Significant Figures
· Why are sig figs important?
o They indicate the precision of an instrument and how well a number is known.
· How to count sig figs:
o All non-zero numbers are significant
o Zeros between two non-zero numbers are significant
o “Place-holding” zeroes are not significant
Example # Sig Figs Scientific Notation
52,000 2 5.2 x 104
52,000. 5 5.2000 x 104
0.0052 2 5.2 x 10-3
0.0052000 5 5.2000 x 10-3
· If you are unsure of the number of significant figures, try to put the number into scientific notation, where every number is significant.
· How to carry sig figs:
o x/÷ result has same number of sig figs
o +/- result has same number of significant decimal places
o To avoid rounding errors, carry all digits to the end and then round
· Practice:
1. PV=nRT Solve for T
P= 1.006 atm V=18.2 L n=1.006 mol R=0.082057 L*atm/mol*K
(Assume R, a physical constant, is known to infinite significant figures – don’t include R for your sig fig considerations)
T=PV/nR = 221.796 K
· Using the multiplication/division rule: The answer will have the same number of sig figs as the value with the least sig figs. The value for volume has 3 sig figs while for pressure and number of moles, there are 4 sig figs (and R is a physical constant). Therefore our answer will have 3 sig figs.
o T=222 K
2. ΔG=ΔH-TΔS Solve for ΔG
ΔH=-226.37 kJ/mol T=376K ΔS=-110.2 J/mol*K
(Hint: follow order of operations to solve)
· Note the different units!!
· TΔS = -41435.2 J/mol = -41.4352 kJ/mol
o This number should have 3 sig figs (following the rule above) – meaning it has one sig fig past the decimal.
· ΔH-TΔS = -226.37 kJ/mol – (-41.4(352) kJ/mol) = -184.9348 kJ/mol
o The answer should have ONE sig fig past the decimal (using the rule above): ΔG = -185.0 kJ/mol
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