Experimental solid-oxide fuel cells that use butane (C₄H₁₀) as the fuel have been reported recently. These cells contain composite metal/metal oxide electrodes and a solid metal oxide electrolyte. The cell half-reactions are (c) How many grams of butane are required to produce a constant current of 10.5 A for 8.00 h? How many liters of gaseous butane at 20 °C and 815 mm Hg pressure are required?

Verified step by step guidance

Identify the half-reaction involving butane (C_4H_{10}) and determine the number of electrons transferred per mole of butane.

Use the formula Q = I \times t to calculate the total charge (Q) in coulombs, where I is the current (10.5 A) and t is the time (8.00 h converted to seconds).

Use Faraday's constant (approximately 96485 C/mol) to convert the total charge to moles of electrons.

Relate the moles of electrons to moles of butane using the stoichiometry of the half-reaction.

Convert moles of butane to grams using the molar mass of butane (C_4H_{10}) and to liters using the ideal gas law, PV = nRT, with the given temperature and pressure.

Verified video answer for a similar problem:

This video solution was recommended by our tutors as helpful for the problem above.

Video duration:

Was this helpful?

Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Electrochemical Reactions

Electrochemical reactions involve the transfer of electrons between chemical species, which is fundamental in fuel cells. In a solid-oxide fuel cell, the oxidation of butane occurs at the anode, releasing electrons that flow through an external circuit, generating electric current. Understanding the half-reactions and the overall cell reaction is crucial for calculating the amount of fuel needed to sustain a specific current.

Current and Charge Relationship

The relationship between current (I), charge (Q), and time (t) is given by the equation Q = I × t. This concept is essential for determining how much charge is required to maintain a current of 10.5 A over 8 hours. By calculating the total charge, one can then relate it to the moles of butane consumed in the electrochemical reaction, allowing for the determination of the mass of butane needed.

Ideal Gas Law

The Ideal Gas Law (PV = nRT) relates the pressure, volume, temperature, and number of moles of a gas. In this context, it is used to calculate the volume of gaseous butane required under specific conditions (20 °C and 815 mm Hg). Understanding how to manipulate this equation is vital for converting the amount of butane from grams to liters, ensuring accurate calculations for the fuel cell operation.

Recommended video:

Guided course

01:15

Ideal Gas Law Formula

Related Practice

Textbook Question

Consider a galvanic cell that utilizes the following half-reactions:

(b) What are the values of E° and the equilibrium constant K for the cell reaction at 25 °C?

Textbook Question

The nickel–iron battery has an iron anode, an NiO(OH) cathode, and a KOH electrolyte. This battery uses the follow-ing half-reactions and has an E° value of 1.37 V at 25 °C. (b) Calculate ∆G° (in kilojoules) and the equilibrium con-stant K for the cell reaction at 25 °C.

Textbook Question

Experimental solid-oxide fuel cells that use butane (C₄H₁₀) as the fuel have been reported recently. These cells contain composite metal/metal oxide electrodes and a solid metal oxide electrolyte. The cell half-reactions are (b) Use the thermodynamic data in Appendix B to calculate the values of E° and the equilibrium constant K for the cell reaction at 25 °C. Will E° and K increase, decrease, or remain the same on raising the temperature?

Textbook Question

The half-reactions that occur in ordinary alkaline batteries can be written as In 1999, researchers in Israel reported a new type of alkaline battery, called a 'super-iron' battery. This battery uses the same anode reaction as an ordinary alkaline battery but involves the reduction of FeO₄^2- ion (from K₂FeO₄) to solid Fe(OH)₃ at the cathode. (a) Use the following standard reduction potential and any data from Appendixes C and D to calculate the standard cell potential expected for an ordinary alkaline battery:

Textbook Question

The half-reactions that occur in ordinary alkaline batteries can be written as In 1999, researchers in Israel reported a new type of alkaline battery, called a 'super-iron' battery. This battery uses the same anode reaction as an ordinary alkaline battery but involves the reduction of FeO₄^2- ion (from K₂FeO₄) to solid Fe(OH)₃ at the cathode. (c) A super-iron battery should last longer than an ordinary alkaline battery of the same size and weight because its cathode can provide more charge per unit mass. Quan-titatively compare the number of coulombs of charge released by the reduction of 10.0 g K₂FeO₄ to Fe(OH)₃ with the number of coulombs of charge released by the reduction 10.0 g of MnO₂ to MnO(OH).

views