[Given:
$\text{Cu}^{2+}\text{(aq)} + 2\text{e}^- \rightarrow \text{Cu(s)} \quad \text{E}^\circ_{\text{red}} = +0.34 \text{ V}$
$\text{O}_2\text{(g)} + 4\text{H}^+ + 4\text{e}^- \rightarrow 2\text{H}_2\text{O} \quad \text{E}^\circ_{\text{red}} = +1.23 \text{ V}$
Molar mass of Cu = $63.54 \text{ g mol}^{-1}$
Molar mass of $\text{O}_2$ = $32 \text{ g mol}^{-1}$
Faraday Constant = $96500 \text{ C mol}^{-1}$
Molar volume at STP = 22.4 L]
Electrolysis: Calculating Total Oxygen Evolved
This problem involves calculating the total volume of oxygen ($O_2$) evolved during the electrolysis of an acidic copper(II) solution ($\text{Cu}^{2+}$). The process occurs in two conceptual phases:
- Phase 1: Deposition of Copper metal ($\text{Cu}$).
- Phase 2: Evolution of Oxygen gas ($\text{O}_2$).
We assume the given current of 600 mA ($0.6$ A) was applied throughout the process, including during copper deposition and subsequent oxygen evolution.
Phase 1: Copper Deposition
First, calculate the amount of charge passed to deposit 300 mg of Copper.
- Calculate moles of Cu:
Mass of Cu = 300 mg = $0.300$ g
Molar mass of Cu = $63.54$ g mol$^{-1}$
Moles of Cu = $\frac{\text{Mass}}{\text{Molar mass}} = \frac{0.300 \, \text{g}}{63.54 \, \text{g mol}^{-1}} \approx 0.004721$ mol
- Calculate moles of electrons for Cu deposition:
The reduction reaction is $\text{Cu}^{2+}\text{(aq)} + 2\text{e}^- \rightarrow \text{Cu(s)}$.
Moles of electrons ($\text{e}^-$) = $2 \times$ Moles of Cu = $2 \times 0.004721 \approx 0.009443$ mol
- Calculate charge ($Q$) for Cu deposition:
Faraday constant (F) = $96500$ C mol$^{-1}$
$Q_{\text{Cu}} = \text{Moles of e}^- \times F = 0.009443 \, \text{mol} \times 96500 \, \text{C mol}^{-1} \approx 911.25$ C
- Calculate time ($t$) for Cu deposition:
Current (I) = $0.6$ A
$t_{\text{Cu}} = \frac{Q_{\text{Cu}}}{I} = \frac{911.25 \, \text{C}}{0.6 \, \text{A}} \approx 1518.75$ seconds
- Calculate O$_2$ evolved during Cu deposition:
The oxidation of water produces $\text{O}_2$: $2\text{H}_2\text{O} \rightarrow \text{O}_2\text{(g)} + 4\text{H}^+ + 4\text{e}^-$.
Moles of $\text{O}_2$ = $\frac{\text{Moles of e}^-}{4} = \frac{0.009443 \, \text{mol}}{4} \approx 0.002361$ mol
- Calculate volume of O$_2$ at STP during Phase 1:
Molar volume at STP = $22.4$ L mol$^{-1}$
Volume $V_{O_2, \text{Cu}} = \text{Moles of } O_2 \times \text{Molar volume at STP}$
$V_{O_2, \text{Cu}} = 0.002361 \, \text{mol} \times 22.4 \, \text{L mol}^{-1} \approx 0.05291$ L
$V_{O_2, \text{Cu}} = 0.05291 \times 1000$ mL $\approx 52.91$ mL
Phase 2: Oxygen Evolution
Calculate the charge passed and oxygen evolved during the additional 28 minutes.
