Question

Calculate the energy required to excite two litres of hydrogen gas at 1 atm 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. True
• B. False

Answer 1

The correct option is B False

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