Transcript Chemistry by the numbers

Chemistry by the numbers
Units of Measurement – The Metric System
meter(m)
•
Length:
•
Mass:
•
Volume:
•
Temperature:
•
Pressure:
Kilo0.001
gram(g)
liter(L)
Celsius(ºC)
atmosphere(atm)
Hecta- Deka0.01
0.1
Base
1
Deci10
Centi100
Milli1000
Chemistry by the numbers
Conversions
●
How do you convert 100 grams into kilograms?
●
Use dimensional analysis (aka Unit Factor Method)
●
Multiply the value by its conversion factor
●
●
Kilo- means 1000 of something (in this case, grams)
Therefore, the conversion factor is 1000 grams = 1 kilogram
The unit we want!
100 grams x 1 kilogram = 0.1 kilograms
1000 grams
We know 1000grams = 1kilogram, but why use a fraction? Why is
kilogram on the top?
The fraction makes the math easy. We can cancel out the ‘grams’ unit
like it was a variable.
The kilogram unit goes on the top because it is the unit we want.
100 grams x 1000 grams
??? Can’t cancel out the units!
1 kilogram
Chemistry by the numbers
Conversions
●
Convert the following
●
1.5 Liters to kiloLiters
●
20,000 micrograms to grams
●
1950 centimeters to meters
●
1.501 kg to grams
●
0.009 L to mL
Chemistry by the numbers
Scientific Notation
●
What is the mass of an electron?
0.000,000,000,000,000,000,000,000,000,000,911 kg
●
What is the distance between our sun and Pluto?
5,913,520,000,000 m
●
Is there a better way to write these numbers?
YES!
Chemistry by the numbers
Scientific Notation
First, locate the first significant digit
●
Move this decimal...
...to just after the first
significant digit
●
Then count the places the decimal moved...
Chemistry by the numbers
Scientific Notation
Your new number is then written times 10
●
to the number of places you moved the decimal
kg
The number is negative because the original
number is a decimal
●
So try it with the other number:
5,913,520,000,000 m →
Accuracy vs. Precision
• Chemistry involves making measurements with tools
•
Accuracy - measurements that are close to the true value.
• Which tool is more accurate to measure the width of a
penny; a meter stick or a caliper?
• Precision - measurements that are consistent.
Measurements are the same or close to the same every
time you measure.
• No tool is 100% accurate.
• Tools can be precise.
Percent Error
• How good are your measurements?
•
Percent error: formula used to determine how close(or
how far) the experimental value is to the accepted value.
•
% error = |accepted value – experimental value| x 100
accepted value
• Experimental value = the measurement or calculation you
made in the experiment
• Accepted value = the measurement that is accepted by the
scientific community as true and exact.
% Error Calculations
●
●
A student measures the mass and volume of a block of
iron and calculates its density as 8.50 g/cm3. The accepted
value is 7.86 g/cm3. What is the % error?
% error = |7.86 g/cm3 - 8.50 g/cm3| x 100
7.86 g/cm3
% error = 8.14%
A chemical reaction produced a solid with a mass of 0.455
grams. However, the expected amount was supposed to be
1.000 grams. What is the percent error for this experiment?
% error = |1.000g - .455 g/cm3| x 100
1.000g
% error = 54.5%
Significant Figures
●
2 kinds of numbers:
●
Exact: The precise amount.
– (ie Money in your pocket)
– Approximate: Anything MEASURED.
– No measurement is perfect
Scientists only use numbers that are reliable.
–
Example:
Mass of a coin on a triple-beam balance is 2.7g
Mass of the same coin on a digital scale is 2.700g
●
Are they the same number?
●
●
To a mathematician, yes.
To a scientist, No!
When to use Significant figures
●
●
2.700g to a scientist means the measurement
is accurate to within one thousandth of a
gram, but the measurement of 2.7g is only
accurate to the 10th of a gram.
The more accurate a measurement is, the
greater the number of significant numbers.
Determining Significant Figures
●
●
Rule 1: All numbers are significant starting
with the first non-zero digit on the left.
1st Exception: In whole numbers that end
in zero, the zeros at the end are not
significant.
???
Has 4 sig figs
Has 3 sig figs
Has 1 sig fig
How many sig figs?






7
40
0.5
0.00003
7 x 105
7,000,000






1
1
1
1
1
1
How do I know how many?






2nd Exception: Any zeroes between two
non-zero numbers are significant.
2002 sec
Has 4 sig figs
3rd Exception: Zeroes to the right of a
decimal are significant.
Has 6 sig figs
11.4000kg
4th Exception: decimal points make all
zeroes to the left significant.
Has 5 sig figs
90100. m
How do I know how many?
Sig Figs & Scientific Notation
Count all the numbers before the x10
9.3x10²cm =
2
4.1000x10³³kg =
5
How many sig figs?






1.2
2100
56.76
4.00
0.0792
7,083,000,000






2
2
4
3
3
4
How many sig figs?
3401
2100
2100.0
5.00
0.00412
8,000,050,000.
4
2
5
3
3
10
Sig Fig Calculations
When Adding or subtracting measurements
– Answer will have the same decimal place
as the least accurate number
–Ex: 2.45 cm + 1.2cm = 3.65cm?  3.7cm
– 1.2cm is least accurate so… round to the
one decimal
7.432L + 2L = 9.432L round to 9L
Sample Problems
123.0cm – 99.82cm =
2100.mL + 101mL =
88.772g – 17.1g =
24.00cm – 18cm =
7234.1m + 1000.0m =
708g – 8.4g =
23.2cm
2201mL
71.7g
6cm
8234.1m
700.g
Sig Fig Calculations
●
Multiplying or dividing, significant figures
Answer will have the same sig. figs as the
least reliable measurement.
56.780cm x 2.45cm = 139.111 cm2
5 sig figs
3 sig figs
Round to 3 sig figs...
139.111 cm2 → 139 cm2
If two numbers have the same reliability, use the least
amount of sig figs.
12.00km x 1.01km = 12.12km2
→ 12.1km2
Sample Problems






1.0cm x 4cm =
4.00cm x 18cm =
7234.1m ÷ 100.0sec =
708g ÷ 8.1L =
298.01kg + 34.112kg =
84m/s x 31.221s =






4cm²
72cm²
72.34m/sec
87.4g/L
332.12kg
2600 m