Chapter 4, Problem 1Q

Summary Introduction

To review:

The value of $\Delta G\text{'}$ for the hydrolysis of ATP (adenosine triphosphate), when the concentration (mM) of ATP, ADP (adenosine diphosphate), and Pi (inorganic phosphate) is: 4.0, 1.35, and 4.65 mM, respectively. Temperature is $\text{37°C}$, pH is 7, and $\text{Δ}{G}^{\text{0'}}$ is –3.05 kJ/mol.

Introduction:

In living cells, the concentration of ATP and the product of hydrolysis of ATP (ADP and Pi) islower than that of the standard 1 M concentrations. This is the reason why the actual free energy of ATP hydrolysis differs from the standard free energy. So, it is difficult to obtain an accurate measure of the concentrations of cellular components.

Explanation of Solution

As per the given data, the actual $\Delta G\text{'}$ for hydrolysis of ATP can be calculated as:

$$$\Delta G\text{'}=\Delta G\text{°'+RTln}\frac{\left[\text{ADP}\right]\left[\text{Pi}\right]}{\left[\text{ATP}\right]}$

Using the values, as given in the statement. The equation becomes:

$\Delta G\text{'}=-30.5+8.134\text{j/mol}\times 310\ln \frac{\left[0.00135\right]\left[0.00465\right]}{\left[0.004\right]}$

The values of ATP, ADP, and Pi are given in mM. So, to covert, these values in M divide each value by 1000. The resulting values obtained would be: 0.004, 0.00135, and 0.00465 for ATP. ADP, and Pi, respectively. Here, R is the gas constant and its value is 8.134 j/mol. The temperature was given in Celsius and has been converted into kelvin for calculation. ( $\text{37°C}\text{+}\text{273}\text{=}\text{310}\text{K}$ ). So, the equation becomes:

$\Delta G\text{'}=-30.5+8.134\text{j/mol}\times 310\ln \frac{\left[0.00135\right]\left[0.00465\right]}{\left[0.004\right]}$

$\Delta G\text{'}=-30.5+2.577(\ln 0.00157)$

$\Delta G\text{'}=-30.5-16.64$

$\Delta G\text{'}=-47.14\text{kj/mol}$

From the above calculation, the actual $\Delta G\text{'}$ for hydrolysis of ATP at $37°$ C and neutral pH is calculated as –47.14 kJ/mol.

Conclusion

Thus, it can be concluded that at a certain concentration of ATP, the actual value of $\Delta G\text{'}$ can bedetermined. From the given data, the actual value of $\Delta G\text{'}$ is –47.14 kJ/mol.