- Calculate time in seconds:
Additional time = 28 minutes = $28 \times 60 = 1680$ seconds
- Calculate charge ($Q$) passed in Phase 2:
$Q_{\text{add}} = I \times t = 0.6 \, \text{A} \times 1680 \, \text{s} = 1008$ C
- Calculate moles of electrons passed in Phase 2:
Moles of $\text{e}^-$ ($\text{e}^-_{\text{add}}$) = $\frac{Q_{\text{add}}}{F} = \frac{1008 \, \text{C}}{96500 \, \text{C mol}^{-1}} \approx 0.010446$ mol
- Calculate moles of O$_2$ evolved in Phase 2:
Moles of $\text{O}_2$ = $\frac{\text{Moles of e}^-_{\text{add}}}{4} = \frac{0.010446 \, \text{mol}}{4} \approx 0.002611$ mol
- Calculate volume of O$_2$ at STP during Phase 2:
$V_{O_2, \text{add}} = \text{Moles of } O_2 \times \text{Molar volume at STP}$
$V_{O_2, \text{add}} = 0.002611 \, \text{mol} \times 22.4 \, \text{L mol}^{-1} \approx 0.05853$ L
$V_{O_2, \text{add}} = 0.05853 \times 1000$ mL $\approx 58.53$ mL
Total Oxygen Volume
Sum the volumes evolved in both phases.
- Calculate total volume of O$_2$:
Total Volume $V_{O_2, \text{total}} = V_{O_2, \text{Cu}} + V_{O_2, \text{add}}$
$V_{O_2, \text{total}} \approx 52.91 \text{ mL} + 58.53 \text{ mL} = 111.44$ mL
- Round to the nearest integer:
The total volume of oxygen evolved is approximately 111 mL.
Similar Questions
- The cycloalkene (X) on bromination consumes one mole of bromine per mole of (X) and gives the product (Y) in which C:Br ratio is 3:1. The percentage of bromine in the product (Y) is _________%. (Nearest integer)
(Given : molar mass in $\text{g mol}^{-1} \text{ H} : 1, \text{ C} : 12, \text{ O} : 16, \text{ Br} : 80$) - Dissociation of a gas $\text{A}_2$ takes place according to the following chemical reaction. At equilibrium, the total pressure is $1 \text{ bar}$ at $300\text{K}$.
$\text{A}_2\text{(g)} \rightleftharpoons 2\text{A(g)}$
The standard Gibbs energy of formation of the involved substances has been provided below:Substance $\Delta G_f^\circ / \text{kJ mol}^{-1}$ $\text{A}_2$ -100.00 A -50.832
The degree of dissociation of $\text{A}_2\text{(g)}$ is given by $(x \times 10^{-2})^{1/2}$ where $x =$ _________. (Nearest integer).
$[\text{Given: } \text{R} = 8 \text{ J mol}^{-1}\text{ K}^{-1}, \log 2 = 0.3010, \log 3 = 0.48]$
Assume degree of dissociation is not negligible. - Which of the following mixture gives a buffer solution with pH = 9.25 ?
Given : $\text{pK}_b (\text{NH}_4\text{OH}) = 4.75$ Identify the correct statements :
A. Hydrated salts can be used as primary standard.
B. Primary standard should not undergo any reaction with air.
C. Reactions of primary standard with another substance should be instantaneous and stoichiometric.
D. Primary standard should not be soluble in water.
E. Primary standard should have low relative molar mass.
Choose the correct answer from the options given below :- Consider $\text{A} \xrightarrow{k_1} \text{B}$ and $\text{C} \xrightarrow{k_2} \text{D}$ are two reactions. If the rate constant ($k_1$) of the $\text{A} \longrightarrow \text{B}$ reaction can be expressed by the following equation $\log_{10} k = 14.34 - \frac{1.5 \times 10^4}{T/K}$ and activation energy of $\text{C} \longrightarrow \text{D}$ reaction ($\text{Ea}_2$) is $\frac{1}{5}$th of the $\text{A} \longrightarrow \text{B}$ reaction ($\text{Ea}_1$), then the value of ($\text{Ea}_2$) is _________ $\text{kJ mol}^{-1}$. (Nearest Integer)
- Consider the following electrochemical cell :
$\text{Pt} \mid \text{O}_2\text{(g)}(1\text{bar}) \mid \text{HCl(aq)} \parallel \text{M}^{2+}\text{(aq, 1.0 M)} \mid \text{M(s)}$
The pH above which, oxygen gas would start to evolve at anode is _________ (nearest integer).
Given :
$\begin{bmatrix} \text{E}^\circ_{\text{M}^{2+}/\text{M}} = 0.994 \text{ V} \\ \text{E}^\circ_{\text{O}_2/\text{H}_2\text{O}} = 1.23 \text{ V} \end{bmatrix} \text{standard reduction potential}$
and $\frac{\text{RT}}{\text{F}} (2.303) = 0.059 \text{ V}$ at the given condition - At $27^\circ\text{C}$ in presence of a catalyst, activation energy of a reaction is lowered by $10 \text{ kJ mol}^{-1}$. The logarithm of ratio of $\frac{k(\text{catalysed})}{k(\text{uncatalysed})}$ is....
