If 0.1 M of a weak acid has a pH of 4.0, what is the Ka of the acid?

If 0.1 M of a weak acid has a pH of 4.0, what is the Ka of the acid?

Step 1: Understand that pH is a measure of the concentration of hydrogen ions (H+) in a solution. The formula to find [H+] from pH is [H+] = 10^(-pH).
Step 2: Since the pH is given as 4.0, calculate [H+] using the formula: [H+] = 10^(-4.0). This gives [H+] = 0.0001 M or 10^(-4) M.
Step 3: Identify the concentration of the weak acid (HA) which is given as 0.1 M.
Step 4: Use the formula for the acid dissociation constant (Ka): Ka = [H+]^2 / [HA].
Step 5: Substitute the values into the formula: Ka = (10^(-4))^2 / 0.1.
Step 6: Calculate (10^(-4))^2 which equals 10^(-8).
Step 7: Now divide 10^(-8) by 0.1 (which is the same as 10^(-1)): Ka = 10^(-8) / 10^(-1) = 10^(-8 + 1) = 10^(-7).
Step 8: Therefore, Ka = 1 x 10^(-7).

Weak Acid Equilibrium – Understanding the dissociation of weak acids and the relationship between pH, hydrogen ion concentration, and acid dissociation constant (Ka).
pH and [H+] – Converting pH to hydrogen ion concentration using the formula [H+] = 10^(-pH).
Ka Calculation – Applying the formula for Ka to find the acid dissociation constant from known concentrations.