Chemistry - Measurements

[Concept] What is a measurement?

A numerical description of a quantity, recorded with a unit and the precision allowed by the measuring device.

[Rule] What metric base units are emphasized in the slides?

Length: meter (m); mass: gram (g); volume: liter (L); time: second (s); temperature: degrees Celsius (°C).

[Concept] Mass versus weight

Mass is the amount of matter; weight is the force of gravity on that matter. Mass remains even when gravity changes.

[Rule] Metric prefixes to memorize

micro (u) = 10^-6; milli (m) = 10^-3; centi (c) = 10^-2; deci (d) = 10^-1; kilo (k) = 10^3; mega (M) = 10^6.

[Rule] Common metric relationships

1 km = 1000 m; 1 m = 100 cm = 1000 mm; 1 kg = 1000 g; 1 g = 1000 mg; 1 L = 1000 mL; 1 mL = 1 cm^3.

[Concept] Exact versus inexact numbers

Exact numbers come from counting or definitions and have no uncertainty; measured numbers are inexact and contain uncertainty.

[Practice] Is “12 students” exact or inexact?

Exact, if the students were counted.

[Practice] Is “12.0 mL” exact or inexact?

Inexact because it is a measurement.

[Rule] How many estimated digits belong in a measurement?

Exactly one estimated digit, always the final recorded digit.

[Concept] What are significant figures?

All certain digits in a measurement plus its one estimated digit.

[Rule] Significant-figure rules

Nonzero digits are significant; zeros between nonzero digits are significant; leading zeros are not; trailing zeros are significant only when a decimal point shows they were measured.

[Practice] How many significant figures are in 0.00450?

3 significant figures.

[Practice] How many significant figures are in 1007?

4 significant figures.

[Practice] How many significant figures are in 72.00?

4 significant figures.

[Practice] How many significant figures are clearly shown in 2500 with no decimal point?

Usually 2; write scientific notation to remove ambiguity.

[Practice] Write 2500 with three significant figures.

2.50 x 10^3.

[Rule] Basic rounding rule

If the first removed digit is 0-4, leave the previous digit unchanged; if it is 5-9, increase the previous digit by 1.

[Practice] Round 7.8462 to three significant figures.

7.85.

[Practice] Round 38,649 to three significant figures.

38,600, or 3.86 x 10^4.

[Rule] Multiplication and division with significant figures

Round the answer to the same number of significant figures as the measured value with the fewest significant figures.

[Rule] Addition and subtraction with significant figures

Round the answer to the same decimal place as the least precise measured value.

[Practice] 4.35677 x 0.0064

0.028; the limiting value has 2 significant figures.

[Practice] 5.352 + 1.6

7.0; the answer must be rounded to the tenths place.

[Practice] 18.2 / 3.15

5.78; both values allow 3 significant figures.

[Practice] 12.11 + 0.3 + 4.567

17.0; the least precise term is in the tenths place.

[Rule] When should you round in a multistep calculation?

Keep extra digits through intermediate steps and round only the final answer.

[Practice] Evaluate (106.91 x 0.5184) + (108.90 x 0.4816).

107.87 after completing both products, adding, and rounding at the end.

[Practice] Evaluate [(0.9832 - 0.9673) / 0.9832] x 100%.

1.62% after applying subtraction precision first and rounding at the end.

[Concept] What is scientific notation?

A number written as A x 10^n, where 1 <= A < 10 and n is an integer.

[Rule] Choosing the exponent in scientific notation

Moving the decimal left gives a positive exponent; moving it right gives a negative exponent.

[Practice] Write 602200000000000000000000 in scientific notation.

6.022 x 10^23.

[Practice] Write 0.000000000300 in scientific notation.

3.00 x 10^-10.

[Practice] Convert 4.56 x 10^4 to ordinary notation.

45,600.

[Practice] Convert 0.000720 to scientific notation.

7.20 x 10^-4.

[Rule] What is a conversion factor?

A ratio made from equivalent quantities; it equals 1 and changes units without changing the physical amount.

[Rule] Dimensional-analysis setup

Arrange conversion factors so unwanted units cancel and the wanted unit remains.

[Trap] What is the fastest way to catch many conversion mistakes?

Check that the units cancel correctly before calculating.

[Practice] Convert 24 nm to meters.

24 nm x (10^-9 m / 1 nm) = 2.4 x 10^-8 m.

[Practice] Convert 0.250 L to gallons using 1 L = 0.265 gal.

0.250 L x 0.265 gal/L = 0.0663 gal.

[Practice] Convert 192 cm to feet using 2.54 cm = 1 in and 12 in = 1 ft.

192 cm x (1 in/2.54 cm) x (1 ft/12 in) = 6.30 ft.

[Practice] Convert 3.50 km to meters.

3.50 x 10^3 m.

[Practice] Convert 640 mg to grams.

0.640 g.

[Rule] Celsius-Kelvin conversions used in the slides

K = °C + 273; °C = K - 273.

[Rule] Celsius-Fahrenheit conversions

°F = (9/5)(°C) + 32; °C = (5/9)(°F - 32).

[Practice] Convert 25 °C to kelvins.

298 K.

[Practice] Convert 310 K to degrees Celsius.

37 °C.

[Practice] Convert 425 °F to degrees Celsius.

About 218 °C.

[Practice] Convert 425 °F to kelvins.

About 491 K after converting to Celsius and adding 273.

[Concept] What is density?

The ratio of mass to volume: d = m/V, commonly in g/mL or g/cm^3.

[Rule] Density equation rearrangements

d = m/V; m = dV; V = m/d.

[Rule] Floating and sinking

An object floats if it is less dense than the liquid and sinks if it is more dense.

[Practice] Find the density of an 18.29 g metal sample with a volume of 7.50 mL.

d = 18.29/7.50 = 2.44 g/mL.

[Practice] Find the mass of 60.0 mL of a liquid with density 1.42 g/mL.

m = 1.42 x 60.0 = 85.2 g.

[Practice] A metal has mass 63.5 g and density 8.96 g/cm^3. Find its volume.

V = 63.5/8.96 = 7.09 cm^3.

[Trap] What two mistakes are common in density problems?

Using the wrong rearrangement and forgetting that the mass and volume units must match the density units.