Answer:
Here's what I get
Explanation:
ATP ⟶ ADP + Pi; ΔG° = -30.5 kJ·mol⁻¹
(a) Rank the favourability of ATP hydrolysis
To get ΔG under physiological conditions, we must use the equation
ΔG = ΔG° + RTlnQ where
[tex]Q = \dfrac{\text{[ADP][P$_{\text{i}}$]}}{\text{[ADP]}}[/tex]
(i) In muscle tissue
[tex]Q = \dfrac{0.9 \times 10^{-3} \times 8.1 \times 10^{-3}}{8.1 \times 10^{-3}} = 0.9 \times 10^{-3}\\\\RT \ln Q = 8.315 \times 310.15 \times \ln (0.9 \times 10^{-3}) = 2579 \times (-7.01) = \text{-18 100 J/mol} = \text{-18.1 kJ/mol}\\\Delta G = \Delta G^{\circ} + RT \ln Q = -30.5 -18.1 = \textbf{-48.6 kJ/mol}[/tex]
(ii) In brain tissue
[tex]Q = \dfrac{0.7 \times 10^{-3} \times 2.7 \times 10^{-3}}{2.6 \times 10^{-3}} = 0.73 \times 10^{-3}\\\\RT \ln Q = 8.315 \times 310.15 \times \ln (0.73 \times 10^{-3}) = 2579 \times (-7.23) = \text{-18 100 J/mol} = \text{-18.6 kJ/mol}\\\Delta G = \Delta G^{\circ} + RT \ln Q = -30.5 -18.6 = \textbf{-49.1 kJ$\cdot$mol$^{\mathbf{-1}}$}[/tex]
(iii) In liver tissue
[tex]Q = \dfrac{1.3 \times 10^{-3} \times 4.8 \times 10^{-3}}{3.4 \times 10^{-3}} = 1.84 \times 10^{-3}\\\\RT \ln Q = 8.315 \times 310.15 \times \ln (0.73 \times 10^{-3}) = 2579 \times (-6.30) = \text{-16 200 J/mol} = \text{-16.2 kJ/mol}\\\Delta G = \Delta G^{\circ} + RT \ln Q = -30.5 -16.2 = \textbf{-46.7 kJ$\cdot$mol$^{\mathbf{-1}}$}[/tex]
[tex]\begin{array}{cc}\textbf{Relative}\\\textbf{Favourability} & \textbf{Tissue}\\1& \text{brain (-49.1 kJ/mol)}\\2& \text{muscle (-48.6 kJ/mol)}\\3& \text{liver (-46.7 kJ/mol)}\\\end{array}[/tex]
(b) ΔG in muscle at 18 °C
T= (18.0 + 273.15) = 291.15 K
[tex]Q = \dfrac{0.9 \times 10^{-3} \times 8.1 \times 10^{-3}}{8.1 \times 10^{-3}} = 0.9 \times 10^{-3}\\\\RT \ln Q = 8.315 \times 291.15 \times \ln (0.9 \times 10^{-3}) = 2421\times (-7.01) = \text{-17 000 J/mol} = \text{-17.0 kJ/mol}\\\Delta G = \Delta G^{\circ} + RT \ln Q = -30.5 -17.0 = \textbf{-47.5 kJ$\cdot$mol}^{\mathbf{-1}}}[/tex]
The most favorable is the brain tissue, followed by the muscle tissue while the least favorable is the liver tissue.
The equation of the reaction is; ATP ------> ADP + Pi ΔG°= -30.5 kJ/mol
For muscle tissue;
Q = [ADP] [Pi]/[ATP]
Q = [0.9 × 10^-3] [8.1 × 10^-3]/[[8.1 × 10^-3]
Q = 9.0 × 10^-4
ΔG =ΔG° + RTlnQ
Where ΔG°= -30.5 kJ/mol or -30.5 × 10^3 J/mol from the equation
ΔG = -30.5 kJ/mol + (8.315 × 310 × ln(9.0 × 10^-4)) kJ/mol
ΔG =-48.6 kJ/mol
For the brain tissue;
Q = [0.7 × 10^-3] [2.7 × 10^-3]/[2.6 × 10^-3]
Q = 7.3 × 10^-4
ΔG = -30.5 kJ/mol + (8.315 × 310 × ln(7.3 × 10^-4)) kJ/mol
ΔG = -49.1 kJ/mol
For the liver tissue;
Q = [1.3 × 10^-3] [4.8 × 10^-3]/[3.4 × 10^-3]
Q = 1.8 × 10^-3
ΔG = -30.5 kJ/mol + (8.315 × 310 × ln( 1.8 × 10^-3)) kJ/mol
ΔG = -46.3 kJ/mol
The most favorable is the brain tissue, followed by the muscle tissue while the least favorable is the liver tissue.
For the muscle tissue at 18°;
ΔG = -30.5 kJ/mol + (8.315 × 291 × ln(9.0 × 10^-4)) kJ/mol
ΔG = -47.5 kJ/mol
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