Chapter 20, Problem 20.53E

Interpretation Introduction

(a)

Interpretation:

The change in the concentration of hydrogen ions is to be calculated.

Concept introduction:

The concentration of hydrogen ion is calculated by the value of $\text{pH}$ of the solution. The change in the concentration of hydrogen ion is calculated by the difference between the initial and final concentration of hydrogen ions present in the solution.

Answer to Problem 20.53E

The change in the hydrogen ion concentration is $9\times {10}^{-7}$.

Explanation of Solution

The concentration of hydrogen ions in a solution is calculated by the following formula.

$\left[{\text{H}}^{+}\right]=1\times {10}^{-\text{pH}}$…(1)

It is given that the initial $\text{pH}$ of substrate solution is $7.0$.

Substitute the value of initial $\text{pH}$ in equation (1).

$\left[{\text{H}}^{+}\right]=1\times {10}^{-7}$

Therefore, the initial concentration of hydrogen ions are $1\times {10}^{-7}$.

It is given that the $\text{pH}$ of solution after $1\min$ is $6.0$.

Substitute the value of initial $\text{pH}$ in equation (1).

$\left[{\text{H}}^{+}\right]=1\times {10}^{-6}$

Therefore, the final concentration of hydrogen ions are $1\times {10}^{-6}$.

The change in the concentration of hydrogen ion is calculated by the following formula.

$\text{Change}\text{in}\text{concentration}=\left(\begin{array}{l}\text{Final}\text{concentration}\text{of}\text{hydrogen}\text{ions}-\\ \text{Initial}\text{concentraion}\text{of}\text{hydrogen}\text{ions}\end{array}\right)$

The initial concentration of hydrogen ions are $1\times {10}^{-7}$.

The final concentration of hydrogen ions are $1\times {10}^{-6}$.

Substitute the value of initial and final concentration of hydrogen ions in the above equation.

$\begin{array}{rll}\text{Change}\text{in}\text{concentration}& =& \left(1\times {10}^{-6}-1\times {10}^{-7}\right)\\ & =& {10}^{-7}\left(10-1\right)\\ & =& 9\times {10}^{-7}\end{array}$

Therefore, the change in the hydrogen ion concentration is $9\times {10}^{-7}$.

Conclusion

The change in the hydrogen ion concentration is $9\times {10}^{-7}$.

Interpretation Introduction

(b)

Interpretation:

The number of molecules of substrate reacted to cause the change in hydrogen ion concentration is to be calculated.

Concept introduction:

The concentration of hydrogen ion is calculated by the value of $\text{pH}$ of the solution. The change in the concentration of hydrogen ion is calculated by the difference between the initial and final concentration of hydrogen ions present in the solution.

Answer to Problem 20.53E

The number of molecules of substrate reacted to cause the change in hydrogen ion concentration is $5.42\times {10}^{17}$.

Explanation of Solution

The number of molecules of substrate reacted to cause the change in hydrogen ion concentration is calculated by the following formula.

$\text{Number}\text{of}\text{molecules}=\text{Change in the hydrogen ion concentration}\times {\text{N}}_{\text{A}}$…(2)

Where,

• ${\text{N}}_{\text{A}}$ is Avogadro number.

The value of ${\text{N}}_{\text{A}}$ is $6.023\times {10}^{23}$.

The change in the hydrogen ion concentration is $9\times {10}^{-7}$.

Substitute the value of hydrogen ion concentration and Avogadro number in equation (2).

$\begin{array}{rll}\text{Number}\text{of}\text{molecules}& =& 9\times {10}^{-7}\times 6.023\times {10}^{23}\\ & =& 54.207\times {10}^{16}\\ & =& 5.42\times {10}^{17}\end{array}$

Therefore, the number of molecules of substrate reacted to cause the change in hydrogen ion concentration is $5.42\times {10}^{17}$.

Conclusion

The number of molecules of substrate reacted to cause the change in hydrogen ion concentration is $5.42\times {10}^{17}$.

Interpretation Introduction

(c)

Interpretation:

The turnover number of enzyme is to be calculated.

Concept introduction:

Enzymes are the biocatalysts. Enzyme enhances the activity of biochemical process. For increasing the rate of biochemical reaction, enzyme should be biologically active. Turnover number is the maximum number of substrate molecule converted by an enzyme in one second.

Answer to Problem 20.53E

The turnover number of enzyme is $9.03\times {10}^{15}{\sec }^{-1}$.

Explanation of Solution

The turnover number is calculated by the following formula.

$\text{Turnover}\text{number}=\frac{\text{Number}\text{of}\text{molecules}\text{reacted}}{\text{Time}\left(\min \right)\times 60\sec }$…(3)

The number of molecules of substrate reacted is $5.42\times {10}^{17}$.

It is given that the time of reaction is $1\min$.

Substitute the value of time and number of molecules reacted in equation (3).

$\begin{array}{rll}\text{Turnover}\text{number}& =& \frac{5.42\times {10}^{17}}{1\times 60\sec }\\ & =& 0.0903\times {10}^{17}{\sec }^{-1}\\ & =& 9.03\times {10}^{15}{\sec }^{-1}\end{array}$

Therefore, the turnover number of enzyme is $9.03\times {10}^{15}{\sec }^{-1}$.

Conclusion

The turnover number of enzyme is $9.03\times {10}^{15}{\sec }^{-1}$.