( ان ا دة اء ) ر
ni ( I 2 ) = nr ( I 2 ) + n( I 2 ) ⇒ n( I 2 ) = ni ( I 2 ) − nr ( I 2 ) : و :MB ا *د ا4%N دةB آ4 هn( I 2 ) n ( I 2 ) = n ( AH ) = 3, 35.10 − 5 mol 4) (P اQ- و10mL 4) *ﺝ*دةB اB= اOB ﺕB= ه?> ا n( AH ).82 nt ( AH ) = = 2,89.10−4 mol . 78mL :* ه2ا &(ﺕ 10 . m = nt ( AH ).M ( AH ) = 0, 05 g : 4 هM= و ا : اازن-4 − p K A1 K A1 10 K = = = 1 0 − p K A 1 + p K A 2 = 1, 4 1 -1 K A 2 1 0 − p K A2 .*رR ﺕI *B-B أي أن اQr ,i = K = 1, 41 -2
:ا!یء 14 6
C.V − xm
--------
:وی# ا$%ا C → 174 N + − 10 e :S د ا-1
. N (t ) = N o .e− λ .t :4 TU اVK ﻥ*ن اK -2 N . N (t 1 2 ) = o JX ه* ا:WP ( اB W( ﺕ-3 2 W( ا73 − λ .t 1 N 1 N (t 12 ) = N o .e 2 = o ⇒ e − λ.t 12 = 2 2 ln(2) λ= ⇐ λ.t 1 2 = ln(2) : - ﻥln لYدZو ﺏ t 12 ln(2) .λ = = 1, 242.10−4 ans −1 : λ ب3 5580ans :* ﻥ_ط ه-4 a(t ) = λ.N (t ) = λ.No .e−λ.t = ao .e−λ.t ⇒ a(t ) = ao .e−λ.t a(t ) = ao .e− λ .t -5 و
:اء -1 − + C6 H 8O6 + H 2O C6 H 7O6 + H 3O : د ا-1 n( AH ) m( AH ) AH = C6 H 8O6 C = = -2 V M ( AH ).V 0,5 .C = = 1, 42.10−2 mol.l −1 : و 176.0.2 -3 − + C 6 H 8O6 + H 2 O C 6 H 7 O6 + H 3O C.V %& ا$ ا ﺏ*)(ة 0 0 -------C.V − x f xf x f &(-ﺕ.ن.
a (t ) a (t ) = e − λ .t ⇒ ln = −λ .t ⇐ ao ao
a (t ) 1 t = ln . = 3341, 49ans ao λ أي3341, 49ans − 1995ans = 1346ans ش )(*ن-6 .a& ا رK ﺱ1346 4) اﻥ ش :&اﻥ : J *ﺕ 4ﻥO ا ﻥ*ن2 ا b&Rﺏ -r1 uuur ur ur : - ﻥAX *ر$B اLM c2ﺱZ و ﺏP + R = m.a وRx = 0 : )نMBd =كI أن اB و ﺏPx + Rx = m.ax
: وPx = m.g.sin (α )
(آ$ و اax = g .sin α = cte ⇐ m.g.sin α = m.ax . ax = 5m.s −2 : رع3 م و ا/(ة ﺏﻥh B23 1 : x = a.t 2 + Vo .t + xo :X د اB ا-2 2 x = 2,5.t 2 : أذنVo = VA = 0 وxo = xA = 0 وVB = 5.tB :(3 ب ا3 -3
xm
xm
: )ن45* ول ا- ا73 وτ =
Qr ,eq
(/ﻥ.ن. xf xm
:م2 & ا3ﻥ
H 3 O + ⇐ τ= ⇐ x f = H 3O + .V وxm = C.V C 10− pH .ود$ ⇐ اτ = = 0, 07 = 7% C 2 H 3O + . A− H 3O + eq eq = = رج ا-3 C − H 3O + [ AH ]eq
(10 ) − pH
2
= 8,9.10−5 : أي أن C − 10− pH .. pK A = 4, 05 ⇐ K A = Qr ,eq = 8,9.10−5 - II : ﻡد ا1-2 C 6 H 8 O 6 + O H − → C 6 H 7 O 6− + H 2 O : <)= ا2-2 − >? هn(C6 H 8O6 ) = n(OH ) = CB .VBE = 2,88.10−4 mol CB دةB ⇐ آVA = 10mL 4) ﺕ*ﺝ4 اB= ا4 هB= ا وVs = 100mL 4) ?اﺏB دة اB اB آ4(ص ه2 ا4) Fﺱ=*رﺏIا وQr ,eq =
ns = 2,88.10−3 mol ⇐
2,88.10−4 mol → VA = 10mL
: ns → Vs = 100mL :4(ص ه2 ا4) *اﺝB اC J دة اBآ ns = 2,88.10−3 mol : mg ا ب3-2
ns =
m ⇒ m = ns .M ( AH ) = 0,5 g = 500mg M ( AH ) . 500mg LM *ي$ C J) (صK أي آ : ni ( I 2 ) %& ا *د ا4%N دةB آ: -3
