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Chapter 4: Problem 108

A fertilizer railroad car carrying \(129,840 \mathrm{~L}\) of commercial aqueous ammonia (30\% ammonia by mass) tips over and spills. The density of the aqueous ammonia solution is \(0.88 \mathrm{~g} / \mathrm{cm}^{3}\) What mass of citric acid, $\mathrm{C}(\mathrm{OH})(\mathrm{COOH})\left(\mathrm{CH}_{2} \mathrm{COOH}\right)_{2}$ (which contains three acidic protons) is required to neutralize the spill?

Short Answer

Expert verified
To neutralize the ammonia spill, \(12,891,885.3\mathrm{~g}\) of citric acid is required.

Step by step solution

01

Find the mass of ammonia

In the given exercise, the ammonia solution has a volume of \(129,840 \mathrm{~L}\) and a density of \(0.88 \mathrm{~g} / \mathrm{cm}^{3}\). Considering the percentage of ammonia in the aqueous solution, we can find the mass of ammonia: First, convert the volume of the solution to cubic centimeters: \[1\mathrm{~L} = 1,000\mathrm{~cm}^3\] \[129,840\mathrm{~L} \times 1,000\mathrm{~cm}^3/\mathrm{L} = 12,984,000\mathrm{~cm}^3\] Next, find the mass of the solution: \[12,984,000\mathrm{~cm}^3 \times 0.88\mathrm{~g}/\mathrm{cm}^3 = 11,425,920\mathrm{~g}\] Now, find the mass of ammonia in the solution (30% by mass): \[11,425,920\mathrm{~g} \times 0.30 = 3,427,776\mathrm{~g}\]
02

Find the moles of ammonia

Using the molar mass of ammonia (NH\(_{3}\)), \(17.031\mathrm{~g/mol}\), we will find the moles of ammonia: \[ \text{moles of ammonia} = \frac{3,427,776\mathrm{~g}}{17.031\mathrm{~g/mol}} = 201,260.2\mathrm{~mol}\]
03

Determine the moles of citric acid needed

Citric acid has three acidic protons, so we need three moles of citric acid to neutralize one mole of ammonia. Thus: \[ \text{moles of citric acid} = \frac{201,260.2\mathrm{~mol}}{3} = 67,086.7\mathrm{~mol}\]
04

Find the mass of citric acid required

Finally, using the molar mass of citric acid, \(192.124\mathrm{~g/mol}\), we will find the mass of citric acid required: \[ \text{mass of citric acid} = 67,086.7\mathrm{~mol} \times 192.124\mathrm{~g/mol} = 12,891,885.3\mathrm{~g}\] To neutralize the spill, \(12,891,885.3\mathrm{~g}\) of citric acid is required.

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Most popular questions from this chapter

You are presented with a white solid and told that due to careless labeling it is not clear if the substance is barium chloride, lead chloride, or zinc chloride. When you transfer the solid to a beaker and add water, the solid dissolves to give a clear solution. Next an $\mathrm{Na}_{2} \mathrm{SO}_{4}(a q)$ solution is added and a white precipitate forms. What is the identity of the unknown white solid? [Section 4.2\(]\)

Write balanced net ionic equations for the reactions that occur in each of the following cases. Identify the spectator ion or ions in each reaction. (a) \(\mathrm{Ba}(\mathrm{OH})_{2}(a q)+\mathrm{FeCl}_{3}(a q) \longrightarrow\) (b) $\mathrm{ZnCl}_{2}(a q)+\mathrm{Cs}_{2} \mathrm{CO}_{3}(a q) \longrightarrow$ (c) $\mathrm{Na}_{2} \mathrm{~S}(a q)+\operatorname{CoSO}_{4}(a q) \longrightarrow$

Separate samples of a solution of an unknown ionic compound are treated with dilute \(\mathrm{AgNO}_{3}, \mathrm{~Pb}\left(\mathrm{NO}_{3}\right)_{2},\) and \(\mathrm{BaCl}_{2}\) Precipitates form in all three cases. Which of the following could be the anion of the unknown salt: $\mathrm{Br}^{-}, \mathrm{CO}_{3}^{2-}, \mathrm{NO}_{3}^{-} ?$

Citric acid, \(\mathrm{C}_{6} \mathrm{H}_{8} \mathrm{O}_{7}\), is a triprotic acid. It occurs naturally in citrus fruits like lemons and has applications in food flavouring and preservatives. A solution containing an unknown concentration of the acid is titrated with KOH. It requires $23.20 \mathrm{~mL}\( of \)0.500 \mathrm{M} \mathrm{KOH}$ solution to titrate all three acidic protons in \(100.00 \mathrm{~mL}\) of the citric acid solution. Write a balanced net ionic equation for the neutralization reaction, and calculate the molarity of the citric acid solution.

Write balanced molecular and net ionic equations for the reactions of (a) manganese with dilute sulfuric acid, (b) chromium with hydrobromic acid, (c) tin with hydrochloric acid, (d) aluminum with formic acid, \(\mathrm{HCOOH}\).
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