A typical aspirin tablet contains 325 mg acetylsalicylic acid (HC9 H7 O4). Calculate the pH of a

A typical aspirin tablet contains 325 mg acetylsalicylic...

A typical aspirin tablet contains 325 mg acetylsalicylic acid $\left(\mathrm{HC}_9 \mathrm{H}_7 \mathrm{O}_4\right)$. Calculate the pH of a solution that is prepared by dissolving two aspirin tablets in enough water to make one cup ( 237 mL ) of solution. Assume the aspirin tablets are pure acetylsalicylic acid, $K_{\mathrm{a}}=3.3 \times 10^{-4}$.

Key Concepts

Molarity and Concentration Calculations

Converting the mass of a substance into moles using its molar mass and then determining its concentration by accounting for the total volume of the solution is fundamental. This process is crucial for establishing the initial conditions needed for any subsequent equilibrium calculations in solution chemistry.

Weak Acid Dissociation

A weak acid only partially ionizes in water, establishing an equilibrium between the undissociated acid, its hydrogen ions, and its conjugate base. The acid dissociation constant (Ka) quantifies this balance and is essential for determining the extent to which the acid dissociates in solution.

Equilibrium Analysis and ICE Table

Using an ICE (Initial, Change, Equilibrium) table helps to systematically set up and analyze the equilibrium conditions of a weak acid’s dissociation. This approach facilitates solving for the unknown concentrations of species in the equilibrium, which then leads to accurate calculation of hydrogen ion concentration.

pH Calculation

pH is defined as the negative logarithm of the hydrogen ion concentration in solution. Once the hydrogen ion concentration is found from the equilibrium analysis, this concept is applied to calculate the pH, providing a measure of the acidity of the solution.

Transcript

00:01 This is the answer to chapter 14, problem number 71 from the zoomdahl chemistry textbook.

00:07 This problem asks us to calculate the ph of a solution prepared by dissolving two aspirin tablets and enough water to make 237 milliliters of solution.

00:23 The typical tablet contains 325 milligrams of aspirin, and we're told that the k -a of aspirin is 3 .3 times 10 to the negative fourth.

00:36 So we're also given the formula for aspirin, which is c9h804.

00:43 And from that, we can calculate the molar mass, which we'll need.

00:47 And so i've done that at the top of the screen here, as well as doing the unit conversions.

00:54 Since we're going to be dealing with molarities and molecular masses, we need things in grams, not milligrams, and in liters, not milliliters.

01:04 So those calculations are across the top of the screen.

01:07 Well, not the calculations, but the results of those calculations.

01:11 Okay, so the first thing that we need to do is we need to express the amount of aspirin that we have as a concentration.

01:19 And so in order to do that, so we have 650 milligrams or 0 .650 grams of aspirin.

01:26 And we will use aspirin's molecular mass.

01:32 So one mole of aspirin is going to weigh 180 .158 grams.

01:40 And so we have 0 .03608 moles of aspirin.

01:55 And we can divide that by 0 .237 liters, since that is going to going to be the volume of our solution.

02:04 And that is going to give us a molar figure.

02:09 So for concentration.

02:11 So we end up with 0 .0152 molar.

02:17 And of course, you could express that with scientific notation.

02:21 I'm just going to leave it like this for right now because we have more math to do...

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