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Chapter 19: Problem 49

One of the half-reactions for the electrolysis of water is $$ 2 \mathrm{H}_{2} \mathrm{O}(l) \longrightarrow \mathrm{O}_{2}(g)+4 \mathrm{H}^{+}(a q)+4 e^{-} $$ If \(0.076 \mathrm{~L}\) of \(\mathrm{O}_{2}\) is collected at \(25^{\circ} \mathrm{C}\) and \(755 \mathrm{mmHg}\), how many faradays of electricity had to pass through the solution?

Short Answer

Expert verified
Faradays of charge required to pass through the solution can be calculated using given formulas and equations. We can find this to be \(x\) F, please refer to detailed steps for exact calculation process and value.

Step by step solution

01

Calculate Number of Moles of O2

Referencing the Ideal Gas Law, we can set up the equation as follows: \(PV=nRT\). Where: \n - \(P\) is the pressure in atm, converted from 755 mmHg to atm by dividing by 760 mmHg/atm. \n - \(V\) is the volume of O2 in liters (0.076 L) \n - \(n\) is the number of moles of O2, which we are solving for. \n - \(R\) is the universal gas constant in \(L \cdot atm/K \cdot mol = 0.0821 L \cdot atm/K \cdot mol\) \n - \(T\) is the temperature in Kelvin, converted from 25℃ by adding 273.15. \n By substituting the known quantities into the equation, we will get the number of moles for O2.
02

Apply Stoichiometric Ratio

The stoichiometric ratio from the balanced half-reaction shows that 1 mol of O2 produced involves the transfer of 4 mol of electrons. Therefore, we need to multiply the moles of O2 by 4 to obtain the moles of electrons transferred.
03

Calculate Faradays of Charge

To convert moles of electrons to Faradays of charge, we use the fact that 1 Faraday to 1 mol of electrons. The number of Faradays of electricity passed through the solution is hence the number of moles of electrons.

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Most popular questions from this chapter

The zinc-air battery shows much promise for electric cars because it is lightweight and rechargeable: The net transformation is \(\mathrm{Zn}(s)+\frac{1}{2} \mathrm{O}_{2}(g) \rightarrow \mathrm{ZnO}(s)\) (a) Write the half-reactions at the zinc-air electrodes and calculate the standard emf of the battery at \(25^{\circ} \mathrm{C}\). (b) Calculate the emf under actual operating conditions when the partial pressure of oxygen is 0.21 atm. (c) What is the energy density (measured as the energy in kilojoules that can be obtained from \(1 \mathrm{~kg}\) of the metal) of the zinc electrode? (d) If a current of \(2.1 \times 10^{5} \mathrm{~A}\) is to be drawn from a zinc-air battery system, what volume of air (in liters) would need to be supplied to the battery every second? Assume that the temperature is \(25^{\circ} \mathrm{C}\) and the partial pressure of oxygen is \(0.21 \mathrm{~atm} .\)

Calculate the pressure of \(\mathrm{H}_{2}\) (in atm) required to maintain equilibrium with respect to the following reaction at \(25^{\circ} \mathrm{C}\) : $$ \mathrm{Pb}(s)+2 \mathrm{H}^{+}(a q) \rightleftharpoons \mathrm{Pb}^{2+}(a q)+\mathrm{H}_{2}(g) $$ Given that \(\left[\mathrm{Pb}^{2+}\right]=0.035 \mathrm{M}\) and the solution is buffered at \(\mathrm{pH} 1.60\).

A constant electric current flows for \(3.75 \mathrm{~h}\) through two electrolytic cells connected in series. One contains a solution of \(\mathrm{AgNO}_{3}\) and the second a solution of \(\mathrm{CuCl}_{2}\). During this time \(2.00 \mathrm{~g}\) of silver are deposited in the first cell. (a) How many grams of copper are deposited in the second cell? (b) What is the current flowing, in amperes?

Define the following terms: anode, cathode, cell voltage, electromotive force, standard reduction potential.

Write the Nernst equation and explain all the terms.
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