أنB ﺏni ( I 2 ) = C2 .V2 = 5,3.10−3.10.10−3 = 5,3.10−5 mol n( I 2 ) MB ا *د ا4%N دةB ا *د *ﺝ ﺏ*)(ة )ن آ4%N . 2 ا &(ﺕ4) *ﺝ*دةB اFﺱ=*رﺏI اCB n( AH ) دةBوي آ3ﺕ .MB ا *د ا4%N دةBد آ$ ::2&B اnr ( I 2 ) ا *د4%N دةB آ$ ﺕJ=B ﻥO (ة اB ﺏ nr ( I 2 ) =
n( S 2O32− ) 5.10−3.7,8.10−3 = = 1,95.10−5 mol 2 2
:$%(ب ا+ -4
VB = 5m.s −2 : و. ع. تt B =
2 xB = 1s ⇐ xB = 2,5.t B 2,5
1 ur r Ee1 = C.uC2 = 0.5.0, 2.10−6.102 = 10−5 J ⇐ t = 0 P = m . a :J *ﺕ4ﻥO ﻥ*ن ا2 اb&R ﺏ: JX اJ دB ا1 -4 2 ax = 0 Px = m.ax = 0 Ee 2 = 0,5.0, 2.10−6.52 = 25.10−7 J ⇐ uC = 5V أنt = 4T ⇐ a y = g Py = m.a y = mg ∆Ee = Ee1 − Ee 2 r - II *ر$B اLM B/ B23 ( B, i ) *ر$B اLM (آ$ و ا r -1 x = V Bx t + x o :X د اB ( و اB, i ) &دةB اKR اC* ﺏF ﻥ ا ?ﺏ?ﺏت و ذ5 ** هB دور ا r م/(ة ﺏﻥh B23 ( B, j ) *ر$B اLM (آ$ و ا . r T* و ا2 4) *ل ﺝ*لBﺏ دB اL إ5* ﻥ2ﺏ3 ا2(R اt ﺏ:Mr د اB ا-2 1 x y = a y t 2 + V By t + y o 2 d u 1 r − K duC 2 . 2C + + .uC = 0 ⇐ : اMr ا ur dt L dt LC VB : =_ ا73 . K = r أن =*ن7- -3 V B x = V B co s α x = 0 - III y و o t = 0 V = V sin α y = 0 B y B o . uR (t ) OB Y2 وZ f R نI u (t ) OB Y1 -1 x = VB cos α .t U 4 x = 4,3.t وZ o = m .R = .20 = 40Ω -2 : و 1 2 U Rm 2 2 y = 5.t + 2,5.t y = gt + VB sin α .t 2 . Z o = R + r ⇒ r = Z o − R = 40 − 20 = 20Ω x 1 وt= :n3 ﻥx X د اB اJ : ﻡد ا(ر2-4 ⇐ Lω = :J ا (ﻥ: L BK ب3 VB cos α Cω g 1 1 y= x 2 + x.tan α : إذنy دB ا4) C* ﺏ = = 0,5 H N o = 50 Hz . L = 2 2 2 2 2VB .cos (α ) C.ω C.(2π .N o ) .Q-MT J * &رةd) U Um . Io = = Rm = 0, 07 A :ة ا رT -4 :*ط23 ة ا3-4 2.Z o 2.R : وxI = HI = 4,3m وx = 2,15.t : WO=B ا4R (ﺏJ ا *ﺕ( ا ل ﺏBK -5 x 4, 3 1 1 I R2 اL *ل إ5*M K(h3B ة اB ا4 هt = = = 1s U c = Z c .I o = .I o = .I o 4, 3 4, 3 Cω C.2π .N o : )( ا4-4 2 U L , r = r 2 + ( Lω ) .I o = : T* ا4R (ﺏJا *ﺕ( ﺏ ur Vx = x& = 4,3 t = 1s )نI R2 اV 2 1 Vy = y& = g.t + VB sin α ⇐ M و B Jﺏ (ا *ﺕ 6 Z BM = r2 + Lω − Cω ur Vx = 4,3m.s −1 14243 V و I =0 −1 Vy = 10.1 + 5.1 = 15m.s U BM = r.I o وJه(ة ا (ﻥu VI = Vx2 + Vy2 = 4,32 + 152 = 15, 6m.s −1 :ا*)ء uc + uL = 0 : ) ا *ﺕ(اتrﻥ*ن إK b&R ﺏ1-
d 2uC r duC 1 di + + .uC = 0 ⇐ uC + ri + LC = 0 ⇐ 2 dt L dt LC dt duc 1 1 وi = C وEt = C.uC2 + L.i 2 :M= اKR ا-2 dt 2 2 2 1 1 duC 2 . Et = C.uC + L C. 2 2 dt dEt du d 2u duC = C.uC . + LC 2 . C . 2C :M= اKR ق ا2T ﺏ-3 dt dt dt dt 2 d u uC . + LC 2C = −r.i : Mr د اB ا73 dt dE du d 2u . t = C. C (uC . + LC 2C ) = i. ( −r.i ) = −r.i 2 ⇐ dt dt dt