Which one of the following statements is incorrect?

We have to examine each statement and decide which one does not agree with the accepted facts about dihydrogen.

Let us start with the fundamental equilibrium for the thermal dissociation of dihydrogen:

$$\mathrm{H_2(g)} \;\rightleftharpoons\; 2\,\mathrm{H(g)}$$

For this reaction the equilibrium constant in terms of pressure is

$$K_p \;=\;\frac{(p_{\mathrm H})^{2}}{p_{\mathrm{H_2}}}$$

where $$p_{\mathrm H}$$ and $$p_{\mathrm{H_2}}$$ are the partial pressures of the atom and the molecule respectively.

Suppose we begin with 1 mol of $$\mathrm{H_2}$$ at 1 bar. After reaching equilibrium at 2000 K, let the degree of dissociation be $$\alpha$$. Then

• moles of $$\mathrm{H_2}$$ become $$1-\alpha$$,
• moles of $$\mathrm{H}$$ become $$2\alpha$$,
• total moles $$=\;1+\alpha$$.

Hence the mole fractions are

$$x_{\mathrm{H_2}}=\frac{1-\alpha}{1+\alpha}, \qquad x_{\mathrm{H}}=\frac{2\alpha}{1+\alpha}.$$

Because the total pressure is 1 bar, the partial pressures equal these mole fractions, so

$$K_p \;=\;\frac{(x_{\mathrm H})^{2}}{x_{\mathrm{H_2}}}$$

Substituting the expressions for the mole fractions, we get

$$K_p=\frac{\left(\dfrac{2\alpha}{1+\alpha}\right)^2}{\dfrac{1-\alpha}{1+\alpha}} =\;4\alpha^{2}\,\frac{1+\alpha}{1-\alpha}.$$

At 2000 K the tabulated value is $$K_p\approx1.6\times10^{-4}$$. Because $$\alpha$$ is very small, we can safely put $$1+\alpha\approx1$$ and $$1-\alpha\approx1$$, giving

$$K_p\;\approx\;4\alpha^{2}$$

and hence

$$\alpha\;\approx\;\frac{1}{2}\sqrt{K_p} =\;\frac{1}{2}\sqrt{1.6\times10^{-4}} =\;\frac{1}{2}\times\,1.26\times10^{-2} \approx6.3\times10^{-3}.$$

This is

$$\alpha\times100\;\approx\;0.63\%,$$

that is, only about $$0.63\%$$ of the molecular hydrogen splits into atoms. The value quoted in the NCERT text is even smaller, $$0.081\%.$$ In either case the dissociation is far below $$8.1\%.$$ Therefore, the statement “At around 2000 K, the dissociation of dihydrogen into its atoms is nearly 8.1 %” is incorrect.

Now we briefly justify the other three statements:

• Atomic hydrogen can indeed be produced by subjecting hot $$\mathrm{H_2}$$ to ultraviolet radiation, so statement A is correct.

• The bond dissociation enthalpy of $$\mathrm{H_2}$$ (about 436 kJ mol-1) is the highest among all diatomic molecules having a single bond; hence statement C is correct.

• Zinc, being amphoteric, liberates $$\mathrm{H_2}$$ both with dilute acids such as $$\mathrm{HCl}$$ and with strong bases such as $$\mathrm{NaOH(aq)}$$, so statement D is also correct.

Since only statement B is wrong, it is the incorrect option.

Hence, the correct answer is Option B.