V = πr2h).

$$V=\frac{M}{D}$$
$$M=105,5 \, , D=13.6g/mL \,,, V= \Pi\times r^2 \times h$$
$$\Pi \times r^2 \times 12.7 =  \frac{105.5}{13,6} \rightarrow \, r= \sqrt{35.96} \rightarrow r= 5,99 \approx 6$$

21.A piece of silver (Ag) metal weighing 194.3 g is placed in a graduated cylinder containing 242.0 mL of water. The volume of water now reads 260.5 mL. From these data calculate the density of silver
$$D=\frac{M}{V}$$
$$M=194.3g \, V=(260.5-242.0) mL =18.5mL$$
$$D=\frac{194.3}{18.5mL}=10.5g/mL$$

22.At what temperature does the numerical reading on a Celsius thermometer equal that on a Fahrenheit thermometer?

$$C=(F-32)\times \frac{5}{9}$$

substituting F by C

$$C=(C-32) \times {5}{9}$$

$$\frac{9}{5}C - C= -32$$

By solving this equation for C :

$$C=F=-40$$

23.Suppose that a new temperature scale has been devised on which the melting point of ethanol (–117.3°C) and the boiling point of ethanol (78.3°C) are taken as 0°S and 100°S, respectively, where S is the symbol for the new temperature scale. Derive an equation relating a reading on this scale to a reading on the Celsius scale. What would this thermometer read at 25°C?

To solve this problem a value of A and B in the following equation should be  found

$$C=A\times S -117.3 C$$

The value of A :

$$\frac{78.3-(-117.3)}{100}=\frac{489}{250}$$

Then The Conversion Equation is

$$C=\frac{489}{250} S - 117.3 C$$

$$S=(C+117.3) \times \frac{250}{489}$$

24.The total volume of seawater is $$1.5 × 10^{21}L$$ Assume that seawater contains 3.1 percent sodium chloride by mass and that its density is 1.03 g/mL. Calculate the total mass of sodium chloride in kilograms and in tons (1 ton = 2000 lb; 1 lb = 453.6 g)

$$M=D \times V$$

$$D=1.03g/mL \times \frac{1kg}{1000g} \times \frac{1000mL}{1L}=1.03Kg/L$$
$$V=1.5\times 10^{21} \times \frac{3.1}{100}=4.65\times 10^{19}$$
$$M=1.03 \times 4.65=4.79\times10^{19}Kg\, or \, 4.79\times10^{16} ton$$

25.If we mix sand with iron filings (powder) in equal amount the mixture is :

[heterogeneous mixture]


26.Typically, room temperature and human body temperature are 25 C 37 C respectively . Find the temperature difference in degree Fahrenheit

$$F=\frac{9}{5}C+32$$

$$F=( \frac{9}{5}\times 25)+32=77F$$

$$F=( \frac{9}{5}\times 37)+32=98.6F$$

$$Then\,the\, difference \,is 98.6-77=21.6 \approx \,22$$

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