Transcript x - Quia
Algebraic Equations •Many relationships in chemistry can be expressed by simple algebraic equations. •SOLVING an equation means rearranging •The unknown quantity is on one side, and all the known quantities are on the other side. Algebraic Equations •An equation is solved using the laws of equality •Laws of equality: if equals are added to, subtracted from, multiplied to, or divided by equals, the results are equal. •This means: as long as you do the same thing to both sides of the equation, the results are equal! ISOLATING VARIABLES IN EQUATIONS The equation can be rearranged using the following rules of algebra to isolate the variable on one side of the equation. Rule 1 An equation remains true if equal values are added to or subtracted from each side. Solve for x: x + 5 = 9. subtract 5 from each side. x+5 -5=9–5 x=9–5 x=4 ISOLATING VARIABLES IN EQUATIONS Rule 1 An equation remains true if equal values are added to or subtracted from each side. Solve for x: x - 7 = 2. add 7 to each side. x -7 + 7 = 2 + 7 x=2+7 x=9 Algebraic Equations •Solve for oC: K = oC + 273 oC = K - 273 ISOLATING VARIABLES IN EQUATIONS Rule 2 An equation remains true if each side is multiplied or divided by the same value. Solve for x: 4x = 24. divide each side by 4. 4x = 24 4 4 x=6 ISOLATING VARIABLES IN EQUATIONS Rule 2 An equation remains true if each side is multiplied or divided by the same value. Solve for x: x = 4. 3 multiply each side by 3. x (3) = 4 (3) 3 x = 12 ISOLATING VARIABLES IN EQUATIONS Rule 3 In a proportion, such as a c = b d you can cross multiply to obtain the new equation ad = bc. ISOLATING VARIABLES IN EQUATIONS Solve for x: x 3 = 8 6 you can cross multiply to obtain the new equation 6x = 24. Divide each side by 6. 6x 24 = 6 6 x=4 Algebraic Equations Solve for T2: V1 V2 T1 T2 = = T2 V2 x T1 V1 Percents • Percent means “parts of 100” or “parts per 100 parts” • The formula: Part Percent = x 100 Whole Percents • If you get 24 questions correct on a 30 question exam, what is your percent? 24/30 x 100 = 80% • A percent can also be used as a RATIO – A friend tells you she got a grade of 95% on a 40 question exam. How many questions did she answer correctly? 40 x 95/100 = 38 correct Proportions Direct Proportion y x y x Inverse Proportion 1 y x y x Logarithms • A logarithm is the exponent to which a fixed number (base) must be raised in order to produce a given number. • Consists of two parts: – The characteristic (whole number part) – The mantissa (decimal part) Logarithms • Log tables are located in many textbooks • Calculators may also be used • Find the log of 176 = 2.2455 • Find the log of 0.0065 = -2.1871 Antilogarithms • The reverse process of converting a logarithm into a number is referred to as obtaining the antilogarithm (the number itself) • Find the antilog of 4.618 = 41495 (or 4.15 x 104)