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# 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

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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

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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

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