Chem I unit 1 And you

1-1 Measurement (Section 2.3, p ) Measurement is an inherent component of any laboratory science. Common variables that are measured in chemistry include: length, mass, volume, and temperature.

Length the following distances are common in science are often referenced to the SI unit the meter (m) by placing the prefix in front of the “m”: kilo (k) deci (d) centi (c) milli (m) micro (µ) nano (n) For example, a kilometer is abbreviated km and a micrometer µm. Any relationship between units in the metric system can be determined from the value of the prefix relative to the base unit, the meter:

Table 1-1 Memorize this table! 1 km = 1000 m (= 10 3 m) 1 m = 10 dm (= 10 1 dm) 1 m = 100 cm (= 10 2 cm) 1 m = 1000 mm (= 10 3 mm) 1 m = 10 6 µm 1 m = 10 9 nm

The prefixes of the metric system can used for any variable. Take, for example, a liter of volume; using the above chart, 1 L = 1000 mL. Similarly, 1 gram = 1000 mg

Mass mass represents the amount of matter in an object. Mass differs from weight in that mass never changes, but weight is affected by the pull of gravity on the mass. Unfortunately, the terms are often interchanged in chemistry. Typical units are based on the gram (g).

Volume The amount of space that a mass occupies. Units are based on the liter (L) or in distance cubed. For example: 1 L = 1000 mL or since 1 mL = 1 cm 3 then 1 L = dm 3.

Volume continued Volume of a slug may be measured by: 1) Water displacement or 2) V = area x height = πr 2 x height

Density how much matter is packed into a certain space. Density = Mass or D = M Volume V units: g/ml or g/cm 3 D M V

Density continued Density can be determined graphically by plotting y axis = ? x axis = ? mass on the y-axis and volume on the x-axis. The slope of the line equals the density

Therefore: mass (g) slope (m) volume (ml) Equation of a line: y = mx + b mass = (slope) (volume) + y intercept * Note the y intercept = 0 here

Rank the three metals in order of decreasing density: Pb > Zn > Al Next, write the equation of the line for Zinc, including the slope as a decimal: y = mx + b 18 = (18/2.5)(2.5) + 0 m = 7.2 g/ml Why do all three graphs include the origin? the y intercept = 0 Pb Zn Al 18 g 2.5 ml

And now…a more complicated graphical interpretation.

Just like in the case of density, it is often useful to compare two variables graphically, with the idea of determining additional information related to the two variables if the mathematical relationship is a straight line. Take, for example, the variables of the rate constant (k) and temperature (T). The qualitative nature of the temperature dependence of the rate constant can be represented graphically in the form below:

ln(k) = -E a /R · (1/T) + ln(A) The variables that scientists change are k and T. Constants are E a, R, and A. To fit the above equation to the form of a straight line (y = m·x + b), keep in mind the phrasing “the temperature dependence of the rate constant “ What would you plot on the y-axis? ln(k) What would you plot on the x-axis? (1/T) What would the slope represent? -E a /R What would the y-intercept represent? ln(A)

Significant Figures are numbers in a measurement that have “meaning” (are certain), plus one additional number that is an estimate. As an example, the volume mL has 4 significant figures: the numbers 2, 3, and 5 are certain and the number 8 is an estimate. By convention, the last significant figure is always an estimate. Significant figures are commonplace in science, since measuring devices have a limit to the number of markings

In the figure above, the length of the mechanical pencil extends just past the 4.7 cm mark. Anyone and everyone measuring the pencil would agree that it is at least 4.7 cm long. However, the tip lies between 4.7 and 4.8 cm and therefore requires an estimate: maybe it is 4.71 or 4.73 cm. All three numbers, the two that are certain and the estimate are considered “significant figures.”

Measurements always include some degree of uncertainty, which comes from the limitations of the markings on the instrument. For example, the pencil length might be expressed as 4.72 cm ± 0.01 cm, which means the measured value might range from 4.71 cm to 4.73 cm. Note how the uncertainty of 0.01 cm has only one significant figure. If the measurement appears to lie “exactly” on the marking, you still need to include a digit that represents the extent to which an estimate can be made. For example,

Why would you include the 0 in the measurement to the left? Note: when measuring volumes, we always put our eye at the bottom of the liquid’s curve, called the “meniscus.”

Why, if the same object is measured by two different rulers, can we have more significant figures in the top ruler?

Finally measurements in science rarely use fractions since a fraction cannot convey the correct number of significant figures: ¼ has no significant figures, whereas 0.25 has 2 sig figs. The number of sig figs will be very important in calculations you make in your studies!