Chemical Thermodynamics Question 427
Question: How many molecules of ATP, undergo hydrolysis to raise the temperature of 180 kg of water which was originally at room temperature by $ 1{}^\circ C $ - C{P,m} water = 75.32 J/mol/K, $ \Delta H{ P } $ for ATP hydrolysis = 7 kcal/mol
Options:
A) $ 1.5\times 10^{25} $
B) $ 2.00\times 10^{23} $
C) $ 3.4\times 10^{25} $
D) $ 4.0\times 10^{24} $
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Answer:
Correct Answer: A
Solution:
- $ q_{p}=\Delta H=C_{p}dT $
$ \Rightarrow q_{p}=75.32\frac{J}{K,mol}\times (299-298)K $
$ \Rightarrow q_{p}=75.32\frac{J}{K,mol} $ For $ 180kg $ of water, no. of moles of water $ =\frac{180\times 10^{3}g}{18g/mol}=10^{4}g,moles, $
$ q_{p}=75.32\frac{J}{mol}\times 10^{4}moles $
$ =753.2\times 10^{3}J=753.2,kJ $
$ \Delta H $ for $ ATP=7kcal/mol $
$ =7\times 4.184,kJ/mol $
$ =29.2kJ/mol $
$ 6.022\times 10^{23} $ molecules of ATP produce $ =29.2kJ $
$ 29.2kJ $ produced from $ 6.022\times 10^{23} $ molecules $ 753.2kJ $ produced from $ 6.022\times 10^{23}\times \frac{75.8}{29.2} $
$ =1.5\times 10^{25} $ molecules
