# Question e2c8d

##### 1 Answer
Jul 15, 2017

ΔG_text(rxn) = "-49.2 kJ·mol"^"-1". The reaction is spontaneous under these conditions.

The equation for the reaction is

$\text{ATP(aq) + H"_2"O(l)" ⇌ "ADP(aq) + HPO"_4^"2-}$

The equation for free energy ΔG is

ΔG = ΔG^@ + RTlnQ

where

ΔG^@ = the standard free energy change for the reaction
$R =$ the Ideal Gas Constant
$T =$ the Kelvin temperature

Q = (["ADP"]["HPO"_4^"2-"])/(["ATP"]

In this problem,

["ADP"] = 0.70 × 10^"-3" color(white)(l)"mol/L"
["HPO"_4^"2-"] = "5.0 mmol/L"
["ATP"] = "5.0 mmol/L"
$R = \text{8.314 J·K"^"-1""mol"^"-1}$
$T = \text{(37.0 + 273.15) K = 310.15 K}$

Q= (0.70 × 10^"-3" × color(red)(cancel(color(black)(5.0))))/color(red)(cancel(color(black)(5.0))) = 7.0 × 10^"-4"

ΔG = "-30 500 J·mol"^"-1" + "8.314 J"·color(red)(cancel(color(black)("K"^"-1")))"mol"^"-1" × 310.15 color(red)(cancel(color(black)("K"))) × ln(7.0 × 10^"-4") = "30 500 J·mol"^"-1" - "18 700 J·mol"^"-1" = "-49 200 J·mol"^"-1" = "-49.2 kJ·mol"^"-1"#