Over a period of time, the concentration of sulfuric acid in a lead storage battery of an automobile has decreased from 38 percent by mass(density=1.29 g/mL) to 26 percent by mass(1.19 g/mL). Assume the volume of the acid remains constant at 715 mL. a)Calculate the total charge in coulombs supplied by the battery.
b)How long in hours will it take to recharge the battery back to the original sulfuric acid using a current of 24.2 A?
I would do this.
Calculate M of each of the solutions.
1.29 g/mL x 1000 mL x 0.38 x (1/98) = ?M
1.19 g/mL x 1000 mL x 0.26 x (1/98) = ?M
Convert each to mols in the 715 mL.
for the 1.29 it is ?M x 0.715 = ?
for the 1.19 is is ?M x 0.715 = ?
Now if you subtract the two mols you will have the mols H2SO4 used by the battery and that times 98 = grams H2SO4 used = ? grams H2SO4.
You know that 96,485 coulombs are used for every 49 grams (98g H2SO4/2e change).
96,485 coulombs x ?g H2SO4/49g) = ?C
For part 2,
C = amperes x seconds.
Plug in the numbers and solve for seconds. Convert seconds to hours.
a) To calculate the total charge supplied by the battery, we need to find the change in mass of sulfuric acid.
First, let's calculate the initial and final mass of sulfuric acid in the battery.
Initial mass of sulfuric acid = 38% of 715 mL
Initial mass = (38/100) * 715 mL * 1.29 g/mL
Final mass of sulfuric acid = 26% of 715 mL
Final mass = (26/100) * 715 mL * 1.19 g/mL
Now, let's calculate the change in mass:
Change in mass = Final mass - Initial mass
b) To calculate the time required to recharge the battery, we need to find the amount of charge needed to restore the original concentration of sulfuric acid.
First, let's calculate the initial and final mass of sulfuric acid in the battery.
Initial mass of sulfuric acid = 38% of 715 mL
Initial mass = (38/100) * 715 mL * 1.29 g/mL
Final mass of sulfuric acid = 38% of 715 mL
Final mass = (38/100) * 715 mL * 1.29 g/mL
Now, let's calculate the change in mass:
Change in mass = Initial mass - Final mass
Next, we need to convert the change in mass to moles of sulfuric acid:
Molar mass of sulfuric acid (H2SO4) = 98.09 g/mol
Number of moles = Change in mass / Molar mass of sulfuric acid
Finally, we can calculate the time required using Faraday's law:
1 Faraday (F) = 96500 C/mol
Total charge (Q) = Number of moles * 2 * F (since each mole of sulfuric acid produces 2 moles of charge)
Time (t) = Q / I, where I is the current
Substituting the values, we can calculate the time required.
To calculate the total charge in coulombs supplied by the battery, we need to find the mass of sulfuric acid that has been lost.
Step 1: Find the initial mass of sulfuric acid
Initial concentration = 38% by mass
Initial density = 1.29 g/mL
Initial volume = 715 mL
Initial mass = initial concentration * initial volume
Initial mass of sulfuric acid = 38% * 715 mL = 0.38 * 715 g = 271.7 g
Step 2: Find the final mass of sulfuric acid
Final concentration = 26% by mass
Final density = 1.19 g/mL
Final volume = 715 mL
Final mass = final concentration * final volume
Final mass of sulfuric acid = 26% * 715 mL = 0.26 * 715 g = 185.9 g
Step 3: Find the mass of sulfuric acid lost
Mass lost = Initial mass - Final mass
Mass lost = 271.7 g - 185.9 g = 85.8 g
Step 4: Find the total charge in coulombs
To find the total charge, we need to convert the mass of sulfuric acid lost to moles and then determine the number of coulombs using Faraday's law.
1 mole of sulfuric acid (H2SO4) contains 2 moles of H+ ions.
The charge on an H+ ion is +1.602x10^-19 C.
First, calculate the number of moles of sulfuric acid lost.
Molar mass of H2SO4 = 2*(H's atomic mass) + S's atomic mass + 4*(O's atomic mass)
= 2*(1.008 g/mol) + 32.06 g/mol + 4*(16 g/mol)
= 98.09 g/mol
Moles of sulfuric acid lost = Mass lost / Molar mass
Moles of sulfuric acid lost = 85.8 g / 98.09 g/mol = 0.875 mol
Since 1 mole of H2SO4 produces 2 moles of H+ ions, the number of moles of H+ ions lost is:
Moles of H+ ions lost = 2 * Moles of sulfuric acid lost = 2 * 0.875 mol = 1.75 mol
Finally, calculate the total charge in coulombs:
Total charge (in C) = Number of moles * Charge on an H+ ion
Total charge = 1.75 mol * 1.602x10^-19 C/mol
Total charge = 2.805x10^-19 C
So, the total charge supplied by the battery is 2.805x10^-19 coulombs.
To calculate the time it will take to recharge the battery back to the original sulfuric acid concentration, we can use Faraday's law of electrolysis.
Faraday's law states that the amount of substance in moles (Moles) being electrolyzed is directly proportional to the electrical charge (Q) passing through the electrolyte and inversely proportional to the Faraday's constant (F).
Equation: Moles = Q / (n * F)
Where:
Q = Total charge in Coulombs (found in part a)
n = Number of electrons (2 electrons in this case because sulfuric acid has 2 moles of H+ ions)
F = Faraday's constant = 96,485 C/mol
Rearranging the equation, we get:
Time (in seconds) = Moles * F / Current
First, calculate the moles of sulfuric acid for the original concentration:
Moles of H+ ions = 2 * Moles of sulfuric acid
Moles of H+ ions = 2 * (Initial concentration * Initial volume) / Molar mass
Moles of H+ ions = 2 * (38% * 715 mL) / 98.09 g/mol
Moles of H+ ions = 5.4707 mol
Now we can calculate the time in seconds:
Time (in seconds) = Moles * F / Current
Time = (5.4707 mol * 96,485 C/mol) / 24.2 A
Finally, convert the time to hours:
Time (in hours) = Time (in seconds) / 3600 seconds/hr
Solve the equation to find the time in hours.
I hope this explanation helps you understand the steps and equations involved in solving these problems!