ch 10 - mathematics Flashcards
how many significant numbers should an answer have
as many as the fewest amount of significant numbers in any one of the species in the question stem
any number to zeroth power
1
multiplication example with exponents and same base number
X^A x X^B = X^(A + B)
division with exponents and same base number
X^A/X^B = X^(A-B)
number raised to an exponent and raised to another
(X^A)^B = X^(AxB)
fraction raised to exponent
(X/Y)^A = (X^A)/Y^A
negative exponents
X^-A = 1/X^A
fractional exponents
numerator is treated as exponent and denominator is root of the number. X^(A/B) = X^A root of B of that number
square root of 2
about 1.414 or 1.4
square root of 3
about 1.732 or 1.7
log sub A x 1
0
log sub A x A
1
log A x B
log A + log B
log (A/B)
log A - log B
log A^B
B log A
log (1/A)
-log A
what is p shorthand for
-log (pH, pKa)
expression for K sub a
K sub a = ([H+][A-])/[HA]
common logarithms
base-ten logs (log sub 10)
natural logarithms
logs that are based on Euler’s number (about 2.718) (log sub e or ln)
conversion between natural logs and common logs
log x = (ln x)/2.303
example of approximating value of log
log (n x 10^m) = log (n) + log (10^m) = m + log (n); because n is number between 1 and 10 its log will be a decimal between 0 and 1 (log 1 = 0, log 10 = 1) the close n is to 1 the closer log n will be to 0.
example of log
find log (9.2 x 10^8) = 8 + 0.92 = 8.92 approx
sine
soh: sin theta = opposite/hypotenuse = a/c; values range from -1 to 1
