1. 2.2 – Notes – Derived Units - Density

2. Derived units
1. Definition – unit defined by the combination of the base units
a. Volume - cm X cm X cm = cm3; the cm is a base unit so cm3 is considered a derived unit ;
b. Density – mass/volume = g/mL or g/cm3; D = m/v;
equation can be transposed to solve for m or v;
volume can be measured in mL if it is a liquid;
is a proportion of mass to volume so two objects with different masses and volumes could have the same density;
solids and liquids have unit g/mL while gases uses g/L (lighter mass so need a lot more of it to be measurable!)

4. Sample problems:
A piece of metal with a mass of 147 g is placed in a 50-mL graduated cylinder. The water level rises from 20.0 mL to 41.0 mL. What is the density of the metal?
D = m/v = 147g/( ) = 147/20.0 = 7.00g/mL
What is the volume of a sample that has a mass of 20.0 g and a density of 4.0 g/mL?
D = m/v  v = m/D = 20.0/4.0 = 5.0mL

5. Temperature
Temperature – measure of how hot or cold an object is relative to other objects;
after a cold winter spell, a day of 40° feels like a heat wave whereas in the fall after feeling hot days, 40° feels very cold; measure of the potential to transfer heat

6. Temperature scales
a. The Celsius temperature scale (°C) is defined on a couple of the properties of water. In degrees Celsius, give the
Freezing point of water: 0°C (= 273 K = 32°F)
Boiling point of water: 100°C (= 373 K = 212°F)
Used to be referred to as the centigrade scale with centi meaning 100

7. Temperature scales
b. Kelvin: The Kelvin scale has the same size degree as the Celsius scale, but starts at 0 degrees. Thus, it has no negative values. Gets difficult to do gas law problems with (-) numbers, result is use this scale; does not require °K, can be written as K, but with zero degrees it looks like OK
Absolute Zero- temperature at which all motion stops;
0°K = °C = °F

8. Temperature scales
c. Fahrenheit: English temperature scale; not used in chemistry; parallels a 4th temperature scale – Rankin; R = °F ; will make all Fahrenheit temperatures (+)
*Rankin scale- has absolute zero as 0, but 1 degree is equal to 1 degree F.

9. Equations
2. Equations- 0°C = 32°F; which one has smaller degrees? °C is divided
into 100 equal parts while °F is spread over 180 equal parts (32 to 212)
therefore °F must be smaller;
°K = °C °F = 1.8 X °C +32
(100 : 180 = 1.8 ratio)
°C = °K °C = (°F – 32)/1.8 OR
= 5/9 (°F – 32)
Can not go from °F to °K, must go to °C first!

10. Sample Problems: Significant Figures are NOT important with temperature; use the whole number
The boiling point of liquid nitrogen is -196°C. What would this be in °F and °K?
°K = °C = = 77°K
°F = 1.8 X °C +32 = 1.8(-196) + 32 = -320.°F

11. . Normal body temperature is 98.6°F. Convert this to °C and °K.
°C = (°F – 32)/1.8 = (98.6 – 32) /1.8 = 37.0°C
°K = °C = = 310.0°K

12. 3. Room temperature is 298°K. What would this be in °C? °F?
°C = °K – 273 = 298 – 273 = 25°C
°F = 1.8 X °C +32 = 1.8(25) + 32 = 77°F