(Consider that the frequency factor for both the reactions is same) - X and Y are the number of electrons involved, respectively during the oxidation of $\text{I}^-$ to $\text{I}_2$ and $\text{S}^{2-}$ to S by acidified $\text{K}_2\text{Cr}_2\text{O}_7$. The value of X + Y is ______.
- Consider two Group IV metal ions $\text{X}^{2+}$ and $\text{Y}^{2+}$.
A solution containing 0.01 M $\text{X}^{2+}$ and 0.01 M $\text{Y}^{2+}$ is saturated with $\text{H}_2\text{S}$. The pH at which the metal sulphide YS will form as a precipitate is ______. (Nearest integer)
(Given: $\text{K}_{sp}(\text{XS}) = 1 \times 10^{-22}$ at $25^\circ\text{C}$, $\text{K}_{sp}(\text{YS}) = 4 \times 10^{-16}$ at $25^\circ\text{C}$, $[\text{H}_2\text{S}] = 0.1\text{M}$ in solution, $\text{K}_{a1} \times \text{K}_{a2}(\text{H}_2\text{S}) = 1.0 \times 10^{-21}$, $\log 2 = 0.30$, $\log 3 = 0.48$, $\log 5 = 0.70$) - Two liquids A and B form an ideal solution at temperature T K. At T K, the vapour pressures of pure A and B are 55 and $15 \text{ kN m}^{-2}$ respectively. What is the mole fraction of A in solution of A and B in equilibrium with a vapour in which the mole fraction of A is 0.8?
Important Questions from Physical Chemistry
- The cycloalkene (X) on bromination consumes one mole of bromine per mole of (X) and gives the product (Y) in which C:Br ratio is 3:1. The percentage of bromine in the product (Y) is _________%. (Nearest integer)
(Given : molar mass in $\text{g mol}^{-1} \text{ H} : 1, \text{ C} : 12, \text{ O} : 16, \text{ Br} : 80$) - Dissociation of a gas $\text{A}_2$ takes place according to the following chemical reaction. At equilibrium, the total pressure is $1 \text{ bar}$ at $300\text{K}$.
$\text{A}_2\text{(g)} \rightleftharpoons 2\text{A(g)}$
The standard Gibbs energy of formation of the involved substances has been provided below:Substance $\Delta G_f^\circ / \text{kJ mol}^{-1}$ $\text{A}_2$ -100.00 A -50.832
The degree of dissociation of $\text{A}_2\text{(g)}$ is given by $(x \times 10^{-2})^{1/2}$ where $x =$ _________. (Nearest integer).
$[\text{Given: } \text{R} = 8 \text{ J mol}^{-1}\text{ K}^{-1}, \log 2 = 0.3010, \log 3 = 0.48]$
Assume degree of dissociation is not negligible. - Which of the following mixture gives a buffer solution with pH = 9.25 ?
Given : $\text{pK}_b (\text{NH}_4\text{OH}) = 4.75$ Identify the correct statements :
A. Hydrated salts can be used as primary standard.
B. Primary standard should not undergo any reaction with air.
C. Reactions of primary standard with another substance should be instantaneous and stoichiometric.
D. Primary standard should not be soluble in water.
E. Primary standard should have low relative molar mass.
Choose the correct answer from the options given below :- Consider $\text{A} \xrightarrow{k_1} \text{B}$ and $\text{C} \xrightarrow{k_2} \text{D}$ are two reactions. If the rate constant ($k_1$) of the $\text{A} \longrightarrow \text{B}$ reaction can be expressed by the following equation $\log_{10} k = 14.34 - \frac{1.5 \times 10^4}{T/K}$ and activation energy of $\text{C} \longrightarrow \text{D}$ reaction ($\text{Ea}_2$) is $\frac{1}{5}$th of the $\text{A} \longrightarrow \text{B}$ reaction ($\text{Ea}_1$), then the value of ($\text{Ea}_2$) is _________ $\text{kJ mol}^{-1}$. (Nearest Integer)
