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Question: What is the pH of 0.01 M glycine solution? For glycine, \(K{a_1} = 4.5 \times {10^{ - 3}}\) and \(K{...

What is the pH of 0.01 M glycine solution? For glycine, Ka1=4.5×10−3K{a_1} = 4.5 \times {10^{ - 3}} and Ka2=1.7×10−10K{a_2} = 1.7 \times {10^{ - 10}} at 298 K.
(1) 3.0
(2) 10.0
(3) 6.1
(4) 7.2

Explanation

Solution

In order to solve this problem first of all we have to find the total rate constant using K=Ka1+Kb1K = K{a_1} + K{b_1} and then we are going to substitute the value of acidic constant in the above equation.After that we are going to find hydrogen ion concentration and with the help of these we can find the value of pH.

Formula used-
i.K=Ka1+Kb1K = K{a_1} + K{b_1}
ii.H+=K.C{H^ + } = \sqrt {K.C}
iii.pH=−log⁡[H+]pH = - \log [{H^ + }]

Complete step by step answer:
Given,
Molarity of the solution = 0.01 M.
Ka1=4.5×10−3K{a_1} = 4.5 \times {10^{ - 3}}
Ka2=1.7×10−10K{a_2} = 1.7 \times {10^{ - 10}}
Temperature = 298 K.
The total rate constant is calculated as shown below.
K=Ka1+Kb1K = K{a_1} + K{b_1}
Substitute the value of Ka1K{a_1} and Ka2K{a_2} in the above equation.
K=(4.5×10−3)×(1.7×10−10)K = (4.5 \times {10^{ - 3}}) \times (1.7 \times {10^{ - 10}})
⇒K=7.74×10−13\Rightarrow K = 7.74 \times {10^{ - 13}}
The hydrogen ion concentration is calculated by the formula as shown below.
H+=K.C{H^ + } = \sqrt {K.C}
Where
H+{H^ + } is hydrogen ion concentration.
K is the rate constant
C is the concentration.
To calculate the H+{H^ + } ion concentration, substitute the values of rate constant and concentration in the equation.
H+=(7.74×10−13)×0.01{H^ + } = \sqrt {(7.74 \times {{10}^{ - 13}}} ) \times 0.01
⇒H+=8.79×10−8\Rightarrow {H^ + } = 8.79 \times {10^{ - 8}}
The pH of the solution is calculated by the formula as shown below.
pH=−log⁡[H+]pH = - \log [{H^ + }]
To calculate the pH of the solute, substitute the value of H+{H^ + } in the above equation.
pH=−log⁡[8.79×10−8]pH = - \log [8.79 \times {10^{ - 8}}]
⇒pH=−(log⁡10−8+log⁡8.7)\Rightarrow pH = - (\log {10^{ - 8}} + \log 8.7)
⇒pH=8−0.93\Rightarrow pH = 8 - 0.93
∴pH=7.07≈7.1\therefore pH = 7.07 \approx 7.1
Thus, the pH of 0.01 M glycine is 7.1.

Therefore, the correct option is 4.

Note: Glycine is the amino acid which is amphoteric in nature which means it can behave as acid as well as base. Glycine has a single hydrogen atom present in the side chain. At low pH the molecule starts protonating with pKap{K_a} value 2.4 and at high pH the molecule loses its proton with pKap{K_a} value 9.6.