When electric current is passed through acidified water, 448 mL of hydrogen gas at STP is collected at the cathode in 965 seconds. The current passed in amperes is :

4.0

The correct answer is option 4. 4.0.

To find the current passed when 448 mL of hydrogen gas is collected at the cathode, we can use Faraday's laws of electrolysis. Here's the step-by-step process:

At STP (Standard Temperature and Pressure), 1 mole of any ideal gas occupies 22.4 liters (or 22,400 mL).

Given:

Volume of hydrogen gas collected = 448 mL

To find the number of moles of hydrogen gas (\(n\)):

\(n = \frac{\text{Volume of gas}}{\text{Molar volume at STP}}\)

\(n = \frac{448 \text{ mL}}{22,400 \text{ mL/mol}} = 0.02 \text{ mol}\)

The electrolysis of water produces hydrogen gas at the cathode. The reaction at the cathode is:

\(2H^+ + 2e^- \rightarrow H_2\)

From the reaction, 2 moles of electrons produce 1 mole of \(H_2\). Thus, 0.02 moles of \(H_2\) would require

\(\text{Moles of electrons} = 2 \times 0.02 \text{ mol} = 0.04 \text{ mol}\)

The Faraday constant (\(F\)) is approximately 96,485 C/mol, which is the charge per mole of electrons. Therefore, the total charge (\(Q\)) required is:

\(Q = \text{Moles of electrons} \times F\)

\(Q = 0.04 \text{ mol} \times 96,485 \text{ C/mol} = 3,859.4 \text{ C}\)

Current (\(I\)) is related to the charge (\(Q\)) and time (\(t\)) by:

\(I = \frac{Q}{t}\)

Given:

Time (\(t\)) = 965 seconds

\(I = \frac{3,859.4 \text{ C}}{965 \text{ s}} \approx 4.0 \text{ A}\)

The current passed is approximately 4.0 amperes. Therefore, the correct answer is: 4.0 A