$\newenvironment {prompt}{}{} \newcommand {\pKa }{\text {p}K_{\text {z}}} \newcommand {\pKb }{\text {p}K_{\text {b}}} \newcommand {\Ka }{K_{\text {z}}} \newcommand {\Kb }{K_{\text {b}}} \newcommand {\Kc }{K_{\text {e}}} \newcommand {\Ke }{K_{\text {e}}} \newcommand {\Kw }{K_{\text {w}}} \newcommand {\pH }{\text {pH}} \newcommand {\pOH }{\text {pOH}} \newcommand {\ungraded }[0]{} \newcommand {\vvr }[1]{{#1}_\rightarrow } \newcommand {\vvl }[1]{{#1}_\leftarrow } \newcommand {\ddegree }[0]{^\circ } \newcommand {\dcelsius }[0]{^\circ C} \newcommand {\Enul }[0]{E^\circ } \newcommand {\declaretranslationfallback }[0]{\declaretranslation {fallback}} \newcommand {\definetranslationfallback }[0]{\definetranslation {fallback}} \newcommand {\redefinetranslationfallback }[0]{\redefinetranslation {fallback}} \newcommand {\addtranslationfallback }[0]{\addtranslation {fallback}} \newcommand {\refeq }[1]{\textup {\ref {#1}}} \newcommand {\lparen }[0]{(} \newcommand {\rparen }[0]{)} \newcommand {\SwapAboveDisplaySkip }[0]{\noalign {\vskip -\abovedisplayskip \vskip \abovedisplayshortskip }} \newcommand {\vdotswithin }[1]{{\mathmakebox [\widthof {\ensuremath {{}#1{}}}][c]{{\vdots }}}} \newcommand {\MTFlushSpaceBelow }[0]{\\\noalign {\nobreak \vskip -\lineskip \vskip -\l_MT_shortvdotswithinadjustbelow_dim \vskip -\origjot \vskip \jot }} \newcommand {\crampedsubstack }[1]{\crampedsubarray {c}#1\endcrampedsubarray } \newcommand {\spreadlines }[1]{\setlength {\jot }{#1}\ignorespaces } \newcommand {\splitfrac }[2]{\genfrac {}{}{0pt}{1}{\textstyle #1\quad \hfill }{\textstyle \hfill \quad \mathstrut #2}} \newcommand {\splitdfrac }[2]{\genfrac {}{}{0pt}{0}{#1\quad \hfill }{\hfill \quad \mathstrut #2}} \newcommand {\textscale }[2]{\leavevmode \begingroup \relscale {#1}#2\endgroup } \newcommand {\Kc }[0]{K_{\text {c}}} \newcommand {\Ke }[0]{K_{\text {e}}} \newcommand {\blue }[1]{{\color {blue}#1}} \newcommand {\red }[1]{{\color {red}#1}} \newcommand {\multirowsetup }[0]{\raggedright } \newcommand {\officialeuro }[0]{{\fontencoding {U}\fontfamily {eurosym}\selectfont {}e}} \newcommand {\eurobars }[0]{{\fontencoding {U}\fontfamily {eurosym}\selectfont {}A}} \newcommand {\eurobarsnarrow }[0]{{\fontencoding {U}\fontfamily {eurosym}\selectfont {}B}} \newcommand {\eurobarswide }[0]{{\fontencoding {U}\fontfamily {eurosym}\selectfont {}C}} \newcommand {\captionnewline }[0]{\\\relax } \newcommand {\memcaptioninfo }[4]{} \newcommand {\captiongroup }[0]{\setcaptiontype } \newcommand {\LTcaptype }[0]{table} \newcommand {\showtodonotes }[0]{disable} \newcommand {\todo }[1]{\typeout {TODO #1}} \newcommand {\tcbpkgprefix }[0]{} \newcommand {\CancelColor }[0]{\color {xmaccent!50!black}} \newcommand {\important }[1]{\ensuremath {\colorbox {orange}{$#1$}}} \newcommand {\textimportant }[1]{\colorbox {orange}{#1}} \newcommand {\pdfnl }[0]{\\} \newcommand {\handoutnl }[0]{\ifhandout \nl \fi } \newcommand {\importantcell }[1]{\ensuremath {#1}} \newcommand {\xmPlotsColor }[0]{ \pgfplotsset { plot1/.style={darkgray,no marks,samples=100},plot2/.style={lightgray,no marks,samples=100},plotresult/.style={blue,no marks,samples=100},plotblue/.style={blue,no marks,samples=100},plotred/.style={red,no marks,samples=100},plotgreen/.style={green,no