Use activity coefficients to find the concentration of hydrogen ions in a solution of 65.0 mM butanoic acid and 0.05 M NaCl. The ionization constant of butanoic acid is Ka = 1.52 × 10-5. Take the size of C3H7COO– to be 500 pm.
Find [H+], pH, and alpha.
Can you please show me step by step with equations?
Thanks
Yes, I do... The only part that I do not know is how to find the activity coefficients...
[H+]=(x)(?)(x)(?)/0.05
The rest of the problem I can do...
Thanks! :)
Sure! To find the concentration of hydrogen ions ([H+]) in the solution, we need to use the activity coefficients. Here's a step-by-step explanation of how to calculate it.
Step 1: Calculate the ionic strength (µ)
The ionic strength is a measure of the total concentration of ions in the solution. It is calculated using the equation:
µ = 1/2 ∑(ci * zi^2)
Where:
- µ is the ionic strength
- ∑ represents the sum of the concentration of each ion present in the solution
- ci is the concentration of each ion
- zi is the charge of each ion
In this case, we have two ions: C3H7COO- and Na+. The concentration of Na+ is 0.05 M, and its charge (zi) is +1. The concentration of C3H7COO- can be calculated using the initial concentration of butanoic acid (65.0 mM) and the size (radius) of C3H7COO- (given as 500 pm, or 500 * 10^-12 m). The concentration of C3H7COO- is determined by assuming complete dissociation of butanoic acid, so it will be the same as the initial concentration of butanoic acid.
Now we can calculate the ionic strength:
µ = 1/2 * [Na+] * z^2 + [C3H7COO-] * z^2
Given: [Na+] = 0.05 M, [C3H7COO-] = 65.0 mM = 65.0 * 10^-3 M, and z = charge of Na+ and C3H7COO- = +1:
µ = 1/2 * (0.05 M * 1^2) + (65.0 * 10^-3 M * 1^2)
Step 2: Calculate the ionic strength-dependent constant (A)
The constant A is related to the activity coefficient of the ion. It can be calculated using the average ionic size (represented by radius r) and the Debye-Hückel equation:
A = (0.509 * z^2 * (µ)^0.5) / (1 + (r * (µ)^0.5))
Given: z = charge of Na+ and C3H7COO- = +1, r = 500 pm = 500 * 10^-12 m:
A = (0.509 * 1^2 * (µ)^0.5) / (1 + (500 * 10^-12 m * (µ)^0.5))
Step 3: Calculate the activity coefficient (γ) for the butanoic acid
The activity coefficient of the butanoic acid (γ) can be calculated using the equation:
γ = 1 + A
Step 4: Calculate the activity (a) of the butanoic acid
The activity (a) is defined as the product of the concentration (c) and the activity coefficient (γ):
a = γ * c
Given: [butanoic acid] = 65.0 mM = 65.0 * 10^-3 M
a = γ * [butanoic acid]
Step 5: Calculate the concentration of hydrogen ions ([H+])
The concentration of hydrogen ions ([H+]) can be calculated by multiplying the activity (a) of the butanoic acid by the ionization constant (Ka):
[H+] = a * Ka
Given: Ka = 1.52 × 10^-5
[H+] = a * Ka
Step 6: Calculate the pH
The pH can be calculated using the negative logarithm of the concentration of hydrogen ions:
pH = -log10([H+])
Step 7: Calculate the degree of ionization (alpha)
The degree of ionization (alpha) represents the fraction of the butanoic acid molecules that have ionized. It can be calculated using the equation:
alpha = [H+] / [butanoic acid]
Now you have all the equations and steps necessary to find [H+], pH, and alpha. Plug in the values and solve each step to obtain the final results.
This is a huge undertaking. Can you tell us what your problem is. Surely you know how to do parts of this.
Thanks. You scare me away when I see that much work ahead.
Here is a table I have in my quant text. I don't know if you're allowed to use that or not but I'll follow up with the Debye-Huckel equation (which you probably have in your text, too).
4-4.5 Angstrom for diameter of the acetate ion. activity coefficient is 0.82 for 0.05M ionic strength.
-log fx = 0.51Z^2*sqrt (u)/[1+0.33ax*sqrt (u)]
fx is the activity coefficient of the species x.
Z is the charge on the species which is +1 for H^+ and -1 for acetate.
u is ionic strength of the solution; I assume you know how to calculate that. It will be dictated largely by the NaCl.
ax (alpha x) is the effective diameter of the hydrated ion X. For acetate the problem tells you to use 500 pm and that should be changed to 5 Angstroms and about 9 for (H3O^+) from my book table. Activity coefficient for H3O^+ at 0.05 u is 0.86 from the same table.