a current is passed through 500 mL of a solution of CaI2. the following electrode reactions occur:
anode: 2I- ---> I2 + 2e-
cathode: 2H2O + 2e- ---> H2 + 2OH-
after some time, analysis of the solution shows that 35.7 mmol of I2 has been formed.
a) how many faradays of charge have passed through the solution?
b) how many coulombs?
c) what volume of dry H2 at STP has been formed?
d) what is the pH of the solution?
1F will deposit 1 eq I2 or 253.8/2 = 126.9 g I2.
35.7 mmol = 0.0357 mol or 0.0357 x 2 = 0.0714 equivalents.
1F x 0.0714 eq/F = 0.0714 F
There are 96,485 C in 1 F; therefore,
0.0714 x 96,485 = ?C
For 35.7 mmol I2 there must be 35.7 mmol H2. You don't have a T listed so I don't know how you correct for the vapor pressure of H2O.
A, 0.0714f
a) To determine the number of faradays of charge that have passed through the solution, we first need to calculate the moles of electrons transferred in the electrode reactions.
From the anode reaction:
2 moles of electrons are transferred for every 1 mole of I2 formed.
From the cathode reaction:
2 moles of electrons are transferred for every 1 mole of H2 formed.
Since 35.7 mmol of I2 has been formed, the number of moles of electrons transferred can be calculated as follows:
Moles of electrons = (35.7 mmol I2) * (2 moles e-/1 mole I2)
= 71.4 mmol e-
Now, we need to convert the moles of electrons to faradays using Faraday's constant. Faraday's constant is equal to 96485 C/mol e-.
Faradays = (71.4 mmol e-) * (1 mol e-/1000 mmol e-) * (1 F/96485 C)
= 0.000740 F
Therefore, approximately 0.000740 faradays of charge have passed through the solution.
b) To determine the number of coulombs, we can use Faraday's constant and the definition of faraday.
Coulombs = (0.000740 F) * (96485 C/F)
= 71.4 C
Approximately 71.4 coulombs of charge have passed through the solution.
c) To determine the volume of dry H2 at STP formed, we need to use the stoichiometry of the cathode reaction.
From the cathode reaction:
2 moles of H2 are formed for every 2 moles of electrons transferred.
Since 71.4 mmol of electrons have been transferred, the number of moles of H2 formed is given by:
Moles of H2 = (71.4 mmol e-) * (2 moles H2/2 moles e-)
= 71.4 mmol H2
At STP (standard temperature and pressure), 1 mole of any gas occupies approximately 22.4 L. Therefore, the volume of H2 gas formed is:
Volume of H2 = (71.4 mmol H2) * (22.4 L/1 mol H2) * (1 L/1000 mL)
= 1.60 L
Approximately 1.60 liters of dry hydrogen gas at STP have been formed.
d) The pH of the solution can be found by considering the anode reaction. The production of I2 suggests that I- ions are being consumed, causing the concentration of OH- to increase due to the reaction at the cathode.
The anode reaction consumes 2 electrons and produces 1 mol of I2. Since I- ions are consumed, the concentration of OH- ions increases.
The increase in OH- concentration results in an increase in the pH of the solution. However, without the initial concentrations of I- and OH-, it is not possible to calculate the exact pH. Additional information is required for an accurate pH determination.
a) To determine the number of faradays that have passed through the solution, we need to calculate the moles of electrons transferred in the reaction. From the given information, we know that 35.7 mmol of I2 has been formed. Since the anode reaction involves the generation of iodine and the transfer of 2 electrons per mole of iodine, we can conclude that the number of moles of electrons transferred is also 35.7 mmol.
Since 1 faraday is equivalent to the charge of 1 mole of electrons (F = 96,485 C/mol), we can convert the moles of electrons to faradays by dividing by Avogadro's number (N₀ = 6.022 × 10^23 mol⁻¹) and multiplying by the charge of 1 electron (1.602 × 10⁻¹⁹ C):
Number of faradays = (35.7 mmol / N₀) × (1.602 × 10⁻¹⁹ C/electron)
Now you can calculate the number of faradays that have passed through the solution.
b) To determine the number of coulombs, we can multiply the number of faradays by the charge of 1 faraday:
Number of coulombs = Number of faradays × 96,485 C/faraday
c) To calculate the volume of dry H2 gas at STP (Standard Temperature and Pressure), we can use the ideal gas law, which states that 1 mole of any gas occupies 22.4 L at STP. We know that for every 2 moles of electrons transferred, 1 mole of H2 gas is produced. So, we need to calculate the moles of H2 gas using the number of moles of electrons transferred.
Moles of H2 gas = (35.7 mmol / N₀) × (1/2)
Now, multiply the moles of H2 gas by the volume occupied by 1 mole of gas at STP to find the volume of dry H2 gas at STP.
d) To determine the pH of the solution, we need to consider the cathode reaction. The cathode reaction generates hydroxide ions (OH-) with the production of H2 gas. This results in an increase in hydroxide ion concentration and a subsequent decrease in hydrogen ion concentration (increase in pH). However, we need additional information about the initial concentration of OH- or pH of the solution to determine the final pH accurately.