Given, Volume of hydrogen gas, $V = 250 \text{ mL} = 0.25 \text{ L}$ Time, $t = 1 \text{ hour} = 3600 \text{ s}$ At STP, the molar volume of a gas is $22.4 \text{ L}$. Number of moles of $H_2$ gas produced: $$ \begin{aligned} n &= \frac{V}{22.4} = \frac{0.25}{22.4} \text{ mol} \approx 0.01116 \text{ mol} \end{aligned} $$ The electrode reaction for the production of hydrogen is: $$ \begin{aligned} 2H^+ + 2e^- &\rightarrow H_2 \end{aligned} $$ From the reaction, $1 \text{ mol } H_2$ requires $2 \text{ moles of electrons}$. So, total moles of electrons ($n_e$) required: $$ \begin{aligned} n_e &= 2 \times n = 2 \times \frac{0.25}{22.4} \text{ mol} \approx 0.02232 \text{ mol} \end{aligned} $$ Total charge ($Q$) passed: $$ \begin{aligned} Q &= n_e \times F = 0.02232 \times 96500 \text{ C} \approx 2153.88 \text{ C} \end{aligned} $$ Since $Q = I \times t$, the current ($I$) is: $$ \begin{aligned} I &= \frac{Q}{t} = \frac{2153.88}{3600} \text{ A} \approx 0.598 \text{ A} \end{aligned} $$ Thus, the current intensity was $0.598 \text{ A}$.