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Essential Math of Chemistry

Essential Math of Chemistry. Scientific Notation. -- used to express very large or very small numbers, and/or to indicate precision. Form: (# from 1 to 9.999) x 10 exponent 800 = 8 x 10 x 10 = 8 x 10 2 2531 = 2.531 x 10 x 10 x 10 = 2.531 x 10 3

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Essential Math of Chemistry

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  1. Essential Math of Chemistry

  2. Scientific Notation -- used to express very large or very small numbers, and/or to indicate precision Form: (# from 1 to 9.999) x 10exponent 800 = 8 x 10 x 10 = 8 x 102 2531 = 2.531 x 10 x 10 x 10 = 2.531 x 103 0.0014 = 1.4 101010 = 1.4 x 10–3 (i.e., to maintain the correct number of significant figures)

  3. Put in standard form. 1.87 x 10–5 = 0.0000187 3.7 x 108 = 370,000,000 7.88 x 101 = 78.8 2.164 x 10–2 = 0.02164 Change to scientific notation. 12,340 = 1.234 x 104 0.369 = 3.69 x 10–1 0.008 = 8 x 10–3 1,000,000,000 = 1 x 109 6.02 x 1023 = 602,000,000,000,000,000,000,000

  4. Using the Exponent Key EE EXP

  5. The EE or EXP or E key means “times 10 to the…” 6 6 6 6 6 1 1 0 0 0 0 0 0 0 x x y x EE EE EE y x 2 2 2 2 2 2 2 2 2 2 3 3 3 3 3 . . . . . How to type out 6.02 x 1023: How to type out 6.02 x 1023: not… WRONG! WRONG! or… and not… TOO MUCH WORK.

  6. Also, know when to hit your (–) sign. (before the number, after the number, or either one)

  7. Type this calculation in like this: 1.2 x 105 2.8 x 1019 1 2 Calculator gives… 4.2857143 –15 9 1 8 2 5 or… 4.2857143 E–15 EE EE This is NOT written… 4.3–15 . . = 4.3 x 10–9 or 4.3 E –9 But instead is written…

  8. 5.76 x 10–16 9.86 x 10–4 = –6.5 x 10–19 7.5 x 10–6 (–8.7 x 10–14) = 5.35 x 103 or 5350 4.35 x 106 (1.23 x 10–3) = 5.84 x 10–13 8.8 x 1011 x 3.3 x 1011 = 2.9 x 1023

  9. Essential Mathof Chemistry

  10. Units must be carried into the answer, unless they cancel. 5.2 kg (2.9 m) 4.8 kg (23 s) kg-m = = (18 s)(1.3 s) (18 s)(37 s) s2 kg s 0.64 0.57

  11. Solve for x. x + y = z x and y are connected by addition. Separate them using subtraction. In general, use opposing functions to separate things. x + y = z – y – y The +y and –y cancel on the left, x = z – y leaving us with…

  12. Solve for x. Numerical Example x – 24 = 13 x and 24 are connected by subtraction. Separate them using the opposite function: addition. x – 24 = 13 +24 +24 The –24 and +24 cancel on the left, x = 37 leaving us with…

  13. Solve for x. F = k x __ F x = k k k (or) F = k x ( ( ) ) __ __ 1 1 k k F = k x x and k are connected by multiplication. Separate them using the opposite function: division. The two k’s cancel on the right, leaving us with…

  14. Numerical Example Solve for x. 8 = 7 x 7 7 (or) 8 = 7 x __ 8 ( ( ) ) __ __ 1 1 x = 7 7 7 8 = 7 x x and 7 are connected by multiplication. Separate them using the opposite function: division. The two 7’s cancel on the right, leaving us with…

  15. Solve for x. ( ( ) ) BAH ___ ___ BA ___ ___ 1 1 ___ TR x = = x TR TR TR H One way to solve this is to cross-multiply. BAH = xTR Then, divide both sides by TR. BAH = xTR The answer is…

  16. Solve for T2, where… P1 = 1.08 atm P2 = 0.86 atm V1 = 3.22 L V2 = 1.43 L T1 = 373 K P1V1 P2V2 ____ = ____ T1 T2 P2V2T1 ______ T2 = P1V1 ( ( ) ) ____ ____ 1 1 (0.86 atm)(1.43 L)(373 K) _____________________ T2 = P1V1 P1V1 = (1.08 atm)(3.22 L) P1V1T2 = P2V2T1 132 K

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