Mathematical Formula Analysis, Exercises of Biochemistry

A series of mathematical formulas and notations, including summations, products, and inequalities. The formulas involve variables such as x, n, i, w, and t, and operations like summation, absolute value, factorial, and multiplication. The document also includes references to arrays, matrices, and functions.

Typology: Exercises

2017/2018

Uploaded on 04/04/2022

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𝐴𝑟𝑖𝑡𝑚𝑒𝑡𝑖𝑐)𝑀𝑒𝑎𝑛)))
𝑋=
(𝑋𝑖)
𝑁
𝑀𝑒𝑎𝑛)𝐷𝑒𝑣𝑖𝑎𝑡𝑖𝑜𝑛
𝑑=
)|𝑋𝑖𝑋|
𝑁
𝑆𝑡𝑎𝑛𝑑𝑎𝑟𝑑)𝐷𝑒𝑣𝑖𝑎𝑡𝑖𝑜𝑛
𝑠=
;
)(𝑋𝑖𝑋)!
𝑁
𝑠=
;
)(𝑋𝑖𝑋)!
𝑁1
𝐸=𝑇𝑉𝑋
𝑅𝐸=) 𝐸
𝑇𝑉)𝑥)100%
𝑋=𝐴𝑟𝑖𝑡𝑚𝑒𝑡𝑖𝑐)𝑀𝑒𝑎𝑛)
𝑋𝑖=𝑖𝑛𝑑𝑖𝑣𝑖𝑑𝑢𝑎𝑙)𝑚𝑒𝑎𝑠𝑢𝑟𝑒𝑚𝑒𝑛𝑡)
𝑁=𝑡𝑜𝑡𝑎𝑙)𝑛𝑢𝑚𝑏𝑒𝑟)𝑜𝑓)𝑠𝑎𝑚𝑝𝑙𝑒)
𝑑=𝑚𝑒𝑎𝑛)𝑑𝑒𝑣𝑖𝑎𝑡𝑖𝑜𝑛)
𝑠=𝑠𝑡𝑎𝑛𝑑𝑎𝑟𝑑)𝑑𝑒𝑣𝑖𝑎𝑡𝑖𝑜𝑛)
𝐸=𝑒𝑟𝑟𝑜𝑟)
𝑅𝐸=𝑟𝑒𝑙𝑎𝑡𝑖𝑣𝑒)𝑒𝑟𝑟𝑜𝑟)
𝑇𝑉=𝑡𝑟𝑢𝑒)𝑣𝑎𝑙𝑢𝑒
)
𝐵𝑜𝑦𝑙𝑒"𝑠)𝐿𝑎𝑤
)
)
𝑉1)𝑃1=𝑉2)𝑃2
𝐶ℎ𝑎𝑟𝑙𝑒𝑠)𝐿𝑎𝑤)
𝑉1)𝑇2=𝑉2)𝑇1)
𝐺𝑎𝑦)𝐿𝑢𝑠𝑎𝑎𝑐"𝑠)𝐿𝑎𝑤)
𝑃1)𝑇2=𝑃2)𝑇1)
𝐼𝑑𝑒𝑎𝑙)𝐺𝑎𝑠)𝐿𝑎𝑤)
𝑃𝑉=𝑛𝑅𝑇))
𝐷𝑒𝑛𝑠𝑖𝑡𝑦)𝑖𝑛)𝐼𝑑𝑒𝑎𝑙)𝐺𝑎𝑠)𝐿𝑎𝑤)
𝑃𝑀=𝑑𝑅𝑇)
𝐶𝑜𝑚𝑏𝑖𝑛𝑒𝑑)𝐺𝑎𝑠)𝐿𝑎𝑤)
𝑉1)𝑃1)𝑇2=𝑉2)𝑃2)𝑇1)
𝐴𝑣𝑜𝑔𝑎𝑑𝑟𝑜"𝑠)𝐿𝑎𝑤)
𝑛𝑜.𝑜𝑓)𝑚𝑜𝑙𝑒𝑐𝑢𝑙𝑒𝑠=𝑛)𝑥)𝐴𝑣𝑜𝑔𝑎𝑑𝑟𝑜"𝑠𝑁𝑢𝑚𝑏𝑒𝑟)
(
𝐴𝑁
)
𝐷𝑎𝑙𝑡𝑜𝑛"𝑠)𝐿𝑎𝑤)
𝑃)𝑡𝑜𝑡𝑎𝑙=𝑃)𝑔𝑎𝑠1+𝑃)𝑔𝑎𝑠)2)
𝐷𝑢𝑚𝑎𝑠)𝑀𝑒𝑡𝑜𝑑)
𝑀𝑤)𝑃𝑉=𝑤𝑡)𝑅𝑇)
𝑅𝑜𝑜𝑡)𝑀𝑒𝑎𝑛)𝑆𝑞𝑢𝑎𝑟𝑒)𝑉𝑒𝑙𝑜𝑐𝑖𝑡𝑦)
𝐶=
;
3𝑅𝑇
𝑚𝑤
𝐶=
;
3𝑛𝑅𝑇
𝑤𝑡)𝑁)
𝐶=
;
3)𝑃𝑉
𝑤𝑡)𝑁
𝑉𝑎𝑛𝑑𝑒𝑟)𝑊𝑎𝑎𝑙𝑠)𝐸𝑞𝑢𝑎𝑡𝑖𝑜𝑛)
𝑃= 𝑛𝑅𝑇
𝑣𝑏𝑎
𝑣2)
𝐶𝑙𝑎𝑢𝑠𝑖𝑠)𝐶𝑙𝑎𝑝𝑒𝑦𝑟𝑜𝑛)𝐸𝑞𝑢𝑎𝑡𝑖𝑜𝑛)
𝑙𝑛𝑃2
𝑃1=−∆𝐻𝑣𝑎𝑝
𝑅)
Z
1
𝑇21
𝑇1
[
)
𝑀𝑜𝑙𝑎𝑟𝑖𝑡𝑦)
𝑀= 𝑛
𝐿)𝑜𝑓)𝑠𝑜𝑙𝑛)
𝑁𝑜𝑟𝑚𝑎𝑙𝑖𝑡𝑦)
𝑁= 𝑒𝑞)𝑤𝑡
𝑙)𝑜𝑓)𝑆𝑜𝑙𝑛)
𝑁=𝑀)𝑥)𝐹)
𝐸𝑞𝑢𝑖𝑣𝑎𝑙𝑒𝑛𝑡)𝑊𝑒𝑖𝑔ℎ𝑡)
𝑒𝑞)𝑤𝑡=) 𝑔
𝑚𝑤𝑥)𝐹)
𝑀𝑜𝑙𝑎𝑙𝑖𝑡𝑦)
𝑚= 𝑛
𝑘𝑔)𝑜𝑓)𝑠𝑜𝑙𝑣𝑒𝑛𝑡)
𝑚𝑜𝑙𝑒𝑠)
𝑛=)𝑤𝑡
𝑚𝑤)
𝑂𝑠𝑚𝑜𝑙𝑎𝑟𝑖𝑡𝑦)
𝑂𝑠𝑚=𝑚𝑂𝑠𝑚
𝐿)𝑜𝑓)𝑆𝑜𝑙𝑛)
𝑚𝑂𝑠𝑚=𝑛)𝑖)
(
1000
)
𝐿)𝑜𝑓)𝑠𝑜𝑙𝑛)
𝑀𝑖𝑙𝑙𝑖𝑒𝑞𝑢𝑖𝑣𝑎𝑙𝑒𝑛𝑡)
𝑚𝐸𝑞=
(
𝑛
)(
𝑓
)
(1000)
𝐿)𝑜𝑓)𝑠𝑜𝑙𝑛

