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Four different solution containing 1M ea...

Four different solution containing 1M each of `Au^(+3), Cu^(+2), Ag^(+), Li^(+)` are being electrolysed by using inert electrodes. In how many samples, metal ions would be deposited at cathode?
`["Given :" E_(Ag^+//Ag)^(0) = 0.8, E_(Au^(+3)//Au)^(0) = 1.00 V`
`E_(Cu^(+2)//Cu)^(0) = 0.34 V, E_(Li^(+)//Li)^(0)= -3.03 V`]

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To solve the problem, we need to analyze the standard reduction potentials of the given metal ions and determine which ions will be reduced (and thus deposited) at the cathode during electrolysis. ### Step-by-Step Solution: 1. **List the Standard Reduction Potentials**: - \( E^{\circ}_{Ag^+/Ag} = 0.80 \, V \) - \( E^{\circ}_{Au^{3+}/Au} = 1.00 \, V \) - \( E^{\circ}_{Cu^{2+}/Cu} = 0.34 \, V \) - \( E^{\circ}_{Li^+/Li} = -3.03 \, V \) 2. **Identify the Reaction at the Cathode**: At the cathode, reduction occurs. The metal ions with higher standard reduction potentials will be reduced first. We need to compare the standard reduction potentials of the metal ions with that of water. 3. **Standard Reduction Potential of Water**: The standard reduction potential for the reduction of water to hydrogen gas is approximately \( E^{\circ}_{H_2O/H_2} = -0.8274 \, V \). 4. **Determine Which Ions Will Be Deposited**: - **Gold (\(Au^{3+}\))**: - \( E^{\circ}_{Au^{3+}/Au} = 1.00 \, V \) (greater than -0.8274 V, will be deposited) - **Silver (\(Ag^+\))**: - \( E^{\circ}_{Ag^+/Ag} = 0.80 \, V \) (greater than -0.8274 V, will be deposited) - **Copper (\(Cu^{2+}\))**: - \( E^{\circ}_{Cu^{2+}/Cu} = 0.34 \, V \) (greater than -0.8274 V, will be deposited) - **Lithium (\(Li^+\))**: - \( E^{\circ}_{Li^+/Li} = -3.03 \, V \) (less than -0.8274 V, will not be deposited) 5. **Conclusion**: The ions that will be deposited at the cathode are \(Au^{3+}\), \(Ag^+\), and \(Cu^{2+}\). Therefore, a total of **3 samples** will have metal ions deposited at the cathode. ### Final Answer: **3**
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