The amount of lactic acid, HC3H5O3, produced in a sample of muscle tissue was analyzed by reaction with hydroxide ion. Hydroxide ion was produced in the sample mixture by electrolysis. The cathode reaction is given below.
2 H2O(l) + 2 e ‾ → H2(g) + 2 OH ‾ (aq)
Hydroxide ion reacts with lactic acid as soon as it is produced. The endpoint of the reaction is detected with an acid-base indicator. It required 106 s for a current of 18.8 mA to reach the endpoint. How many grams of lactic acid (a monoprotic acid) were present in the sample?
To find the number of grams of lactic acid present in the sample, we need to determine the number of moles of lactic acid and then convert it to grams using the molar mass.
First, let's calculate the number of moles of electrons that passed through the circuit using Faraday's laws of electrolysis:
Number of moles of electrons (n) = (current in amperes (I) * time in seconds (t)) / Faraday's constant (F)
Given:
Current (I) = 18.8 mA = 0.0188 A
Time (t) = 106 s
Faraday's constant (F) = 96,485 C/mol e-
n = (0.0188 A * 106 s) / 96,485 C/mol e-
n ≈ 0.0000206 mol e-
Since the reaction between hydroxide ion (OH-) and lactic acid (HC3H5O3) involves a 1:1 ratio, the number of moles of lactic acid is equal to the number of moles of electrons.
Therefore, the number of moles of lactic acid (n) ≈ 0.0000206 mol
Next, we need to calculate the molar mass of lactic acid to convert moles to grams. The molar mass of lactic acid (HC3H5O3) is:
Molar mass (M) of lactic acid = (1 * atomic mass of H) + (3 * atomic mass of C) + (5 * atomic mass of H) + (3 * atomic mass of O)
Using the atomic masses of elements from the periodic table:
H: 1.00784 g/mol
C: 12.0107 g/mol
O: 15.999 g/mol
M ≈ (1 * 1.00784 g/mol) + (3 * 12.0107 g/mol) + (5 * 1.00784 g/mol) + (3 * 15.999 g/mol)
M ≈ 90.078 g/mol
Finally, we can calculate the mass of lactic acid using the equation:
Mass of lactic acid = Number of moles of lactic acid * Molar mass of lactic acid
Mass of lactic acid ≈ 0.0000206 mol * 90.078 g/mol
Mass of lactic acid ≈ 0.00185 g
Therefore, approximately 0.00185 grams of lactic acid were present in the sample.
To determine the amount of lactic acid present in the sample, we can use the stoichiometry of the reaction between hydroxide ion and lactic acid.
First, let's convert the current from milliamperes (mA) to amperes (A):
18.8 mA = 18.8 × 10^(-3) A = 0.0188 A
We can use Faraday's law of electrolysis to determine the number of moles of electrons transferred in the electrolysis reaction. Faraday's constant (F) is the charge of one mole of electrons and is equal to 96,485 C/mol.
The charge (Q) transferred during electrolysis is given by:
Q = I × t
Where I is the current and t is the time in seconds.
Using the given values:
Q = 0.0188 A × 106 s = 1.9928 C
Now, we can calculate the number of moles of electrons (n) transferred using Faraday's law:
n = Q / F
n = 1.9928 C / 96485 C/mol ≈ 2.0652 × 10^(-5) mol
Since the reaction between hydroxide ion and lactic acid occurs in a 1:1 ratio, the number of moles of lactic acid (n) is equal to the number of moles of hydroxide ion.
Finally, we can calculate the mass of lactic acid using its molar mass.
The molar mass of lactic acid (HC3H5O3) is:
Molar mass = (1.01 g/mol × 1) + (12.01 g/mol × 3) + (1.01 g/mol × 5) + (16.00 g/mol × 3)
Molar mass = 90.08 g/mol
Therefore, the mass of lactic acid present in the sample is:
Mass = n × molar mass
Mass = 2.0652 × 10^(-5) mol × 90.08 g/mol ≈ 0.001862 g or 1.862 mg
So, approximately 1.862 mg of lactic acid were present in the sample.