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Chapter 3: Problem 71

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 \(\mathrm{mg}\) of vitamin \(\mathrm{C}\) , what amount (moles) of vitamin C is contained in 10 tablets? What number of vitamin C molecules is in eight tablets?

Short Answer

Expert verified
The molar mass of ascorbic acid is \(176.14 \, \mathrm{g/mol}\). There are approximately \(0.0284 \, \mathrm{mol}\) of vitamin C in 10 tablets, and there are approximately \(1.37 \times 10^{22}\) vitamin C molecules in 8 tablets.

Step by step solution

01

Calculate the molar mass of ascorbic acid

To calculate the molar mass of ascorbic acid, we need to know the molar masses of carbon (C), hydrogen (H), and oxygen (O). From the periodic table, these are: - Carbon: 12.01 g/mol - Hydrogen: 1.01 g/mol - Oxygen: 16.00 g/mol Now, we simply find the total molar mass by multiplying the molar mass of each element by the number of their atoms in the formula and summing them up: Molar mass of ascorbic acid = \((6 \times 12.01) + (8 \times 1.01) + (6 \times 16.00)\)
02

Compute the molar mass

Performing the calculation from Step 1, we get: Molar mass of ascorbic acid = \((72.06) + (8.08) + (96.00)\) g/mol = \(176.14 \, \mathrm{g/mol}\)
03

Calculate the amount of moles in 10 tablets

To find the amount of moles in 10 tablets, first convert the mass of vitamin C in one tablet from milligrams (mg) to grams (g) by dividing by 1000: 500.0 mg = \(500.0/1000\) g = \(0.5 \, \mathrm{g}\) Next, multiply by 10 to find the mass of vitamin C in 10 tablets: Mass of vitamin C in 10 tablets = \(0.5 \, \mathrm{g} \times 10 = 5.0 \, \mathrm{g}\) Now, divide the mass by the molar mass to find the amount of moles: Moles of vitamin C = \(\frac{5.0 \, \mathrm{g}}{176.14 \, \mathrm{g/mol}}\)
04

Compute the number of moles

Performing the calculation from Step 3, we get: Moles of vitamin C = \(\frac{5.0}{176.14}\) mol ≈ \(0.0284 \, \mathrm{mol}\)
05

Calculate the number of molecules in 8 tablets

To find the number of molecules in 8 tablets, first find the mass of vitamin C in 8 tablets: Mass of vitamin C in 8 tablets = \(0.5 \, \mathrm{g} \times 8 = 4.0 \, \mathrm{g}\) Next, divide the mass by the molar mass to find the amount of moles: Moles of vitamin C = \(\frac{4.0 \, \mathrm{g}}{176.14 \, \mathrm{g/mol}}\) Now, multiply the number of moles by Avogadro's constant (the number of molecules in one mol) to find the number of molecules: Number of molecules = Moles of vitamin C × \(6.022 \times 10^{23}\)
06

Compute the number of molecules

Performing the calculation from Step 5, we get: Moles of vitamin C = \(\frac{4.0}{176.14}\) mol ≈ \(0.0227 \, \mathrm{mol}\) Number of molecules = \(0.0227 \, \mathrm{mol} \times 6.022 \times 10^{23} \, \mathrm{molecules/mol}\) ≈ \(1.37 \times 10^{22}\) molecules In conclusion, the molar mass of ascorbic acid is \(176.14 \, \mathrm{g/mol}\), there are approximately \(0.0284 \, \mathrm{mol}\) of vitamin C in 10 tablets, and there are approximately \(1.37 \times 10^{22}\) vitamin C molecules in 8 tablets.

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