   Chapter 19, Problem 113SCQ

Chapter
Section
Textbook Problem

A hydrogen-oxygen fuel cell operates on the simple reaction H 2 ( g )  +  1 2  O 2 ( g ) →  H 2 O ( l ) If the cell is designed to produce 1.5 A of current and if the hydrogen is contained in a 1.0-L tank at 200 atm pressure at 25 °C, how long can the fuel cell operate before the hydrogen runs out? (Assume there is an unlimited supply of O2.)

Interpretation Introduction

Interpretation:

The time of fuel cell operate before the hydrogen runs out has to be determined.

Concept introduction:

The Faraday’s first law of electrolysis state that the mass of the substance (m) deposited at any electrode is directly proportional to the charge (Q) passed. The mathematical form of the Fraday’s first law is written as’

m=(QF)(MZ)

Here,

The symbol F is the Faraday’s constant.

The symbol M is the molar mass of the substance in grams per mol.

The symbol Z is the valency number of ions of the substance (electrons transferred per ion).

In the simple case of constant current electrolysis, Q=I×t leading to

m=(I×tF)(MZ) (1)

The above formula is written in terms of the number of moles (n),

n=(I×tF)(1Z) (2)

Here, t is the total time the constant current (I) is applied.

The ideal gas law is written as,

PV=nRT (3)

Here,

The pressure of the gas is P.

The volume of the gas container is V.

The number of moles of gas particles is n.

The temperature is T.

The gas constant is R.

Explanation

Given:

The pressure of the gas is 200atm.

The volume of the gas container is 1L.

The temperature is 298K.

The gas constant is R=0.0821atmLmol1K1.

The constant current is 1.5A.

The faraday’s constant F is equal to 96500Cmol1.

The hydrogen-oxygen fuel cell reaction is written as,

H2(g)+12O2(g)H2O(l)

Here, Z=2

Substitute the value of pressure, volume, temperature and gas constant in equation (3) to calculate the number of moles of hydrogen,

(200atm)(1L)=n(0

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