   Chapter 18, Problem 132AE

Chapter
Section
Textbook Problem

# In the electrolysis of a sodium chloride solution, what volume of H2(g) is produced in the same time it takes to produce 257 L Cl2(g), with both volumes measured at 50°c and 2.50 atm?

Interpretation Introduction

Interpretation:

The volume of Hydrogen gas produced during the electrolysis of Sodium Chloride at a given pressure and temperature is to be calculated.

Concept introduction:

According to Faraday’s second law of electrolysis, when the same amount of electricity is passed through different electrolytes, the amount of substance that gets deposited at each electrode is directly proportional to their equivalent weight.

w1w2=E1E2

To determine: The volume of Hydrogen gas produced during the electrolysis of Sodium Chloride at a given pressure and temperature.

Explanation

Given,

The volume of Chlorine gas is 257.0L .

The pressure is 25.0atm .

The temperature is 50°C .

The conversion of degree Celsius (°C) into Kelvin (K) is done as,

T(K)=T(°C)+273.15

Hence, the conversion of 50°C to K is done as,

T(K)=50°C+273.15=323.15K

Molar mass of Hydrogen gas is 2.0g/mole

Molar mass of Chlorine gas is 71.0g/mole

The ideal gas equation is,

PV=nRT

Where,

• P is the pressure of the gas.
• V is the volume of the gas.
• n is the number of moles of gas.
• R is the universal gas constant (0.0821Latm/Kmol) .
• T is the temperature of the gas.

The equation is further simplified as,

PV=nRT=wMRT

Where,

• w is the given mass of the gas.
• M is the molar mass of the gas.

Rearrange the above equation to obtain the mass of Chlorine gas produced,

wCl2=PVMRT

Substitute the values of P , V , M , R and T in the above equation as,

wCl2=PVMRT=(2.50atm)(257L)(71.0g/mol)(0.0821LatmmolK)(323.15K)=1719.43g

The value of E is given as,

E=Molarmassn

Where,

• n is the number of electrons exchanged.
• E is the equivalent weight.

Substitute the value of molar mass of Hydrogen and n to obtain the value of its equivalent weight as,

EH2=Molarmassn=2gmol2e

Similarly, substitute the value of molar mass of Chlorine and n to obtain the value of its equivalent weight as,

ECl2=Molarmassn=71gmol2e

According to Faraday’s second law of electrolysis,

wH2wCl2=EH2ECl2

Where,

• wH2 is the mass of Hydrogen gas

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