Question

How many number of moles of photon would contain sufficient energy to raise the temperature of 225 g of water from ${21}^{o}C$ to ${96}^{o}C$?
The specific heat of water is 4.18 $J{g}^{-1}{K}^{-1}$ and the frequency of light radiation used is $2.45\times {10}^9{s}^{-1}$.
[Given: Energy required to raise the temperature = mass x specific heat x ΔT]

• A. $7.22\times {10}^{4}mol$
• B. $72.2\times {10}^{4}mol$
• C. $7.22\times {10}^{6}mol$
• D. $0.722\times {10}^{4}mol$

Answer 1

The correct option is A $7.22\times {10}^{4}mol$

Energy associated with one mole of photons
$=N_{0}hv$
$=6.02\times {10}^{23}\times 6.626\times {10}^{-34}\times 2.45\times {10}^9$
$=97.727\times {10}^{-2}Jmo{l}^{-1}$
Energy required to raise the temperature of 225 g of water by ${75}^{0}C$
$=m\times s\times t$
$=225\times 4.18\times 75=70537.5J$
Hence,number of moles of photons required
$\frac{m\times s\times t}{N_{0}hv}=7.22\times {10}^{4}mol$