Question

A critical reaction in the production of energy to do work or drive chemical reactions in biological systems is the hydrolysis of adenosine triphosphate, ATP, to adenosine diphosphate, ADP, as described by:

ATP(aq) + H2O(l) <----> ADP(aq) + HPO42-(aq)
for which delta Gorxn = - 30.50 kJ/mol at 37.0 oC and pH 7.0. Calculate the value of delta Grxn in a biological cell at human body temperature in which the concentrations of ATP, ADP, and HPO42- are 5.6 mM, 0.3 mM, and 4.98 mM, respectively.

Report your answer in units of kJ/mol to 2 decimal places.

Answer 1

Alright fam, let's dive into this biochem stuff. It's all about energy, which is something we can all vibe with, right?

First up, we got the standard change in Gibbs free energy (ΔGº). That's like the default energy change happening when ATP breaks up into ADP and a phosphate ion. In this case, it's -30.50 kJ/mol at body temp (37.0 oC), at pH 7.0.

But things get interesting when we step into the real-world scenario, aka inside a human cell, where the ATP, ADP, and phosphate ion (HPO42-) concentrations aren't at "standard" levels (which are usually 1 Molar for each reactant and product).

Now, to calculate the Gibbs free energy (ΔG) under these conditions, we use a super handy formula:

ΔG = ΔGº + RT ln(Q)

where:

- R is the universal gas constant (8.314 J/mol*K), but for kJ/mol, we'll use 0.008314

- T is the temperature in Kelvin (we add 273.15 to the Celsius temperature to convert it, so 37.0 oC becomes 310.15 K)

- Q is the reaction quotient, which is products over reactants. For us, it's the concentrations of ADP and phosphate ion divided by the concentration of ATP. Keep in mind that water is not included 'cause its concentration is assumed to be constant in biological reactions.

So now let's run the numbers:

ΔG = -30.50 kJ/mol + (0.008314 kJ/mol*K * 310.15 K) * ln((0.3 mM * 4.98 mM) / 5.6 mM)

= -30.50 kJ/mol + (2.58 kJ/mol) * ln(1.49)

= -30.50 kJ/mol + 1.04 kJ/mol

And finally, we get:

ΔG = -29.46 kJ/mol

So that's it. In the cell, the Gibbs free energy change is -29.46 kJ/mol, a bit different from the "standard" conditions, thanks to the concentration levels in a human cell. The negative sign tells us the reaction is spontaneous, meaning it happens on its own without needing an energy push. So yeah, your cells are legit energy machines.

Hope that's clear, and remember, biochem is like the most epic game of tiny molecular Legos you could ever play!