marks,samples=100},plotpurple/.style={purple,no marks,samples=100} } } \newcommand {\xmPlotsBlackWhite }[0]{ \pgfplotsset { plot1/.style={black,loosely dashed,no marks,samples=100},plot2/.style={black,loosely dotted,no marks,samples=100},plotresult/.style={black,no marks,samples=100},plotblue/.style={black,no marks,samples=100},plotred/.style={black,dotted,no marks,samples=100},plotgreen/.style={black,dashed,no marks,samples=100},plotpurple/.style={black,dashdotted,no marks,samples=100} } } \newcommand {\xmPlotsColorAndStyle }[0]{ \pgfplotsset { plot1/.style={darkgray,no marks,samples=100},plot2/.style={lightgray,no marks,samples=100},plotresult/.style={blue,no marks,samples=100},plotblue/.style={xmblue,no marks,samples=100},plotred/.style={xmred,dashed,thick,no marks,samples=100},plotgreen/.style={xmgreen,dotted,very thick,no marks,samples=100},plotpurple/.style={purple,no marks,samples=100} } } \newcommand {\geqnoslant }[0]{\geq } \newcommand {\geq }[0]{\geqslant } \newcommand {\leqnoslant }[0]{\leq } \newcommand {\leq }[0]{\leqslant } \newcommand {\emph }[1]{\textit {#1}} \newcommand {\ds }[0]{\displaystyle } \newcommand {\ts }[0]{\textstyle } \newcommand {\bron }[1]{\begin {scriptsize} \emph {#1} \end {scriptsize}} \newcommand {\R }[0]{\ensuremath {\mathbb {R}}} \newcommand {\Rnul }[0]{\ensuremath {\mathbb {R}_0}} \newcommand {\Reen }[0]{\ensuremath {\mathbb {R}\setminus \{1\}}} \newcommand {\Rnuleen }[0]{\ensuremath {\mathbb {R}\setminus \{0,1\}}} \newcommand {\Rplus }[0]{\ensuremath {\mathbb {R}^+}} \newcommand {\Rmin }[0]{\ensuremath {\mathbb {R}^-}} \newcommand {\Rnulplus }[0]{\ensuremath {\mathbb {R}_0^+}} \newcommand {\Rnulmin }[0]{\ensuremath {\mathbb {R}_0^-}} \newcommand {\Rnuleenplus }[0]{\ensuremath {\mathbb {R}^+\setminus \{0,1\}}} \newcommand {\N }[0]{\ensuremath {\mathbb {N}}} \newcommand {\Nnul }[0]{\ensuremath {\mathbb {N}_0}} \newcommand {\Z }[0]{\ensuremath {\mathbb {Z}}} \newcommand {\Znul }[0]{\ensuremath {\mathbb {Z}_0}} \newcommand {\Zplus }[0]{\ensuremath {\mathbb {Z}^+}} \newcommand {\Zmin }[0]{\ensuremath {\mathbb {Z}^-}} \newcommand {\Znulplus }[0]{\ensuremath {\mathbb {Z}_0^+}} \newcommand {\Znulmin }[0]{\ensuremath {\mathbb {Z}_0^-}} \newcommand {\C }[0]{\ensuremath {\mathbb {C}}} \newcommand {\Cnul }[0]{\ensuremath {\mathbb {C}_0}} \newcommand {\Cplus }[0]{\ensuremath {\mathbb {C}^+}} \newcommand {\Cmin }[0]{\ensuremath {\mathbb {C}^-}} \newcommand {\Cnulplus }[0]{\ensuremath {\mathbb {C}_0^+}} \newcommand {\Cnulmin }[0]{\ensuremath {\mathbb {C}_0^-}} \newcommand {\Q }[0]{\ensuremath {\mathbb {Q}}} \newcommand {\Qnul }[0]{\ensuremath {\mathbb {Q}_0}} \newcommand {\Qplus }[0]{\ensuremath {\mathbb {Q}^+}} \newcommand {\Qmin }[0]{\ensuremath {\mathbb {Q}^-}} \newcommand {\Qnulplus }[0]{\ensuremath {\mathbb {Q}_0^+}} \newcommand {\Qnulmin }[0]{\ensuremath {\mathbb {Q}_0^-}} \newcommand {\perdef }[0]{\overset {\mathrm {def}}{=}} \newcommand {\pernot }[0]{\overset {\mathrm {notatie}}{=}} \newcommand {\perinderdaad }[0]{\overset {!}{=}} \newcommand {\perhaps }[0]{\overset {?