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Chapter 5: Problem 109

Elixirs such as Alka-Seltzer use the reaction of sodium bicarbonate with citric acid in aqueous solution to produce a fizz: $$\begin{aligned}3 \mathrm{NaHCO}_{3}(a q)+\mathrm{C}_{6} \mathrm{H}_{8} \mathrm{O}_{7}(a q) & \longrightarrow \\\3 \mathrm{CO}_{2}(g)+3 \mathrm{H}_{2} \mathrm{O}(l) &+\mathrm{Na}_{3} \mathrm{C}_{6} \mathrm{H}_{5} \mathrm{O}_{7}(a q)\end{aligned}$$ 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. The mass of \(\mathrm{C}_{6} \mathrm{H}_{8} \mathrm{O}_{7}\) that should be used for every \(1.0 \times 10^{2} \, \mathrm{mg} \, \mathrm{NaHCO}_{3}\) is: $$\rm Mass \thinspace of \thinspace C_{6}H_{8}O_{7} = (moles \thinspace of \thinspace C_{6}H_{8}O_{7})\times (192\,g/mol)$$ b. The mass of \(\mathrm{CO}_{2}(g)\) that could be produced from such a mixture is: $$\rm Mass \thinspace of \thinspace CO_2 = (moles \thinspace of \thinspace CO_2)\times (44\,g/mol)$$

Step by step solution

01

Identify the balanced chemical equation

The balanced chemical equation for the reaction is given by: $$3 \mathrm{NaHCO}_{3}(a \mathrm{q})+\mathrm{C}_{6} \mathrm{H}_{8}\mathrm{O}_{7}(a \mathrm{q}) \longrightarrow 3 \mathrm{CO}_{2}(g)+3 \mathrm{H}_{2}\mathrm{O}(l)+\mathrm{Na}_{3} \mathrm{C}_{6} \mathrm{H}_{5}\mathrm{O}_{7}(a\mathrm{q})$$
02

Determine the stoichiometric ratios

From the balanced chemical equation, we can see that: - 3 moles of \(\mathrm{NaHCO}_{3}\) reacts with 1 mole of \(\mathrm{C}_{6}\mathrm{H}_{8}\mathrm{O}_{7}\) to produce 3 moles of \(\mathrm{CO}_2\). - Hence, the stoichiometric ratio between \(\mathrm{NaHCO}_{3}\) and \(\mathrm{C}_{6}\mathrm{H}_{8}\mathrm{O}_{7}\) is 3:1, and between \(\mathrm{NaHCO}_{3}\) and \(\mathrm{CO}_2\) is 1:1.
03

Convert mass to moles

Given that the mass of \(\mathrm{NaHCO}_{3}\) is \(1.0 \times 10^2 \, \mathrm{mg}\), we can convert this into moles using the molar mass of \(\mathrm{NaHCO}_{3}\) (84 g/mol): $$\rm moles \thinspace of \thinspace NaHCO_3= \frac{1.0 \times 10^2\,mg \times \frac{1\,g}{10^3\,mg}}{84\,g/mol}$$
04

Calculate the required mass of citric acid

From the stoichiometric ratio, we know that for every 3 moles of \(\mathrm{NaHCO}_3\), 1 mole of \(\mathrm{C}_{6}\mathrm{H}_{8}\mathrm{O}_{7}\) is required. Hence, $$\rm moles \thinspace of \thinspace C_{6}H_{8}O_{7} = \frac{1}{3}\times moles \thinspace of \thinspace NaHCO_3$$ Next, convert moles of \(\mathrm{C}_{6}\mathrm{H}_{8}\mathrm{O}_{7}\) to mass using its molar mass (192 g/mol): $$\rm Mass \thinspace of \thinspace C_{6}H_{8}O_{7} = (moles \thinspace of \thinspace C_{6}H_{8}O_{7})\times (192\,g/mol)$$
05

Calculate the mass of carbon dioxide produced

From the stoichiometric ratio, we know that for every mole of \(\mathrm{NaHCO}_3\), 1 mole of \(\mathrm{CO}_2\) is produced. Hence, $$\rm moles \thinspace of \thinspace CO_2 = moles \thinspace of \thinspace NaHCO_3$$ Next, convert moles of \(\mathrm{CO}_2\) to mass using its molar mass (44 g/mol): $$\rm Mass \thinspace of \thinspace CO_2 = (moles \thinspace of \thinspace CO_2)\times (44\,g/mol)$$

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Most popular questions from this chapter

The compound \(\mathrm{As}_{2} \mathrm{I}_{4}\) is synthesized by reaction of arsenic metal with arsenic triiodide. If a solid cubic block of arsenic \(\left(d=5.72 \mathrm{g} / \mathrm{cm}^{3}\right)\) that is \(3.00 \mathrm{cm}\) on edge is allowed to react with \(1.01 \times 10^{24}\) molecules of arsenic triiodide, what mass of \(\mathrm{As}_{2} \mathrm{I}_{4}\) can be prepared? If the percent yield of \(\mathrm{As}_{2} \mathrm{I}_{4}\) was \(75.6 \%\) what mass of \(\mathrm{As}_{2} \mathrm{I}_{4}\) was actually isolated?

Consider the following reaction: $$4 \mathrm{NH}_{3}(g)+5 \mathrm{O}_{2}(g) \longrightarrow 4 \mathrm{NO}(g)+6 \mathrm{H}_{2} \mathrm{O}(g)$$ If a container were to have 10 molecules of \(\mathrm{O}_{2}\) and 10 molecules of \(\mathrm{NH}_{3}\) initially, how many total molecules (reactants plus products) would be present in the container after this reaction goes to completion?

Silicon is produced for the chemical and electronics industries by the following reactions. Give the balanced equation for each reaction. a. \(\operatorname{SiO}_{2}(s)+\mathrm{C}(s) \frac{\text { Electric }}{\text { arc furnace }} \mathrm{Si}(s)+\mathrm{CO}(g).\) b. Liquid silicon tetrachloride is reacted with very pure solid magnesium, producing solid silicon and solid magnesium chloride. c. \(\mathrm{Na}_{2} \mathrm{SiF}_{6}(s)+\mathrm{Na}(s) \rightarrow \mathrm{Si}(s)+\mathrm{NaF}(s).\)

The space shuttle environmental control system handles excess \(\mathrm{CO}_{2}\) (which the astronauts breathe out; it is \(4.0 \%\) by mass of exhaled air) by reacting it with lithium hydroxide, LiOH, pellets to form lithium carbonate, \(\mathrm{Li}_{2} \mathrm{CO}_{3}\), and water. If there are seven astronauts on board the shuttle, and each exhales 20. L of air per minute, how long could clean air be generated if there were 25,000 g of LiOH pellets available for each shuttle mission? Assume the density of air is 0.0010 g/mL.

A binary compound between an unknown element \(\mathrm{E}\) and hydrogen contains \(91.27 \%\) E and \(8.73 \%\) H by mass. If the formula of the compound is \(\mathrm{E}_{3} \mathrm{H}_{8},\) calculate the atomic mass of E.
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