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Arithmetic Mean rAd) *eTN Mean Deviation E1x-XI a N Standard Deviation _ fe ai-xye --e= _ fe ai-xye S= VO N=1 F=1V-Xx re = ~ x 100% ~ Ty ~ X = Arithmetic Mean Xi = individual measurement N = total number of sample d = mean deviation Ss tandard deviation E =error RE elative error TV = true value Boyle's Law V1P1=V2P2 Charles Law V1T2=V2T1 Gay Lusaac's Law P1T2=P2T1 Ideal Gas Law PV = nRT Density in Ideal Gas Law PM = dRT Combined Gas Law V1P1T2=V2P2T1 Avogadro's Law Dalton’ s Law P total = P gas1 +P gas2 Dumas Method Mw PV = wt RT Root Mean Square Velocity 3RT mw ce BY ~ Jwt N Vander Waals Equation _ nRT a ~v—b v2 Clausis Clapeyron Equation 2 _—aloap (1 1) "pi oR \T2 TA no. of molecules = nx Avogadro'sNumber (AN) mEq = Molarity n M =———_ Lof soln Normality __eqwt ~ Lof Soln N=MxF Equivalent Weight eqwt = xk mw Molality n ™ = keg of solvent moles wt mw Osmolarity mOsm ~Tof Soin i (1000) L of soln Osm mOsm = Milliequivalent _ (000) Lof soln