}{=}} \newcommand {\degree }[0]{^\circ } \DeclareMathOperator {\dom }{dom} \DeclareMathOperator {\codom }{codom} \DeclareMathOperator {\bld }{bld} \DeclareMathOperator {\graf }{graf} \DeclareMathOperator {\rico }{rico} \DeclareMathOperator {\co }{co} \DeclareMathOperator {\gr }{gr} \DeclareMathOperator {\bgsin }{bgsin} \DeclareMathOperator {\bgcos }{bgcos} \DeclareMathOperator {\bgtan }{bgtan} \DeclareMathOperator {\bgcot }{bgcot} \DeclareMathOperator {\bgsinh }{bgsinh} \DeclareMathOperator {\bgcosh }{bgcosh} \DeclareMathOperator {\bgtanh }{bgtanh} \DeclareMathOperator {\bgcoth }{bgcoth} \newcommand {\d }[0]{\mathrm {d}} \newcommand {\dx }[0]{\d x} \newcommand {\dd }[1]{\frac {\mathrm {d}}{\mathrm {d}#1}} \newcommand {\ddx }[0]{\dd {x}} \newcommand {\afg }[1]{{#1}’} \newcommand {\xmshortabstract }[0]{} \newcommand {\theabstract }[0]{} \newcommand {\xmopje }[1]{\iftoggle {showxmopje}{#1}{}} \newcommand {\xmcolorbox }[2]{ \cellcolor {#1}#2 } \newcommand {\xmopmerking }[1]{ {\footnotesize #1} } \newcommand {\proofname }[0]{Bewijs} \newcommand {\xmonlineChoice }[1]{\pdfOnly {\wordchoicegiventrue }\wordChoice {#1}\pdfOnly {\wordchoicegivenfalse }} \newcommand {\onlineChoice }[1]{\pdfOnly {\wordchoicegiventrue }\wordChoice {#1}\pdfOnly {\wordchoicegivenfalse }} \newcommand {\TJa }[0]{\nlentext { Ja }{ Yes }} \newcommand {\TNee }[0]{\nlentext { Nee }{ No }} \newcommand {\TJuist }[0]{\nlentext { Juist }{ True }} \newcommand {\TFout }[0]{\nlentext { Fout }{ False }} \newcommand {\choiceTrue }[0]{{\wordChoice {\choice [correct]{\TJuist }\choice {\TFout }}}} \newcommand {\choiceFalse }[0]{{\wordChoice {\choice {\TJuist }\choice [correct]{\TFout }}}} \newcommand {\choiceYes }[0]{{\wordChoice {\choice [correct]{\TJa }\choice {\TNee }}}} \newcommand {\choiceNo }[0]{{\wordChoice {\choice {\TJa }\choice [correct]{\TNee }}}} \newcommand {\choiceminimumverticalsize }[0]{\vphantom {$\tfrac {2}{2}$}} \newcommand {\setchoicedefanswer }[0]{ \ifdefined \HCode \else \let \inlinechoice \inlinechoicedefanswer \fi } \newcommand {\xmsection }[0]{\subsection } \newcommand {\xmsubsection }[0]{\subsubsection } \newcommand {\activitychapter }[1]{ \typeout {ACTIVITYCHAPTER #1} \chapterstyle \activity {#1} } \newcommand {\activitysection }[1]{ \typeout {ACTIVITYSECTION #1} \sectionstyle \activity {#1} } \newcommand {\practicesection }[1]{ \typeout {PRACTICESECTION #1} \sectionstyle \activity {#1} } \newcommand {\figurename }[0]{Figuur} \newcommand {\tablename }[0]{Tabel} \newcommand {\printFull }[0]{ \hintstrue \handoutfalse \toggletrue {showonline} } \newcommand {\nl }[0]{\ \par } \newcommand {\ifonline }[2]{ \begin {onlineOnly}#1\end {onlineOnly}\pdfOnly {#2} } \newcommand {\xmFixFormatLength }[0]{} \newcommand {\xmFixFormat }[1]{\makebox [\xmFixFormatLength ][l]{#1}} \newcommand {\basicSkip }[0]{} \newcommand {\instructorNotes }[0]{\setbox 0\vbox \bgroup } \newcommand {\nlen }[2]{#1} \newcommand {\nlentext }[2]{\text {#1}} \newcommand {\nlentextbf }[2]{\textbf {#1}} \newcommand {\TWaar }[0]{\nlentext { Waar }{ True }} \newcommand {\TOnwaar }[0]{\nlentext { Vals }{ False }} \newcommand {\Ten }[0]{\nlentext { en }{ and }} \newcommand {\Tof }[0]{\nlentext { of }{ or }} \newcommand {\Tdus }[0]{\nlentext { dus }{ so }} \newcommand {\Tendus }[0]{\nlentext { en dus }{ and thus }} \newcommand {\Tvooralle }[0]{\nlentext { voor alle }{ for all }} \newcommand {\Took }[0]{\nlentext { ook }{ also }} \newcommand {\Tals }[0]{\nlentext { als }{ when }} \newcommand {\Twant }[0]{\nlentext { want }{ as }} \newcommand {\Tmaal }[0]{\nlentext { maal }{ times }} \newcommand {\Toptellen }[0]{\nlentext { optellen }{ add }} \newcommand {\Tde }[0]{\nlentext { de }{ the }} \newcommand {\Thet }[0]{\nlentext { het }{ the }} \newcommand {\Tis }[0]{\nlentext { is }{ is }} \newcommand {\Tmet }[0]{\nlentext { met }{ where }} \newcommand {\Tnooit }[0]{\nlentext { nooit }{ never }} \newcommand {\Tmaar }[0]{\nlentext { maar }{ but }} \newcommand {\Tniet }[0]{\nlentext { niet }{ not }} \newcommand {\Tuit }[0]{\nlentext { uit }{ from }} \newcommand {\Ttov }[0]{\nlentext { t.o.v. }{ w.r.t. }} \newcommand {\Tzodat }[0]{\nlentext { zodat }{ such that }} \newcommand {\Tdeth }[0]{\nlentext {de }{th }} \newcommand {\Tomdat }[0]{\nlentext {omdat }{because }} \newcommand {\circuitikz }[0]{\begin {tikzpicture}} \newcommand {\arrowtikz }[0]{ \enspace \begin {tikzpicture}[baseline=-0.7ex] \draw [-Stealth](0,0)--(0.5,0); \end {tikzpicture} \enspace } \newcommand {\arraystretch }[0]{1.4} \newcommand {\cellgape }[0]{} \newcommand {\cellalign }[0]{cc} \newcommand {\cellrotangle }[0]{90} \newcommand {\theadfont }[0]{\footnotesize } \newcommand {\theadset }[0]{} \newcommand {\theadgape }[0]{\gape } \newcommand {\rotheadgape }[0]{} \newcommand {\theadalign }[0]{cc} \newcommand {\bottopstrut }[0]{\gape {\strut }} \newcommand {\topstrut }[0]{\gape [t]{\strut }} \newcommand {\botstrut }[0]{\gape [b]{\strut }} \newcommand {\celldiagratio }[0]{(5,-2)} \newcommand {\tdplotsinandcos }[3]{\pgfmathsetmacro {#1}{sin(#3)}\pgfmathsetmacro {#2}{cos(#3)}} \newcommand {\tdplotdiv }[3]{\pgfmathsetmacro {#1}{#2/#3}} \newcommand {\tdplotcheckdiff }[5]{\par \par \pgfmathparse { abs(#2 -#1)<#3 } \par \ifthenelse {\equal {\pgfmathresult }{1}}{#4}{#5} } \newcommand {\tdplotsetmaincoords }[2]{\pgfmathsetmacro {\tdplotmaintheta }{#1} \pgfmathsetmacro {\tdplotmainphi }{#2} \tdplotcalctransformmainscreen \tikzset {tdplot_main_coords/.style={x={(\raarot cm,\rbarot cm)},y={(\rabrot cm,\rbbrot cm)},z={(\racrot cm,\rbcrot cm)}}}} \newcommand {\tdplotcalctransformmainscreen }[0]{\tdplotsinandcos {\sintheta }{\costheta }{\tdplotmaintheta }\tdplotsinandcos {\sinphi }{\cosphi }{\tdplotmainphi }\tdplotmult {\stsp }{\sintheta }{\sinphi }\tdplotmult {\stcp }{\sintheta }{\cosphi }\tdplotmult {\ctsp }{\costheta }{\sinphi }\tdplotmult {\ctcp }{\costheta }{\cosphi }\pgfmathsetmacro {\raarot }{\cosphi }\pgfmathsetmacro {\rabrot }{\sinphi }\pgfmathsetmacro {\racrot }{0}\pgfmathsetmacro {\rbarot }{-\ctsp }\pgfmathsetmacro {\rbbrot }{\ctcp }\pgfmathsetmacro {\rbcrot }{\sintheta }\pgfmathsetmacro {\rcarot }{\stsp }\pgfmathsetmacro {\rcbrot }{-\stcp }\pgfmathsetmacro {\rccrot }{\costheta }} \newcommand {\tdplotcalctransformrotmain }[0]{\tdplotsinandcos {\sinalpha }{\cosalpha }{\tdplotalpha } \tdplotsinandcos {\sinbeta }{\cosbeta }{\tdplotbeta } \tdplotsinandcos {\singamma }{\cosgamma }{\tdplotgamma } \tdplotmult {\sasb }{\sinalpha }{\sinbeta } \tdplotmult {\sbsg }{\sinbeta }{\singamma } \tdplotmult {\sasg }{\sinalpha }{\singamma } \tdplotmult {\sasbsg }{\sasb }{\singamma } \tdplotmult {\sacb }{\sinalpha }{\cosbeta } \tdplotmult {\sacg }{\sinalpha }{\cosgamma } \tdplotmult {\sbcg }{\sinbeta }{\cosgamma } \tdplotmult {\sacbsg }{\sacb }{\singamma } \tdplotmult {\sacbcg }{\sacb }{\cosgamma } \tdplotmult {\casb }{\cosalpha }{\sinbeta } \tdplotmult {\cacb }{\cosalpha }{\cosbeta } \tdplotmult {\cacg }{\cosalpha }{\cosgamma } \tdplotmult {\casg }{\cosalpha }{\singamma } \tdplotmult {\cacbsg }{\cacb }{\singamma } \tdplotmult {\cacbcg }{\cacb }{\cosgamma } \pgfmathsetmacro {\raaeul }{\cacbcg -\sasg } \pgfmathsetmacro {\rabeul }{-\cacbsg -\sacg } \pgfmathsetmacro {\raceul }{\casb } \pgfmathsetmacro {\rbaeul }{\sacbcg + \casg } \pgfmathsetmacro {\rbbeul }{-\sacbsg + \cacg } \pgfmathsetmacro {\rbceul }{\sasb } \pgfmathsetmacro {\rcaeul }{-\sbcg } \pgfmathsetmacro {\rcbeul }{\sbsg } \pgfmathsetmacro {\rcceul }{\cosbeta } } \newcommand {\tdplotcalctransformmainrot }[0]{\tdplotsinandcos {\sinalpha }{\cosalpha }{\tdplotalpha } \tdplotsinandcos {\sinbeta }{\cosbeta }{\tdplotbeta } \tdplotsinandcos {\singamma }{\cosgamma }{\tdplotgamma } \tdplotmult {\sasb }{\sinalpha }{\sinbeta } \tdplotmult {\sbsg }{\sinbeta }{\singamma } \tdplotmult {\sasg }{\sinalpha }{\singamma } \tdplotmult {\sasbsg }{\sasb }{\singamma } \tdplotmult {\sacb }{\sinalpha }{\cosbeta } \tdplotmult {\sacg }{\sinalpha }{\cosgamma } \tdplotmult {\sbcg }{\sinbeta }{\cosgamma } \tdplotmult {\sacbsg }{\sacb }{\singamma } \tdplotmult {\sacbcg }{\sacb }{\cosgamma } \tdplotmult {\casb }{\cosalpha }{\sinbeta } \tdplotmult {\cacb }{\cosalpha }{\cosbeta } \tdplotmult {\cacg }{\cosalpha }{\cosgamma } \tdplotmult {\casg }{\cosalpha }{\singamma } \tdplotmult {\cacbsg }{\cacb }{\singamma } \tdplotmult {\cacbcg }{\cacb }{\cosgamma } \pgfmathsetmacro {\raaeul }{\cacbcg -\sasg } \pgfmathsetmacro {\rabeul }{\sacbcg + \casg } \pgfmathsetmacro {\raceul }{-\sbcg } \pgfmathsetmacro {\rbaeul }{-\cacbsg -\sacg } \pgfmathsetmacro {\rbbeul }{-\sacbsg + \cacg } \pgfmathsetmacro {\rbceul }{\sbsg } \pgfmathsetmacro {\rcaeul }{\casb } \pgfmathsetmacro {\rcbeul }{\sasb } \pgfmathsetmacro {\rcceul }{\cosbeta } } \newcommand {\tdplotsetrotatedcoords }[3]{\pgfmathsetmacro {\tdplotalpha }{#1} \pgfmathsetmacro {\tdplotbeta }{#2} \pgfmathsetmacro {\tdplotgamma }{#3} \tdplotcalctransformrotmain \par \tdplotmult {\raaeaa }{\raarot }{\raaeul } \tdplotmult {\rabeba }{\rabrot }{\rbaeul } \tdplotmult {\raceca }{\racrot }{\rcaeul } \tdplotmult {\raaeab }{\raarot }{\rabeul } \tdplotmult {\rabebb }{\rabrot }{\rbbeul } \tdplotmult {\racecb }{\racrot }{\rcbeul } \tdplotmult {\raaeac }{\raarot }{\raceul } \tdplotmult {\rabebc }{\rabrot }{\rbceul } \tdplotmult {\racecc }{\racrot }{\rcceul } \tdplotmult {\rbaeaa }{\rbarot }{\raaeul } \tdplotmult {\rbbeba }{\rbbrot }{\rbaeul } \tdplotmult {\rbceca }{\rbcrot }{\rcaeul } \tdplotmult {\rbaeab }{\rbarot }{\rabeul } \tdplotmult {\rbbebb }{\rbbrot }{\rbbeul } \tdplotmult {\rbcecb }{\rbcrot }{\rcbeul } \tdplotmult {\rbaeac }{\rbarot }{\raceul } \tdplotmult {\rbbebc }{\rbbrot }{\rbceul } \tdplotmult {\rbcecc }{\rbcrot }{\rcceul } \pgfmathsetmacro {\raarc }{\raaeaa + \rabeba + \raceca } \pgfmathsetmacro {\rabrc }{\raaeab + \rabebb + \racecb } \pgfmathsetmacro {\racrc }{\raaeac + \rabebc + \racecc } \pgfmathsetmacro {\rbarc }{\rbaeaa + \rbbeba + \rbceca } \pgfmathsetmacro {\rbbrc }{\rbaeab + \rbbebb + \rbcecb } \pgfmathsetmacro {\rbcrc }{\rbaeac + \rbbebc + \rbcecc } \tikzset {tdplot_rotated_coords/.append style={x={(\raarc cm,\rbarc cm)},y={(\rabrc cm,\rbbrc cm)},z={(\racrc cm,\rbcrc cm)}}}} \newcommand {\tdplotsetrotatedcoordsorigin }[1]{\tikzset {tdplot_rotated_coords/.append style={shift=#1}}} \newcommand {\tdplotresetrotatedcoordsorigin }[0]{\tikzset {tdplot_rotated_coords/.append style={shift={(0,0,0)}}}} \newcommand {\tdplotsetthetaplanecoords }[1]{\tdplotresetrotatedcoordsorigin \tdplotsetrotatedcoords {270 + #1}{270}{0}} \newcommand {\tdplotsetrotatedthetaplanecoords }[1]{\tdplotsetrotatedcoords {\tdplotalpha }{\tdplotbeta }{\tdplotgamma + #1}\tikzset {tdplot_rotated_coords/.append style={y={(\raarc cm,\rbarc cm)},z={(\rabrc cm,\rbbrc cm)},x={(\racrc cm,\rbcrc cm)}}}} \newcommand {\tdplotsetpolarplotrange }[4]{\pgfmathsetmacro {\tdplotlowerphi }{#3} \pgfmathsetmacro {\tdplotupperphi }{#4} \pgfmathsetmacro {\tdplotlowertheta }{#1} \pgfmathsetmacro {\tdplotuppertheta }{#2} } \newcommand {\tdplotresetpolarplotrange }[0]{\pgfmathsetmacro {\tdplotlowerphi }{0} \pgfmathsetmacro {\tdplotupperphi }{360} \pgfmathsetmacro {\tdplotlowertheta }{0} \pgfmathsetmacro {\tdplotuppertheta }{180} } \newcommand {\tdplotgetpolarcoords }[3]{\pgfmathsetmacro {\vxcalc }{#1} \pgfmathsetmacro {\vycalc }{#2} \pgfmathsetmacro {\vzcalc }{#3} \pgfmathsetmacro {\vcalc }{ sqrt((\vxcalc )^2 + (\vycalc )^2 + (\vzcalc )^2) } \par \pgfmathsetmacro {\vxycalc }{ sqrt((\vxcalc )^2 + (\vycalc )^2) } \par \pgfmathsetmacro {\tdplotrestheta }{asin(\vxycalc /\vcalc )} \pgfmathparse {\vzcalc <0} \ifthenelse {\equal {\pgfmathresult }{1}}{\pgfmathsetmacro {\tdplotrestheta }{180 -\tdplotrestheta } } {} \ifthenelse {\equal {\vxcalc }{0.0}}{\pgfmathparse {\vycalc <0} \ifthenelse {\equal {\pgfmathresult }{1}}{\pgfmathsetmacro {\tdplotresphi }{270} } {\pgfmathparse {\vycalc >0} \ifthenelse {\equal {\pgfmathresult }{1}}{\pgfmathsetmacro {\tdplotresphi }{90} } {\pgfmathsetmacro {\tdplotresphi }{0} } } } {\pgfmathsetmacro {\tdplotresphi }{atan(\vycalc /\vxcalc )} \pgfmathparse {\vxcalc <0} \ifthenelse {\equal {\pgfmathresult }{1}}{\pgfmathsetmacro {\tdplotresphi }{\tdplotresphi +180} } { } \par \pgfmathparse {\tdplotresphi <0} \ifthenelse {\equal {\pgfmathresult }{1}}{\pgfmathsetmacro {\tdplotresphi }{\tdplotresphi +360} } {} } } \newcommand {\myoplus }[0]{\begin {tikzpicture}[scale=0.5] \draw (0,0) circle [radius=0.2cm]; \draw (-0.13,0) --(0.13,0); \draw (0,-0.13) --(0,0.13); \end {tikzpicture}} \newcommand {\myominus }[0]{\begin {tikzpicture}[scale=0.5] \draw (0,0) circle [radius=0.2cm]; \draw (-0.13,0) --(0.13,0); \end {tikzpicture}} \newcommand {\myoplus }[0]{\scalebox {0.5}{ \tikz [baseline=(char.base)]{ \node [shape=circle,draw,inner sep=0pt] (char) {$+$}; } } } \newcommand {\myominus }[0]{\scalebox {0.5}{ \tikz [baseline=(char.base)]{ \node [shape=circle,draw,inner sep=0pt] (char) {$-$}; } } } \newcommand {\myocharge }[1]{\scalebox {0.5}{ \tikz [baseline=(char.base)]{ \node [shape=circle,draw,inner sep=1pt] (char) {$#1$}; } } } \newcommand {\tikzitOptions }[0]{} \newcommand {\tikzitOptions }[0]{[scale=1.5,transform shape]} \newcommand {\xmlabel }[1]{\label {#1}} \newcommand {\xmlevel }[1]{} \newcommand {\xmusedin }[1]{} \newcommand {\xmtopic }[1]{}$

