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Zorluk: OrtaFaraday's Laws of Electrolysis and Quantitative Calculations

During the electrolysis of dilute tetraoxosulfate(VI) acid, a steady current of 2.50 A2.50\text{ A} is passed through the electrolyte for 1930 seconds1930\text{ seconds}. What volume of hydrogen gas, measured at STP, is liberated at the cathode?

[1 Faraday=96500 C mol−1,Molar volume of gas at STP=22.4 dm3mol−1][1\text{ Faraday} = 96500\text{ C mol}^{-1}, \text{Molar volume of gas at STP} = 22.4\text{ dm}^3\text{mol}^{-1}]

  1. 0.56 dm30.56\text{ dm}^3Cevap
  2. B
    0.60 dm30.60\text{ dm}^3
  3. C
    1.12 dm31.12\text{ dm}^3
  4. D
    1.20 dm31.20\text{ dm}^3

Cevap

The volume of hydrogen gas liberated at STP is 0.56 dm30.56\text{ dm}^3.
The correct answer is derived by calculating the electric charge passed (Q=2.50×1930=4825 CQ = 2.50 \times 1930 = 4825\text{ C}), converting to moles of electrons (0.050 mol0.050\text{ mol}), applying the electrode reduction stoichiometry (2 mol e−2\text{ mol } e^- per 1 mol H21\text{ mol } H_2), and converting the resulting 0.025 mol H20.025\text{ mol } H_2 to volume at STP using 22.4 dm3mol−122.4\text{ dm}^3\text{mol}^{-1}, which yields 0.56 dm30.56\text{ dm}^3.

Adım Adım Çözüm

1
Calculate total quantity of electricity (QQ) passed.
Q=I×t=2.50 A×1930 s=4825 CQ = I \times t = 2.50\text{ A} \times 1930\text{ s} = 4825\text{ C}
Faraday's first law states quantity of charge is the product of current and time in seconds.
2
Calculate the amount of electrons in moles transferred.
n(e−)=QF=4825 C96500 C mol−1=0.050 moln(e^-) = \frac{Q}{F} = \frac{4825\text{ C}}{96500\text{ C mol}^{-1}} = 0.050\text{ mol}
One Faraday (96500 C96500\text{ C}) represents one mole of electrons.
3
Determine moles of H2H_2 gas produced using the cathode half-reaction stoichiometry.
Cathode reaction: 2H++2e−→H2(g)2H^+ + 2e^- \rightarrow H_2(g). Moles of H2=0.050 mol e−2=0.025 mol H2H_2 = \frac{0.050\text{ mol } e^-}{2} = 0.025\text{ mol } H_2
Two moles of electrons are required to reduce hydrogen ions to produce one mole of hydrogen gas.
4
Calculate the volume of hydrogen gas at STP.
V=0.025 mol×22.4 dm3mol−1=0.56 dm3V = 0.025\text{ mol} \times 22.4\text{ dm}^3\text{mol}^{-1} = 0.56\text{ dm}^3
One mole of any ideal gas occupies 22.4 dm322.4\text{ dm}^3 at STP.

Anahtar Kavram

Quantitative application of Faraday's Laws of Electrolysis for gas evolution at electrodes.
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Faraday's Laws of Electrolysis and Quantitative Calculations

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