Significant Figures and the Determination of the Volume of a Picnometer (the flask)

Determine the volume of a flask. At 23.0 °C the density of water is 0.99753 g/cm³

Weigh dry flask and stopper	50.0440 g
Fill with water, stopper, wipe, and weigh flask	77.8923 g
Determine the volume of the flask using the density of water

The rationale: if I know the mass of the water in the flask I can easily convert it to the volume of the water. DENSITY

Mass of water in the flask

77.8923 g - 50.0440 g 27.8483 g

Should I use 1.00 g/cm³ as the density? No, use the density of water at the temperature of the experiment should be used. At 23.0 °C the density of water is 0.99753 g/cm³.

Using Significant figures

Two important steps with sigfigs...

1. Determining the number of significant figures in a measurement.

a. All non-zero numbers are significant.

b. Zero's are significant if

i. they are between two non-zero numbers

ii. they occur before and after the decimal point of a number whose absolute value is > 1

e.g. in 10.0 the zeros are significant.

iii. they occur after a non-zero number in a number whose absolute value is < 1.

e.g. in 0.0560 the leading zeros are not significant, but the trailing zero is.

2. Determining the number of significant figures that should remain after performing mathematical manipulations with the numbers.

There are two sets of rules

a. addition/subtraction

the result of adding two numbers together should be precise to the place that corresponds to the least precise measurement

b. multiplication/division

the result of multiplying two numbers should have the same number of significant figures as the number with the fewest significant figures.

Things to watch out for Combining Mathematical operations/order of operations. Losing sig figs during subtraction. Exact numbers (definitions, things that can be counted, the 1 in numbers like 19.6 g/cm3) Scientific notation.

So, volume of the flask...

From the density of water we know that 1 cm³ weighs 0.99753 g, or you could say 0.99753 g water occupies 1 cm³.

So, if 0.99753 g of water occupies 1 mL, then 27.8474 g of water occupy what volume?

Mathematically,

to the correct number of sig figs...

(However, when performing further calculations use 27.9173 keeping in mind that the last significant digit is the second 7.)