De covalente binding (atoombinding)

Een covalente binding (ook atoombinding genoemd) is een chemische binding tussen twee niet-metaal atomen die een elektronenpaar met elkaar gemeenschappelijk stellen.

Bij een gewone covalente binding stellen beide bindingspartners elk een ongepaard elektron ter beschikking.

Bij een datief covalente binding komen de (twee) bindende elektronen van hetzelfde atoom (de elektronendonor).

Beide bindingspartners van de covalente binding zijn elektronegatief en hebben geen neiging om elektronen af te geven. Ze willen beide eerder extra elektronen opnemen ter vorming van een stabiele edelgasconfiguratie. De enige mogelijkheid voor deze atomen om allebei extra elektronen op te nemen is hun elektronen gemeenschappelijk te gebruiken. Ze stellen elk ongepaarde valentie-elektronen gemeenschappelijk ter beschikking en vormen een bindend elektronenpaar dat de twee atomen samenhoudt.

Waterstofchloride (HCl) bevat een covalente binding tussen H en Cl:

Beide bindingspartners kunnen elk 1, 2 of 3 ongepaarde elektronen ter beschikking stellen en vormen zo met hun bindingspartner een enkelvoudige, dubbele of drievoudige binding.

Vorming van een enkelvoudige covalente binding in waterstofchloride ( $\ce {HCl}$ ).

De elektronenconfiguraties van $\ce {H}$ en $\ce {Cl}$ zijn

$\ce {H}$ :	$1s^{\blue {1}}$
$\ce {Cl}$ :	$1s^2\ 2s^2\ 2p^6\ 3s^2\ 3p_x^2\ 3p_y^2\ 3p_z^{\blue {1}}$

en de twee ongepaarde elektronen vormen samen een binding:

Vorming van een drievoudige covalente binding in stikstofgas ( $\ce {N2}$ ).

De elektronenconfiguratie van $\ce {N}$ is $1s^2\ 2s^2\ 2p_x^{\blue {1}}\ 2p_y^{\blue {1}}\ 2p_z^{\blue {1}}$

en de twee keer drie ongepaarde elektronen vormen samen een drievoudige binding:

Welk type binding verwacht je aan te treffen in onderstaande verbindingen?

$\ce {CO2}$ bevat .

Het molecule bevat enkel niet-metalen.

$\ce {CoCl2}$ bevat .

Het molecule bevat zowel metalen als niet-metalen.

$\ce {Al}$ bevat .

Aluminium en andere metalen komen niet voor als een enkel atoom maar als een metaalrooster. Hierin zijn de atomen gebonden aan hun buren met ...

$\ce {H2SO4}$ bevat .

Ook al bevat het molecule meer dan twee verschillende elementen, elk ervan is een niet-metaal dus de enige mogelijke bindingen zijn ...

$\ce {He}$ bevat .

Als edelgas zal dit deeltje geen bindingen aangaan met buren.

Welke van de volgende uitspraken over een verbinding bestaande uit een combinatie van metaal en niet-metaal atomen kunnen waar zijn?

I.: Deze verbinding bestaat uitsluitend uit ionbindingen.
II.: Deze verbinding bestaat uitsluitend uit covalente bindingen.
III.: Deze verbinding bestaat uit zowel ionbindingen als covalente bindingen.

Laten we twee voorbeelden bekijken:

Als eerste $\ce {NaCl}$ : Hier is $\ce {Na}$ een metaal en $\ce {Cl}$ een niet-metaal, en beiden zijn aan elkaar verbonden via een ionbinding. Er zijn geen andere bindingen dus stelling I kan waar zijn.

Daarnaast kunnen we ook $\ce {Na2SO4}$ beschouwen. Deze verbinding bevat naast ionbindingen tussen de $\ce {Na}$ atomen en de sulfaat groep, eveneens covalente bindingen tussen de $\ce {S}$ en $\ce {O}$ atomen. Uitspraak III kan dus ook waar zijn.

