if 8.7 g of butanoic acid is dissolved in enough water to make 1.0 L of solution, what is the resulting pH
Let's call butanoic acid HB. Then
HB ==> H^+ + B^-
K = (H^+)(B^-)/(HB)
Convert 8.7 g butanoic acid to moles and that dissolved in 1.0L = the molarity.
You don't list K but you must have it. Substitute K and set up an ICE chart for the equilibrium, solve for H^+ and convert to pH.
To determine the resulting pH of a solution of butanoic acid, we need to calculate the concentration of hydrogen ions (H+) in the solution. This can be done by considering butanoic acid as a weak acid and using the acid dissociation constant (Ka) for butanoic acid.
The balanced chemical equation for the dissociation of butanoic acid (C4H8O2) in water is as follows:
C4H8O2(aq) ⇌ H+(aq) + C4H7O2-(aq)
The Ka for butanoic acid is given as 1.5 x 10^-5 at 25°C.
First, let's determine the number of moles of butanoic acid in the solution:
moles = mass / molar mass
moles = 8.7 g / 88.11 g/mol (molar mass of butanoic acid)
moles ≈ 0.0987 mol
Since we have 1.0 L of solution, the concentration of butanoic acid (C4H8O2) can be expressed as:
concentration = moles / volume
concentration = 0.0987 mol / 1.0 L
concentration = 0.0987 M
Now, let's set up an ICE (Initial, Change, Equilibrium) table to determine the concentration of H+ ions at equilibrium:
C4H8O2(aq) ⇌ H+(aq) + C4H7O2-(aq)
Initial 0.0987 M 0 M 0 M
Change -x +x +x
Equilibrium 0.0987-x x x
Using the Ka expression for butanoic acid:
Ka = [H+][C4H7O2-] / [C4H8O2]
We can express the concentration of H+ ions in terms of x (the concentration of H+ ions):
x^2 / (0.0987 - x) ≈ 1.5 x 10^-5
Since x is a small value compared to 0.0987, we can assume that 0.0987 - x ≈ 0.0987:
x^2 / 0.0987 ≈ 1.5 x 10^-5
Let's solve for x:
x^2 ≈ 1.5 x 10^-5 * 0.0987
x^2 ≈ 1.4805 x 10^-6
x ≈ √(1.4805 x 10^-6)
x ≈ 0.001217 M
Now that we know the concentration of H+ ions is approximately 0.001217 M, we can calculate the pH using the equation:
pH = -log[H+]
pH ≈ -log(0.001217)
pH ≈ 2.915
Therefore, the resulting pH of the solution is approximately 2.915.