(I) At pH = 2
(highly acidic), the structure of the peptide will be as shown below.
Net charge +2
|Z1| = 2 at pH = 2
(ii) At pH = 6 (neutral solution)
In neutral medium, the given tripeptide exists as Zwitter ion.
net charge = 0
|Z2| = 0 at pH = 6
(iii)At pH = 11 (basic medium)
In basic medium the given tripeptide exists in anionic form.
Net charge = β3
So, |Z3| = |-3|
|Z1| + |Z2| + |Z3| = 2 + 0 + 3 = 5
A temperature difference can generate e.m.f. in some materials. Let $ S $ be the e.m.f. produced per unit temperature difference between the ends of a wire, $ \sigma $ the electrical conductivity and $ \kappa $ the thermal conductivity of the material of the wire. Taking $ M, L, T, I $ and $ K $ as dimensions of mass, length, time, current and temperature, respectively, the dimensional formula of the quantity $ Z = \frac{S^2 \sigma}{\kappa} $ is:
Let $ a_0, a_1, ..., a_{23} $ be real numbers such that $$ \left(1 + \frac{2}{5}x \right)^{23} = \sum_{i=0}^{23} a_i x^i $$ for every real number $ x $. Let $ a_r $ be the largest among the numbers $ a_j $ for $ 0 \leq j \leq 23 $. Then the value of $ r $ is ________.
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