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Chapter 18: Problem 100

What volumes of \(\mathrm{H}_{2}(g)\) and \(\mathrm{O}_{2}(g)\) at STP are produced from the electrolysis of water by a current of \(2.50 \mathrm{~A}\) in \(15.0 \mathrm{~min} ?\)

Short Answer

Expert verified
The volumes of hydrogen and oxygen gas produced during the electrolysis of water by a current of 2.50 A in 15.0 min are \(0.262 \mathrm{~L}\) H₂ and \(0.131 \mathrm{~L}\) O₂, respectively.

Step by step solution

01

Calculate the charge passed through the circuit

We are given that the current (I) is 2.50 A and the electrolysis takes place over 15.0 minutes. With this information, we can calculate the charge (Q) passed through the circuit using the formula: Q = I × t where t is the time in seconds. First, convert the minutes to seconds: t = 15.0 min × (60 s/min) = 900 s Now, calculate the charge: Q = 2.50 A × 900 s = 2250 C (coulombs)
02

Determine the moles of electrons passed through the circuit

Next, we need to find the moles of electrons that passed through the circuit in this process. We know that 1 mole of electrons has a charge of 96485 C (Faraday's constant). So, we can find the number of moles (n) of electrons using the formula: n = Q / Faraday's constant n = 2250 C / 96485 C/mol = 0.0233 moles of electrons
03

Determine the stoichiometry of the electrolysis reaction

Now we need to find how many moles of gases are produced by the given moles of electrons in the electrolysis of water. The balanced electrolysis reaction is: 2H₂O (l) → 2H₂ (g) + O₂ (g) From the stoichiometry of the reaction, we find that 4 moles of electrons are required to produce 2 moles of hydrogen gas and 1 mole of oxygen gas: 4 e⁻ + 2H₂O (l) → 2H₂ (g) + O₂ (g)
04

Calculate the moles of gases produced

Now, we can calculate the moles of gases produced using the stoichiometry from the balanced reaction: Moles of H₂ = (0.0233 moles e⁻ / 4 moles e⁻) × 2 moles H₂ = 0.0117 moles H₂ Moles of O₂ = (0.0233 moles e⁻ / 4 moles e⁻) × 1 moles O₂ = 0.00583 moles O₂
05

Convert moles of gases to volumes at STP

Finally, we can convert the moles of gases to volumes at STP (Standard Temperature and Pressure: 273 K and 1 atm). Using the molar gas volume at STP, which is 22.4 L/mol, we can find the volumes of hydrogen and oxygen gas: Volume of H₂ = 0.0117 moles H₂ × 22.4 L/mol = 0.262 L H₂ Volume of O₂ = 0.00583 moles O₂ × 22.4 L/mol = 0.131 L O₂ The volumes of hydrogen and oxygen gas produced during the electrolysis of water by a current of 2.50 A in 15.0 min are 0.262 L and 0.131 L, respectively.

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Most popular questions from this chapter

A chemist wishes to determine the concentration of \(\mathrm{CrO}_{4}^{2}\) electrochemically. A cell is constructed consisting of a saturated calomel electrode (SCE; see Exercise 115 ) and a silver wire coated with \(\mathrm{Ag}_{2} \mathrm{CrO}_{4}\). The \(\mathscr{E}^{\circ}\) value for the following half-reaction is \(0.446 \mathrm{~V}\) relative to the standard hydrogen electrode: $$ \mathrm{Ag}_{2} \mathrm{CrO}_{4}+2 \mathrm{c}^{-} \longrightarrow 2 \mathrm{Ag}+\mathrm{CrO}_{4}{ }^{2-} $$ a. Calculate \(\mathscr{E}_{\text {cell }}\) and \(\Delta G\) at \(25^{\circ} \mathrm{C}\) for the cell reaction when \(\left[\mathrm{CrO}_{4}{ }^{2-}\right]=1.00 \mathrm{~mol} / \mathrm{L}\) b. Write the Nernst equation for the cell. Assume that the SCE concentrations are constant. c. If the coated silver wire is placed in a solution (at \(25^{\circ} \mathrm{C}\) ) in which \(\left[\mathrm{CrO}_{4}{ }^{2-}\right]=1.00 \times 10^{-5} M\), what is the expected cell potential? d. The measured cell potential at \(25^{\circ} \mathrm{C}\) is \(0.504 \mathrm{~V}\) when the coated wire is dipped into a solution of unknown \(\left[\mathrm{CrO}_{4}{ }^{2-}\right]\). What is \(\left[\mathrm{CrO}_{4}{ }^{2-}\right]\) for this solution? e. Using data from this problem and from Table \(18.1\), calculate the solubility product \(\left(K_{\mathrm{sp}}\right)\) for \(\mathrm{Ag}_{2} \mathrm{CrO}_{4}\)

An aqueous solution of \(\mathrm{PdCl}_{2}\) is electrolyzed for \(48.6\) seconds, and during this time \(0.1064 \mathrm{~g}\) of \(\mathrm{Pd}\) is deposited on the cathode. What is the average current used in the electrolysis?

Combine the equations $$ \Delta G^{\circ}=-n F \mathscr{C}^{\circ} \quad \text { and } \quad \Delta G^{\circ}=\Delta H^{\circ}-T \Delta S^{\circ} $$ to derive an expression for \(\mathscr{E}^{\circ}\) as a function of temperature. Describe how one can graphically determine \(\Delta H^{\circ}\) and \(\Delta S^{\circ}\) from measurements of \(\mathscr{E}^{\circ}\) at different temperatures, assuming that \(\Delta H^{\circ}\) and \(\Delta S^{\circ}\) do not depend on temperature. What property would you look for in designing a reference half-cell that would produce a potential relatively stable with respect to temperature?

An electrochemical cell is set up using the following unbalanced reaction: $$ \mathrm{M}^{a+}(a q)+\mathrm{N}(s) \longrightarrow \mathrm{N}^{2+}(a q)+\mathrm{M}(s) $$ The standard reduction potentials are: $$ \begin{array}{ll} \mathrm{M}^{a+}+a \mathrm{e}^{-} \longrightarrow \mathrm{M} & \mathscr{E}^{\circ}=0.400 \mathrm{~V} \\ \mathrm{~N}^{2+}+2 \mathrm{e}^{-} \longrightarrow \mathrm{N} & \mathscr{E}^{\circ}=0.240 \mathrm{~V} \end{array} $$ The cell contains \(0.10 \mathrm{M} \mathrm{N}^{2+}\) and produces a voltage of \(0.180 \mathrm{~V}\). If the concentration of \(\mathrm{M}^{a+}\) is such that the value of the reaction quotient \(Q\) is \(9.32 \times 10^{-3}\), calculate \(\left[\mathrm{M}^{a+}\right]\). Calculate \(w_{\max }\) for this electrochemical cell.

Three electrochemical cells were connected in series so that the same quantity of electrical current passes through all three cells. In the first cell, \(1.15 \mathrm{~g}\) chromium metal was deposited from achromium(III) nitrate solution. In the second cell, \(3.15 \mathrm{~g}\) osmium was deposited from a solution made of \(\mathrm{Os}^{n+}\) and nitrate ions. What is the name of the salt? In the third cell, the electrical charge passed through a solution containing \(\mathrm{X}^{2+}\) ions caused deposition of \(2.11 \mathrm{~g}\) metallic \(\mathrm{X}\). What is the electron configuration of \(\mathrm{X}\) ?
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