Caffeine (C₈H₁₀N₄O₂) is a weak base with a pK_b of 10.4. Calculate the pH of a solution containing a caffeine concentration of 455 mg/L.

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Hey everyone. We're asked to calculate the ph of a solution containing mg per liter of morphine. And we know that morphine is a weak base with a P K. B. Of 5.80 first. Let's go ahead and determine the polarity of our morphine. We were told that we had 545 mg per liter of morphine. And we're going to first convert this into grams and we know that we have 10 to third milligrams per one g, Calculating morphine smaller mass. We find that it's 285.33, 2 g per mole. And we can go ahead and assume that we have one leader of our morphine, Calculating this out and canceling out our units. We end up with a polarity of 0.00191 Molar. Now let's go ahead and write our reaction. We have our morphine and its formula is C. 17 H. 19 N. 03. And we react this with water. When we do this, we get the pro native version of morphine, which is C. 17 H. 19 N. 03 H. Plus. And we also get our hydroxide ions Creating our ice chart. We found that we had 0.00191 molar of our morphine. And we had zero of our products formed initially. We can go ahead and disregard our water since it is a liquid and our change is going to be a minus X on our react inside and a plus X. On our product side. Since we're losing reactant and gaining products at equilibrium, we have 0.191 minus X. For our reactant and an X. And an X. In our products. In order to find RK. B. We can go ahead and take 10 to the negative 5.80, which was our PKB. This will get us to K. B of 1.6 times 10 to the -6. Now we can go ahead and solve for R. X. And we know that r K P is equivalent to our products over our reactant. Before we move forward, we can go ahead and check if we can disregard our X and our denominator. And we can do so by taking our 0.191 and divided by our kb of 1.6 times 10 to the negative six. And if we get a value greater than 500 we can simply disregard our X. And our denominator and in this case we do so we can disregard it. Simplifying this a bit further, we get X squared over 0.191 is equal to 1.6 times 10 to the negative six, Multiplying both sides by 0. and subsequently taking the square root of both sides. We end up with an X. That is equal 5.5-8 Times 10 to the -5 Mueller. And this is going to be our concentration of hydroxide ions, solving for our p. O. H. We can take the negative log of 5.5 to 81 times 10 to the negative five. And this will get us to a p o. H of 4.26. And since the question asked us to solve for RP. H, we can simply take 14.0 And subtract 4.26. And this will get us to a ph of 9.74, which is going to be our final answer. So I hope this made sense and let us know if you have any questions.

Caffeine (C₈H₁₀N₄O₂) is a weak base with a pK_b of 10.4. Calculate the pH of a solution containing a caffeine concentration of 455 mg/L.

Verified Solution

Key Concepts

Weak Bases and pKb

pH and pOH Relationship

Concentration and Molarity

Caffeine (C8H10N4O2) is a weak base with a pKb of 10.4. Calculate the pH of a solution containing a caffeine concentration of 455 mg/L.

Verified Solution

Key Concepts

Weak Bases and pKb

pH and pOH Relationship

Concentration and Molarity

Caffeine (C₈H₁₀N₄O₂) is a weak base with a pK_b of 10.4. Calculate the pH of a solution containing a caffeine concentration of 455 mg/L.