Download CHEM 152 WORKSHOP On Measurement and Problem Solving

CHEM 152 WORKSHOP On Measurement and Problem Solving (Fremland)
Measurements have value, unit and uncertainty.
Value: the number
Unit: the dimension….meter, gram etc
Uncertainty: Expressed through significant figures: All measured values + 1 guess. Last sig. fig. is the
guess and its ± 1 in the decimal place with the guess.
Rules:
1. All nonzero digits are significant.
2. Zeroes between significant figures are significant.
3. Zeroes after a significant figure and after a decimal point are significant.
Calculations with Significant Figures
Bottom line is you only get 1 guess so cut off after first guess:


Addition and subtraction – see above rule. Line up decimals and not last sig fig.
Multiplication and division – to the least number of significant figures

If both Addition/Subtraction & Multiplication/Division - operations are performed and both rules are
applied at the end of the calculation. Keep track of sig. fig. at each step and round at the end.
Dimensional Analysis (Powerful!!)
Think of it like a map: This is where I am and this is where I’m going.
1.
2.
3.
4.
5.
Write units of answer
Figure out starting point.
Do make units of operation agree with units of answer.
Do same operation on numbers as you did on units.
Check. Does this answer make physical sense? Are the units correct?
Problems:
1. For each of the following, give the number of significant figures and the precision.
a. 11.5 3 ± 0.1
b. 1150 3 ± 10
c. 0.0115 3 ± 0.0001
d. 0.01150 4 ± 0.00001
e. 1.250 X 103 4 ± 1
2. Do the following calculations to the correct number of significant figures
a. 4.25 g + 4.100 g = 4.35g
b. 9.34g + 8.13g = 17.47
c. 17.59g/2.63mL = 6.69g/mL
d. (8.4 + 3.9) / (1.6 – 0.80) = 12.3 / 0.8 = 20
e. (3.05 X 105) + ( 4.2 X 107) = 4.2 X 107
3. Do the following conversions to the correct number of significant figures.
a. 41.8 g
=
kg
41.8g X 1 kg = 0.0418 kg
1000g
b. 0.055 μm
=
cm
0.055 μm X 1m
X 100 cm = 5.5 X 10-6 cm
6
10 μm
m
c. 24.6°C
= 297.8 K
d. 56.943 mm3
=
53.943 mm3 X
L
1 cm3 X
1L
=
1000mm3 1000 cm3
5.3943 X 10-5 L
4. More fun problems:
a. What volume of mercury (13.6g/mL) has a mass of 55.37g?
55.37g X
1 mL
13.6g
= 4.07mL
b. A 35.0 mL sample of ethyl alcohol (density = 0.789 g/mL) is added to a graduated cylinder that has a
mass of 49.28 g. What will be the mass of the cylinder plus the alcohol?
35.0 mL X
0.789 g
mL
= 27.6g; new mass = 49.28 + 27.6 = 79.9g
c. What is the mass of a copper (8.604g/mL) ball of radius 12.84mm? (V = 4/3 πr3)
V = 4/3 πr3 = (4/3)π(12.84mm)3 = 8867mm3 X 1 cm3 X 8.604g = 76.29g
1000mm3 cm3