Measurement in Chemistry (and elsewhere)

Types of observations

QualitativeProperties that can be observed and described that do not involve measurement. If they do refer to quantities, they are vague (ie fast, hot, large etc…)

QuantitativeProperties that can be observed and described numerically and which result from measurement.

Commonly measured values in chemistry

Mass (grams) Volume (liters) Length (meters) Temperature (degrees Celsius or

degrees Kelvin) Time (seconds) Pressure (atmospheres) Concentration (percent, molar)

Length, Mass and Volume

Length - distance between two points

Mass - amount of matter in an object

(weight is dependent upon the force of

gravity on the object)

Volume - the amount of space an object occupies

Length, Mass and Volume

Fig 2.2

Volume is derived from length

Some units of measurement

Metric Base Unit SI Unit

Length meter (m) meter

Mass gram (g) kilogram (kg)

Volume liter (L) meter3

TemperatureCelsius (C) Kelvin (K)

Common metric prefixes

Table 2.1Table 2.1

Common metric prefixes

1000 base / 1 kilo 1000 g / 1 kilogram 1 x 103

100 centi / 1 base 100 centimeters/ 1 meter 1 x 102

1000 milli / 1 base 1000 millimeters/ 1 meter 1 x 103

1,000,000 micro / 1 base 1,000,000 micrometers/1 meter 1 x 106

Converting between units(Dimensional analysis – factor label method)

Given unit x (Desired unit) = Desired unit (Given unit)

12.4 kg x (1000 g) = 12,400 g (1kg)

1265 mm x (1 m) = 1.265 m (1 x 103 mm)

Exact and inexact numbers

Exact numbers No uncertainty to their value Value is known exactlyDefinedConversions within a systems

Inexact numbers Uncertainty of their true valueMeasuredConversions between different systems

Expressing numbers in scientific notation

Why do it?

How to enter them into your calculator

1.5 x 1023

1 . 5 EXP (or EE) 2 3

2.67 x 10-16

2 . 6 7 EXP (or EE) +/- 1 6

Making measurements

Accuracy: How close a measured value is to the true value

Precision: How close multiple measured values are to each other

There is estimation (and therefore uncertainty)

in all measurements

Significant figures

The digits in a measurement that are known with certainty, plus the single estimated digit

Only applies to measured (inexact) values

Does not apply to defined (exact) values

Measured ValuesMeasured ValuesWhat figures (digits) are significant?What figures (digits) are significant?

(not applied to defined or exact values such as conversions within the same system)

Non zeros are significant

Zeros between non zeros are significant

Zeros at the beginning are not significant

Zeros at end after decimal are significant

Zeros at end before the decimal depend

Three ways to represent these zeros

How many significant figures are in these measured values?

0.2304 cm

30.030 L

0.0034 m

100 kg

1.0300 x 10-4 mg

Rules for working with measured values

Since there is uncertainty in measurement, we risk “amplifying” the uncertainty when we add, subtract, multiply and divide measured values

So…. There are rules for working with measured values

Calculations involving measured values

Multiplying and dividing:Answer can have no more total sig. figs. than the starting value with the fewest total sig. figs.

Adding and Subtracting:Answer can have no more sig. figs. after the decimal than any original number

Dimensional analysis helps solve conversion problems

What are you starting with? What do you need to convert it into? What conversion factor(s) do you need?

Must know conversions within the metric system.

Must know other conversions we will identify.

Do not have to memorize conversions between systems.

English/Metric conversions (Table 2.2)

Density

Mass of material per given volume Commonly: grams/mL SI: kg/m3

Density is a conversion factor for converting between mass and volume

grams (mL/g) = milliliter

milliliter (g/mL) = grams

Temperature scales

K = C + 273 C = K - 273

Calories and specific heat

calorie: amount of heat 1 cal raises 1 g of water 1° C

60 Calories = 60 kcal = 60,000 calories

Specific heat of any substanceAmount of heat (in calories) required to raise 1 gram of the substance 1° C