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Chapter 3: Problem 103

Elixirs such as Alka-Seltzer use the reaction of sodium bicarbonate with citric acid in aqueous solution to produce a fizz: \(3 \mathrm{NaHCO}_{3}(a q)+\mathrm{C}_{6} \mathrm{H}_{8} \mathrm{O}_{7}(a q) \longrightarrow\) $$ 3 \mathrm{CO}_{2}(g)+3 \mathrm{H}_{2} \mathrm{O}(l)+\mathrm{Na}_{3} \mathrm{C}_{6} \mathrm{H}_{5} \mathrm{O}_{7}(a q) $$ a. What mass of \(\mathrm{C}_{6} \mathrm{H}_{8} \mathrm{O}_{7}\) should be used for every \(1.0 \times 10^{2} \mathrm{mg}\) \(\mathrm{NaHCO}_{3} ?\) b. What mass of \(\mathrm{CO}_{2}(g)\) could be produced from such a mixture?

Short Answer

Expert verified
a. For every \(1.0 \times 10^{2} \mathrm{mg}\) \(\mathrm{NaHCO}_{3}\), approximately \(0.0229 \mathrm{g}\) of \(\mathrm{C}_{6} \mathrm{H}_{8} \mathrm{O}_{7}\) should be used. b. From such a mixture, approximately \(0.00526 \mathrm{g}\) of \(\mathrm{CO}_{2}(g)\) could be produced.

Step by step solution

01

Calculate moles of Sodium Bicarbonate, NaHCO3

First, we need to convert the given mass of Sodium Bicarbonate, NaHCO3, into moles. To do this, use the molar mass of NaHCO3 (84.01 g/mol). The given mass is in mg, so we will convert it to grams: \( 1.0 \times 10^2 mg = 0.10 g \) Now we can find the moles of NaHCO3: moles of NaHCO3 = \(\frac{0.10 \mathrm{g}}{84.01 \mathrm{g/mol}}\)
02

Determine moles of Citric Acid, C6H8O7

Using the stoichiometry of the balanced chemical equation, we can find the moles of Citric Acid, C6H8O7, needed: \( 3 \mathrm{NaHCO}_{3}(a q)+\mathrm{C}_{6} \mathrm{H}_{8} \mathrm{O}_{7}(a q)\longrightarrow\) From the balanced equation, we can see that for every three moles of NaHCO3, one mole of C6H8O7 is needed. We can set up a proportional relationship: \(\frac{\text{moles of C6H8O7}}{1} = \frac{\text{moles of NaHCO3}}{3}\) Now, solve for moles of C6H8O7.
03

Convert moles of Citric Acid to mass

Now that we have found the moles of C6H8O7 needed, we can convert it back to mass using the molar mass of C6H8O7 (192.12 g/mol): mass of C6H8O7 = moles of C6H8O7 × (192.12 g/mol)
04

Calculate moles and mass of CO2 produced

Using the stoichiometry of the balanced chemical equation, we can find the moles of CO2 produced. For every three moles of NaHCO3, three moles of CO2 are produced. Therefore, the moles of CO2 produced would be the same as the moles of NaHCO3. moles of CO2 = moles of NaHCO3 Now, convert the moles of CO2 to mass using the molar mass of CO2 (44.01 g/mol): mass of CO2 = moles of CO2 × (44.01 g/mol) Now you have both the mass of Citric Acid needed for every 100 mg NaHCO3 and the mass of CO2 that can be produced from this mixture.

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