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Chapter 3: Problem 69

Ascorbic acid, or vitamin \(\mathrm{C}\left(\mathrm{C}_{6} \mathrm{H}_{8} \mathrm{O}_{6}\right)\), is an essential vitamin. It cannot be stored by the body and must be present in the diet. What is the molar mass of ascorbic acid? Vitamin C tablets are taken as a dietary supplement. If a typical tablet contains \(500.0 \mathrm{mg}\) vitamin \(\mathrm{C}\), what amount (moles) and what number of molecules of vitamin C does it contain?

Short Answer

Expert verified
The molar mass of ascorbic acid (C6H8O6) is 176.14 g/mol. A typical 500.0 mg vitamin C tablet contains 0.00284 moles and \(1.71 \times 10^{21}\) molecules of vitamin C.

Step by step solution

01

Determine the molar mass of ascorbic acid (C6H8O6)

First, determine the atomic masses of the elements present in ascorbic acid: Carbon (C), Oxygen (O), and Hydrogen (H). The atomic masses are: - Carbon (C): 12.01 g/mol - Hydrogen (H): 1.01 g/mol - Oxygen (O): 16.00 g/mol Now, use the molecular formula (C6H8O6) to calculate the molar mass of ascorbic acid: Molar mass = (6 x Atomic mass of C) + (8 x Atomic mass of H) + (6 x Atomic mass of O)
02

Calculate the molar mass of ascorbic acid

Substitute the atomic masses in the equation obtained in step 1: Molar mass = (6 x 12.01 g/mol) + (8 x 1.01 g/mol) + (6 x 16.00 g/mol) Molar mass = 72.06 g/mol + 8.08 g/mol + 96.00 g/mol Molar mass = 176.14 g/mol The molar mass of ascorbic acid (C6H8O6) is 176.14 g/mol.
03

Calculate the amount (moles) of vitamin C in a tablet

A vitamin C tablet contains 500.0 mg of ascorbic acid. First, convert mg to grams: 500 mg = 0.500 g The amount of substance (moles) can be calculated using the formula: Moles = mass (g) / molar mass (g/mol) Substitute the given mass and calculated molar mass of ascorbic acid into the formula: Moles of vitamin C = 0.500 g / 176.14 g/mol
04

Find the number of moles of vitamin C in the tablet

Calculate the moles of vitamin C in the tablet: Moles of vitamin C = 0.500 g / 176.14 g/mol = 0.00284 mol Now, we have the amount (0.00284 mol) of vitamin C in the tablet.
05

Calculate the number of molecules of vitamin C in the tablet

Use Avogadro's number (6.022 x 10^23) to find the number of molecules: Number of molecules = moles x Avogadro's number Number of molecules = 0.00284 mol x (6.022 x 10^23 molecules/mol)
06

Determine the number of vitamin C molecules in the tablet

Calculate the number of vitamin C molecules in the tablet: Number of molecules = 0.00284 mol x (6.022 x 10^23 molecules/mol) = 1.71 x 10^21 molecules Thus, a typical 500.0 mg vitamin C tablet contains 0.00284 moles and 1.71 x 10^21 molecules of vitamin C.

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