Final answer:
To find the [H3O+] in a 0.279 M formic acid solution, use the Ka value (1.8 × 10⁻⁴) and assume that the concentration change is negligible. Solve the simplified equation to find [H3O+] to be approximately 7.08 × 10⁻⁵ M.
Step-by-step explanation:
Finding the [H3O+] Concentration in Formic Acid Solution
To find the concentration of H3O+ in a 0.279 M formic acid solution, we will use the acid dissociation constant (Ka) for formic acid which is given as 1.8 × 10⁻⁴. The equilibrium expression that describes the dissociation of formic acid (HCO2H) in water is:
HCO2H(aq) → H⁺(aq) + HCO2⁻(aq)
The equilibrium concentration of H3O+ ([H3O+]) is represented by x in this dissociation reaction. Using the expression for Ka, we have:
Ka = [H⁺][HCO2⁻]/[HCO2H]
Since x will be small relative to the initial concentration of formic acid (0.279 M), we can simplify the calculation by assuming that the change in concentration of HCO2H is negligible and therefore the denominator remains approximately the initial concentration.
The Ka expression simplifies to:
1.8 × 10⁻⁴ = (x)(x)/0.279
By solving the quadratic equation, we find the value of x, which gives us the equilibrium concentration of H3O+.
The calculation is as follows:
x² = (1.8 × 10⁻⁴) × 0.279
x = √(1.8 × 10⁻⁴ × 0.279)
x = √(5.022 × 10⁻⁵)
x = 7.08 × 10⁻⁵ M
The [H3O+] concentration in the 0.279 M solution of formic acid is therefore approximately 7.08 × 10⁻⁵ M.