How many moles of photon would contain sufficient energy to raise the temperature of 245 g of water — Atomic Structure Chemistry Question
Question
How many moles of photon would contain sufficient energy to raise the temperature of 245 g of water from $19.5^\circ\text{C}$ to $99.5^\circ\text{C}$? Specific heat of water is 4.2 J/$^\circ\text{C}$·g and frequency of light radiation used is $2.45 \times 10^{10}$ per second. ($6.626 \times 0.15 = 1.0, N_A = 6 \times 10^{23}$)
💡 Solution & Explanation
Heat required $q = m \cdot s \cdot \Delta T = 245 \times 4.2 \times (99.5 - 19.5) = 245 \times 4.2 \times 80 = 82320$ J. Energy of one mole of photons $E_{mol} = N_A h \nu = 6 \times 10^{23} \times 6.626 \times 10^{-34} \times 2.45 \times 10^{10} = 6 \times 6.626 \times 2.45 \times 10^{-1}$. Using the hint $6.626 \times 0.15 = 1.0 \implies 6.626 = \frac{1}{0.15}$, we get $E_{mol} = 6 \times \frac{1}{0.15} \times 0.245 = 40 \times 0.245 = 9.8$ J. Number of moles = $\frac{82320}{9.8} = 8400$. Therefore, correct answer is 8400.