Đáp án đúng: A
Cách 1:
Gọi số mắc xích của Gly là x và Lys là y ta có CTTQ của E là
$\displaystyle $$\displaystyle {{C}_{2x+\,6y}}{{H}_{3x\,+\,12y\,+\,2}}{{O}_{x+\,y+\,1}}{{N}_{x+\,2y}}\xrightarrow{{{O}_{2}},{{t}^{0}}}\ (2x+6y)C{{O}_{2}}\,\,+\,\,(1,5x+6y+1){{H}_{2}}O$
Ta có:
$\left\{ \begin{array}{l}{{n}_{C{{O}_{2}}}}={{n}_{{{H}_{2}}O}}\to 2x+\,6y=\frac{3x+12y+2}{2}\\{{n}_{NaOH}}={{n}_{E}}.(x+y)\to \frac{14,88}{57\text{x}+128y+3}(x+y)=0,18\end{array} \right.$
$\Rightarrow \left\{ \begin{array}{l}x=2\\y=0,7353\end{array} \right.\Rightarrow {{n}_{E}}=0,0658\ mol$
$\displaystyle \xrightarrow{BT:\ Gly-Lys}\left\{ \begin{array}{l}{{n}_{GlyNa}}=x{{n}_{E}}=0,1316\,mol\\{{n}_{LysNa}}=y{{n}_{E}}=0,0484\,mol\end{array} \right.$
⇒ a/b = 1,57
Cách 2:
Ta có :$\displaystyle Gl{{y}_{m}}Ly{{s}_{n}}(E)+{{H}_{2}}O\xrightarrow{{{H}^{+}}}mGly+nLys$
$\Rightarrow {{n}_{C{{O}_{2}}}}={{n}_{{{H}_{2}}O}}\,\Rightarrow \,0,5x+y=z\ (1)$
$\left\{ \begin{array}{l}\xrightarrow{BTKL}75{{n}_{Gly}}+146{{n}_{Lys}}={{m}_{E}}+18{{n}_{{{H}_{2}}O}}\\\xrightarrow{BT:\ Na}{{n}_{GlyNa}}+{{n}_{LysNa}}={{n}_{NaOH}}\,\,\end{array} \right.\,$
$\Rightarrow \left\{ \begin{array}{l}75x+146y=14,88+18z\\x+y=0,18\end{array} \right.\,\,\,(2)$
Từ (1), (2) ta tính được:$\displaystyle x=\,0,1316\ mol\ ;\ y=0,0484\ mol;\ z=0,1141\ mol$.
Vậy a/b = 1,57.
Cách 3:
+ Ta có:
và ${{C}_{6}}{{H}_{12}}{{O}_{2}}{{N}_{2}}(Lys)\xrightarrow{{}}{{C}_{2}}{{H}_{3}}ON+{{(C{{H}_{2}})}_{4}}NH+{{H}_{2}}O$
$+\ E\left\{ \begin{array}{l}{{C}_{2}}{{H}_{3}}ON:\,x\,mol\\{{H}_{2}}O:\,y\,mol\\{{(C{{H}_{2}})}_{4}}NH:\,z\,mol\end{array} \right.\xrightarrow{{{O}_{2}},\,{{t}^{0}}}\left\{ \begin{array}{l}\xrightarrow{BT:\,C}{{n}_{C{{O}_{2}}}}=2x+4z\\\xrightarrow{BT:\,{{H}_{2}}}{{n}_{{{H}_{2}}O}}=1,5x+4,5z+y\end{array} \right.$
Mà${{n}_{{{H}_{2}}O}}={{n}_{C{{O}_{2}}}}\Rightarrow 0,5\text{x}-0,5\text{z}=y\ (1)$
+ Ta có :
$x={{n}_{NaOH}}=0,18\ mol\xrightarrow{BTKL}71{{n}_{{{(C{{H}_{2}})}_{4}}NH}}+18{{n}_{{{H}_{2}}O}}={{m}_{E}}-57{{n}_{{{C}_{2}}{{H}_{3}}ON}}$
$\Rightarrow 71x+18y=4,62\,(2)$
+ Từ (1), (2) ta tính được:
$\displaystyle \left\{ \begin{array}{l}y=0,0658\ mol\\z=0,0484\ mol\end{array} \right.$
$\displaystyle \Rightarrow \left\{ \begin{array}{l}{{n}_{GlyNa}}=x-z=0,1316\,mol\\{{n}_{LysNa}}=z=0,0484\ mol\end{array} \right.$
⇒ a/b = 1,57.
