Question

How many molecules of ATP, undergo hydrolysis to raise the temperature of $180kg$ of water which was originally at room temperature by $1^{\circ }C$ ? $C\{P,m\}$ water $=75.32J/mol/K$, $\Delta H\{P\}$ for ATP hydrolysis $=7kcal/mol$

• A. $1.5\times 10^{25}$
• B. $2.00\times 10^{23}$
• C. $3.4\times 10^{25}$
• D. $4.0\times 10^{24}$

Answer 1

Answer: (A)

$q_p=\Delta H=C_{p}dT$
$\Rightarrow q_p=75.32\frac{J}{\text{K mol }}\times (299-298)K$
$\Rightarrow q_p=75.32\frac{J}{\text{K mol }}$
For $180kg$ of water, no. of moles of water
$=\frac{180\times 10^{3}g}{18g/mol}=10^4\text{ moles }$
$q_p=75.32\frac{J}{\text{mol }}\times 10^4\text{ moles }$
$=753.2\times 10^{3}J=753.2kJ$
$\Delta H\text{ for ATP }=7kcal/mol$
$=7\times 4.184kJ/mol=29.2kJ/mol$
$29.2kJ$ produced from $6.022\times 10^{23}$ molecules
$753.2kJ$ produced from $6.022\times 10^{23}\times \frac{753.2}{29.2}$
$=1.5\times 10^{25}$ molecules