Question

Calculate the energy required to excite two litre of hydrogen gas at 1 atom and 298 k to the first excited state of atomic hydrogen. The energy for the disassociation of H${}_2$ bond is 436 kJ mol${}^{-1}$. Also calculate the minimum frequency of photon to break this bond.

• A. 8.523 $\times$ 10${}^{15}$ Hz
• B. 1.096 $\times$ 10${}^{15}$ Hz
• C. 1.633 $\times$ 10${}^{15}$ Hz
• D. 2.806 $\times$ 10${}^{15}$ Hz

Answer 1

The correct option is B 1.096 $\times$ 10${}^{15}$ Hz

Moles of H${}_2$ = $\frac{Pv}{RT}$ = $\frac{1\times 2}{0.0821\times 298}$ = 0.0817Energy required for dissociation is 436 $\times$ 0.0817 = 35.62 KJEnergy required to excite one H atom to first excited state (n = 2) = 10.2 $\times$ 1.6 $\times$ 10${}^{-19}$ J
Energy required to excite given sample is(2 $\times$ 0.0817) $\times$ 6 $\times$ 10${}^{23}$ $\times$ (10.2 $\times$ 1.6 $\times$ 10${}^{-19}$) $\times$ 10${}^{-3}$ kJ=160 kJ $\Rightarrow$ Total energy required = (35.62 + 160) = 195.62 kJ Also, E = hv
$\Rightarrow$ v = $\frac{E}{h}$ = $\frac{436\times {10}^3}{6\times {10}^{23}}$ $\frac{1}{6.63\times 106-34}$ = 1.096 $\times$ 10${}^{15}$ Hz