Een metaal en een niet-metaal zijn steeds via een ionbinding aan elkaar gebonden. Er moet dus in deze verbinding minstens 1 ionbinding voorkomen. Uitspraak II kan nooit waar zijn.

Daarom besluiten we dat optie D correct is.

Bij een datief covalente binding (ook coördinatief covalente binding) komen de (twee) bindende elektronen van hetzelfde atoom (de elektronendonor). De datief covalente binding verschilt enkel van de ’gewone’ covalente binding door de manier waarop ze tot stand komt. Nadat de binding gevormd is kan er geen onderscheid meer gemaakt worden.

De datieve binding wordt soms weergegeven met behulp van een pijltje in de richting van elektronendonor naar elektronenacceptor.

De verbinding chlorigzuur ( $\ce {HClO2}$ ) bevat naast twee enkelvoudige gewone covalente bindingen eveneens een datief covalente binding tussen Cl en O (voorgesteld door de pijl). Cl stelt een elektronenpaar ter beschikking en is de elektronendonor terwijl O de elektronen van Cl ontvangt en is de elektronenacceptor.

2024-06-12 21:20:38

Press...	...to do
left/right arrows	Move cursor
shift+left/right arrows	Select region
ctrl+a	Select all
ctrl+x/c/v	Cut/copy/paste
ctrl+z/y	Undo/redo
ctrl+left/right	Add entry to list or column to matrix
shift+ctrl+left/right	Add copy of current entry/column to to list/matrix
ctrl+up/down	Add row to matrix
shift+ctrl+up/down	Add copy of current row to matrix
ctrl+backspace	Delete current entry in list or column in matrix
ctrl+shift+backspace	Delete current row in matrix

Type...	...to get
norm	$\|\|\blue{[?]}\|\|$
text	$\text{\blue{[?]}}$
sym_name	$\backslash\texttt{\blue{[?]}}$
abs	$\left\|\blue{[?]}\right\|$
sqrt	$\sqrt{\blue{[?]}}$
paren	$\left(\blue{[?]}\right)$
floor	$\lfloor \blue{[?]} \rfloor$
factorial	$\blue{[?]}!$
exp	${\blue{[?]}}^{\blue{[?]}}$
sub	${\blue{[?]}}_{\blue{[?]}}$
frac	$\dfrac{\blue{[?]}}{\blue{[?]}}$
int	$\displaystyle\int{\blue{[?]}}d\blue{[?]}$
defi	$\displaystyle\int_{\blue{[?]}}^{\blue{[?]}}\blue{[?]}d\blue{[?]}$
deriv	$\displaystyle\frac{d}{d\blue{[?]}}\blue{[?]}$
sum	$\displaystyle\sum_{\blue{[?]}}^{\blue{[?]}}\blue{[?]}$
prod	$\displaystyle\prod_{\blue{[?]}}^{\blue{[?]}}\blue{[?]}$
root	$\sqrt[\blue{[?]}]{\blue{[?]}}$
vec	$\left\langle \blue{[?]} \right\rangle$
mat	$\left(\begin{matrix} \blue{[?]} \end{matrix}\right)$
*	$\cdot$
infinity	$\infty$
arcsin	$\arcsin\left(\blue{[?]}\right)$
arccos	$\arccos\left(\blue{[?]}\right)$
arctan	$\arctan\left(\blue{[?]}\right)$
sin	$\sin\left(\blue{[?]}\right)$
cos	$\cos\left(\blue{[?]}\right)$
tan	$\tan\left(\blue{[?]}\right)$
sec	$\sec\left(\blue{[?]}\right)$
csc	$\csc\left(\blue{[?]}\right)$
cot	$\cot\left(\blue{[?]}\right)$
log	$\log\left(\blue{[?]}\right)$
ln	$\ln\left(\blue{[?]}\right)$
alpha	$\alpha$
beta	$\beta$
gamma	$\gamma$
delta	$\delta$
epsilon	$\epsilon$
zeta	$\zeta$
eta	$\eta$
theta	$\theta$
iota	$\iota$
kappa	$\kappa$
lambda	$\lambda$
mu	$\mu$
nu	$\nu$
xi	$\xi$
omicron	$\omicron$
pi	$\pi$
rho	$\rho$
sigma	$\sigma$
tau	$\tau$
upsilon	$\upsilon$
phi	$\phi$
chi	$\chi$
psi	$\psi$
omega	$\omega$
Gamma	$\Gamma$
Delta	$\Delta$
Theta	$\Theta$
Lambda	$\Lambda$
Xi	$\Xi$
Pi	$\Pi$
Sigma	$\Sigma$
Phi	$\Phi$
Psi	$\Psi$
Omega	$\Omega$

De covalente binding (atoombinding)

Controls

Symbols

Settings