How many molecules of ATP, undergo hydrolysis to raise the temperature of 180 kg of water which was originally at room temperature by 1°C? C{P,m} water = 75.32 J/mol/K, ΔH{P} for ATP hydrolysis = 7 kcal/mol
(a) 1.5 × 1025
(b) 2.00 × 1023
(c) 3.4 × 1025
(d) 4.0 × 1024
Correct answer: (a) 1.5 × 1025
Explanation:
qp = ΔH = CpdT
⇒ qp = 75.32 \(\frac{J}{K\;mol}\) x (299 - 298)K
⇒ qp = 75.32 \(\frac{J}{K\;mol}\)
For 180 kg of water, no. of moles of water
= \(\frac{180 \times 10^3g}{18g/mol}\) = 104 g moles
qp = 75.32 \(\frac{J}{K\;mol} \times 10^4\) moles
= 753.2 × 103 J = 753.2 kJ
ΔH for ATP = 7 kcal / mol
= 7 × 4.184 kJ/mol
= 29.2 kJ/mol
6.022 × 1023 molecules of ATP produce
= 29.2 kJ
29.2 kJ produced from
6.022 × 1023 molecules
753.2 kJ produced from
6.022 x 1023 x \(\frac{75.8}{29.2}\)
= 1.5 × 1025 molecules