Laboratory Measurements

Laboratory Measurements

Purpose

To learn how to properly measure mass and volume in the chemistry laboratory and to use these skills to determine the density of water.

Are some measuring devices more accurate than others?

If three people measure the same thing will the measurements be the same?

If three people measure the same thing will all three measurements have the same number of significant figures?

In this class we will all read measurements to the same precision!

Steps to producing reproducible measurements:

Every measurement must include the value that is certain, an estimate of the closeness that the measurement is to the certain value, an indicator of the uncertainty of the measurement, and the unit of the measurement.We will use the symbols, N, m, M, u and U in our discussion.

N:The measured value is at least this numbered mark (N) on the scale.(This value is certain)

m * M:The number of marks (m) past N multiplied by the value of each mark, M.(This value is also certain.)

u * U:The number of uncertain steps (u) past the last certain mark multiplied by the value of the uncertainty (U).(This value is uncertain.)

A measurement -- sums these parts:N + (m * M) + (u * U)

-- includes the uncertainty :± U

-- includes the unit of measurement (mL, g, cm...)

example: ( a measurement of length in cm)

1.The measured value is at least which numbered mark (N) on the scale?

Example:The measured value is greater than 3 cm.N = 3 cm

2.Determine the value of each division or mark of the scale (M):

Choose a range (two adjacent numbers) and subtract the values.

Example:Range = 4 cm-3 cm = 1 cm

Determine the number of divisions in the range by counting the spaces between the two numbers.

Example:Divisions = 10 spaces between 3 and 4 cm

Divide the range by the number of divisions - this is the value of each division or mark.

Example:Value of mark = Range/Divisions = 1/10 = 0.1 cm

The value of the mark or division is certain (known with confidence).

Example:Each of the small markings between 3 and 4 represent 0.1 cm.

M = 0.1 cm

3.Determine the number of marks past N.This value is m.

Count the number of lines over from the highest numbered mark that is less than the measurement.

Example:The measurement is 1 line beyond the 3 cm mark.m = 1

4.Record the certain part of the measurement:N + (m * M)

Example:3 cm + 1 * 0.1 cm= 3.1 cm

The actual measurement is at least 3.1 cm.

But each measurement must also include an estimate of how close the actual measurement is to the certain part of the measurement.In fact, we can see that the line we are measuring goes past 3.1 cm.We will estimate to the nearest 10% of each line.This is done as follows:

5.Determine the uncertainty (U) of the scale:

Divide the mark value (M) by 10 to represent 10 imaginary divisions in the space between the lines.

Example:U = M/10 = 1 cm / 10 = 0 .01 cm

This tells you how many decimal places to record this measurement.

Example:A measurement using this scale will have two decimal places.

6.The measurement lies how many uncertain steps (u) beyond the last mark (N + m * M).

Remember that each space between marks has ten imaginary lines or steps.You have to estimate which of these imaginary lines the measurement indicator is on.If the indicator is pointing right at a line, then the uncertain steps (u) is 0.If it is half way between two lines, then u = 5.If it is slightly less than half way, you might use a 3 or 4 and if it is slightly more than halfway, you might use a 6 or 7.If it is just below the higher line, then u = 8 or 9.If it is just above the lower line, then u = 1 or 2.While the measurement is uncertain, you want the most precise possible estimate so that your measurements will be reproducible. This takes practice!Note that the final digit in your measurement (the estimate) must be a multiple of the uncertainty and have the same number of decimal places as the uncertainty.(If the uncertainty had been 0.2, the estimate would have to be evenly divisible by 2.)

Example:The indicator is just about in between so u = 5.

7.Determine the uncertain part of the measurement:u * U

This part of the measurement is uncertain since two individuals may estimate u differently.

Example:u * U ± U = 5 * 0.01 = 0.05

8.Determine the measurement by adding the certain (N + m * M) and uncertain (u * U) components together.

Example:N + (m * M) + (u * U) = 3 + 1*0.1 + 5*0.01 = 3.15 cm

The actual measurement should be within ± U (± 0.01 in this example), so this is how we record the measurements.

9.Record the measurement, the uncertainty and the unit.

Example:3.15 ± 0.01 cm

Example 2

N _4__m __8__M__0.2__u __2__U__0.02__

measurement:4 + (8 * .2) + (2 * .02)= 5.64 ± .02 mL

Practice

mL scale

N _____m _____M______u _____U______

General InstructionsRecord all data in INK directly into your lab notebook.Do not erase.Do not use white out.If you make a mistake, draw a single line through the error, and record the correct value nearby.Do not write your results on another sheet of paper with the intention of transferring it to the lab notebook.Failure to follow these instructions on every lab will result in drastic reductions to your lab average.

Have your instructor initial your lab notebook before you leave lab.

MEASUREMENT PRACTICE(Done in the lab period.)

Record the measurements indicated below.N + (m * M) + (u * U)± U unit

1.gram scale