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Question: What is the pH of \(0.01 \text{M}\) glycine solution? For glycine \(K_{a_{1}}=4.5 \times 10^{-3}\...

What is the pH of 0.01M0.01 \text{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 298K298 \text{K}
A. 3.03.0
B. 10.010.0
C. 7.067.06
D. 8.28.2

Explanation

Solution

We know that the dissociation constant for the complete reaction process is calculated by multiplying the dissociation constant of first and the second step. Thus we can say that the overall dissociation constant is used to calculate the hydrogen ion concentration.

Complete step by step answer:
We can take the given value of Ka1K_{a_{1}} and Ka2K_{a_{2}} from the question which are 4.5×10−34.5 \times 10^{-3} and 1.7×10−101.7 \times 10^{-10} respectively. The overall value of the dissociation constant is calculated as shown below.

K=Ka×Ka2 =4.5×10−3×1.7×10−10 =7.65×10−13\begin{aligned} K &=K_{a} \times K_{a_{2}} \\\ &=4.5 \times 10^{-3} \times 1.7 \times 10^{-10} \\\ &=7.65 \times 10^{-13} \end{aligned}

We know that the hydrogen ion concentration is calculated by the relation shown as follows. We will substitute the value of dissociation constant and the concentration of acid to calculate the value of hydrogen ion concentration.
[H+]=K×c =7.65×10−13×0.01M =8.74×10−8M\begin{aligned}\left[\mathrm{H}^{+}\right] &=\sqrt{K \times c} \\\ &=\sqrt{7.65 \times 10^{-13} \times 0.01 \mathrm{M}} \\\ &=8.74 \times 10^{-8} \mathrm{M} \end{aligned}

Now, it is known that the pH is negative logarithm of hydrogen ion concentration, therefore, by putting the value of hydrogen ion concentration in the relation we can calculate the value of pH of the glycine solution which is shown as follows.
pH=−log⁡[H+] =−log⁡(8.74×10−8) =7.06\begin{aligned} \mathrm{pH} &=-\log \left[\mathrm{H}^{+}\right] \\\ &=-\log \left(8.74 \times 10^{-8}\right) \\\ &=7.06 \end{aligned}

Thus, we can say that the correct option is C.

Note:
We know that the pH of any solution depends on the hydrogen ion concentration present in it. We can say that when there is the greater hydrogen ion concentration, the magnitude of the pH will be smaller for the solution and thus we conclude about the nature of the solution depending upon the magnitude of the power of hydrogen.