A 0.942 M sample of carbonic acid, H2CO3, has a measured hydronium ion concentration of 6.36 ´ 10–4 M. Calculate the acid-ionization constant of carbonic acid. The equilibrium equation is:
H2CO3(aq) + H2O(l) <--><--> H3O+(aq) + HCO-3(aq)
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To calculate the acid-ionization constant (Ka) of carbonic acid (H2CO3), we can use the formula:
Ka = [H3O+][HCO3-] / [H2CO3]
Given that the measured hydronium ion concentration ([H3O+]) is 6.36 ´ 10–4 M and the sample concentration of carbonic acid ([H2CO3]) is 0.942 M, we need to determine the concentration of bicarbonate ion ([HCO3-]).
The equilibrium equation for the dissociation of carbonic acid is:
H2CO3(aq) + H2O(l) <--><--> H3O+(aq) + HCO3-(aq)
At equilibrium, the concentration of H2CO3 will be equal to the initial concentration, 0.942 M. We can assume that the concentration of HCO3- at equilibrium is x, and the concentration of H3O+ will also be x.
Therefore, we have the following equation:
x^2 / (0.942 - x) = 6.36 ´ 10–4
Now, we solve this equation to find the concentration of HCO3- (x). This can be done either by using a numerical method or by making the assumption that x << 0.942, which allows us to simplify the equation:
x^2 / 0.942 ≈ 6.36 ´ 10–4
Simplifying further:
x^2 ≈ 0.942 × (6.36 ´ 10–4)
x ≈ √(0.942 × 6.36 ´ 10–4)
After calculating this, you will find the approximate concentration of HCO3-.
Now that we have the concentrations of H3O+ and HCO3-, we can substitute them back into the formula for the acid-ionization constant (Ka):
Ka = [H3O+][HCO3-] / [H2CO3]
Substitute the values and calculate Ka to find the acid-ionization constant of carbonic acid.