El ácido fenilacético (HC8 H7 O2) es una de las sustancias que se acumulan en la sangre de los p

El ácido fenilacético (HC8 H7 O2) es una de las sustancias...

$\mathrm{El}$ ácido fenilacético $\left(\mathrm{HC}_8 \mathrm{H}_7 \mathrm{O}_2\right)$ es una de las sustancias que se acumulan en la sangre de los pacientes con fenilcetonuria, un trastorno hereditario que produce retardo mental o incluso la muerte. $\mathrm{El} \mathrm{pH}$ de una disolución 0.085 $M$ de $\mathrm{HC}_8 \mathrm{H}_7 \mathrm{O}_2$ resulta ser de 2.68. Calcule el valor de la $K_a$ de este ácido.

Key Concepts

Approximations in Equilibrium Calculations

When calculating the degree of dissociation for weak acids, it is common to use approximations such as assuming that the change in concentration due to dissociation is small compared to the initial concentration. This simplification facilitates solving the equilibrium expression without the need for solving a full quadratic equation, while still providing an accurate estimate of the acid's dissociation constant.

pH and Hydrogen Ion Concentration

The pH of a solution is a measure of its acidity, which is directly related to the concentration of hydrogen ions present. In acid-base chemistry, pH is calculated as the negative logarithm of the hydrogen ion concentration. This relationship is crucial for determining the degree of dissociation of the acid in solution.

Weak Acid Equilibrium

In the context of weak acids, the acid only partially dissociates in water, establishing an equilibrium between the undissociated acid and its ions. Understanding this equilibrium is important to relate the initial concentration of the acid to the concentrations of its dissociation products, typically using an equilibrium expression that includes K_a.

Acid Dissociation Constant (K_a)

The acid dissociation constant, K_a, quantifies the strength of a weak acid in solution by representing the extent to which the acid dissociates into its conjugate base and proton. It is defined by the equilibrium expression for the ionization reaction, where a higher K_a signifies a stronger acid capable of releasing more protons into the solution.

Transcript

00:01 Chapter 16, problem 22, from the textbook, chemistry, the central science.

00:08 So the question is asking, we have this phenyl acetate acid that is found in the blood when you have some certain type of disease.

00:19 And they're asking you to find the k value when you're given a certain concentration of the phenyl acetate acid.

00:31 And the ph.

00:33 So the first thing we're going to do is write out the equation of this acid in your blood.

00:40 So we have c6h5, c .o .h2 -c -o -h.

00:47 And since it's in blood, it's added to water.

00:55 And then that is going to then go into c -6 -h -5 -c -h -5 -h.

01:05 2 -c -o -0 -mine plus a hydronium ion.

01:13 So now since we have the equation of the reaction that is happening, we now can solve the problem more into death.

01:22 Something else to note that they have given us is they have given us the ph of the hydronium ion, and so we can find the concentration of our hydronium ion.

01:39 So we know that that hydronium concentration is equal to the antilog of your ph.

01:50 And so when we plug in this to our calculator, we get the concentration of 2 .1 times 10 to the negative 3 molars.

02:11 All right.

02:11 So that's the first thing we know.

02:13 We also know that the starting solution is 0 .085 molars of the c6h5 ch2oh.

02:24 So we're going to do an ice table...

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