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Chapter 22: Problem 76

What volume of \(\mathrm{H}_{2}(\mathrm{g})\) at \(25^{\circ} \mathrm{C}\) and \(752 \mathrm{mmHg}\) is required to hydrogenate oleic acid, \(\mathrm{C}_{17} \mathrm{H}_{33} \mathrm{COOH}(1)\) to produce one mole of stearic acid, \(\mathrm{C}_{17} \mathrm{H}_{35} \mathrm{COOH}(\mathrm{s}) ?\) Assume reaction (22.52) proceeds with a 95\% yield.

Short Answer

Expert verified
The required volume of \(\mathrm{H}_{2}(\mathrm{g})\) is approximately 26.3 L.

Step by step solution

01

Write the balanced chemical equation

Firstly, the balanced chemical equation for the hydrogenation of oleic acid is required to be written. This can be written as: \(\mathrm{C}_{17}\mathrm{H}_{33} \mathrm{COOH} + \mathrm{H}_{2} \rightarrow \mathrm{C}_{17} \mathrm{H}_{35} \mathrm{COOH}\). Here it can be seen that one mole of \(\mathrm{H}_{2}(\mathrm{g})\) is required to produce one mole of stearic acid.
02

Adjust mole quantity for yield

The reaction proceeds with a 95 \% yield, meaning that only 95 \% of the theoretical amount is actually used. This implies that for one mole of stearic acid to be produced, \(1 \, mole/\ 0.95 = 1.05 \, moles\) of \(\mathrm{H}_{2}(\mathrm{g})\) are actually required.
03

Calculate volume using Ideal Gas Law

With the use of the Ideal Gas Law \(PV = nRT\), the volume of the \(\mathrm{H}_{2}(\mathrm{g})\) can be calculated. In this case, \(P = 752 \, mmHg = 0.99 \, atm\), \(T = 25^{\circ}C = 298 \, K\), \(n = 1.05 \, moles\), and \(R = 0.0821 \, L \cdot atm/(K \cdot mole)\). Plugging these values into the formula results in: \(V = nRT/P = 1.05 \, mole \cdot 0.0821 \, L \cdot atm/(K \cdot mole) \cdot 298 \, K / 0.99 \, atm = 26.3 \, L\).
04

Conversion to significant digits

Giving the answer in three significant figures, as the given data all have three significant figures, the volume is around 26.3 L.

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Most popular questions from this chapter

Use information from this chapter and previous chapters to write plausible chemical equations to represent the following: (a) the reaction of silver metal with \(\mathrm{HNO}_{3}(\mathrm{aq})\) (b) the complete combustion of the rocket fuel, unsymmetrical dimethylhydrazine, \(\left(\mathrm{CH}_{3}\right)_{2} \mathrm{NNH}_{2}\) (c) the preparation of sodium triphosphate by heating a mixture of sodium dihydrogen phosphate and sodium hydrogen phosphate.

The amide anion \(\mathrm{NH}_{2}^{-}\) is a very strong base. On the basis of molecular orbital theory, would you expect \(\mathrm{NH}_{2}^{-}\) to be linear or bent?

Write a plausible chemical equation to represent the reaction of \((\mathrm{a}) \mathrm{Cl}_{2}(\mathrm{g}) \quad\) with cold \(\quad \mathrm{NaOH}(\mathrm{aq})\) (b) \(\mathrm{NaI}(\mathrm{s})\) with hot \(\mathrm{H}_{2} \mathrm{SO}_{4}(\text { concd aq }) ;\) (c) \(\mathrm{Cl}_{2}(\mathrm{g})\) with \(\mathrm{KI}_{3}(\mathrm{aq}) ; \quad\) (d) \(\quad \mathrm{NaBr}(\mathrm{s}) \quad\) with hot \(\mathrm{H}_{3} \mathrm{PO}_{4}\) \((\text { concd aq })\) (e) \(\mathrm{NaHSO}_{3}(\mathrm{aq})\) with \(\mathrm{MnO}_{4}^{-1}(\mathrm{aq})\) in dilute \(\mathrm{H}_{2} \mathrm{SO}_{4}(\mathrm{aq})\).

Use VSEPR theory to predict the probable geometric structures of (a) \(\mathrm{XeO}_{3} ;\) (b) \(\mathrm{XeO}_{4} ;\) (c) \(\mathrm{XeF}_{5}^{+}\).

Write equations to show how to prepare \(\mathrm{H}_{2}(\mathrm{g})\) from each of the following substances: \((a) \mathrm{H}_{2} \mathrm{O} ;\) (b) \(\mathrm{HI}(\mathrm{aq})\) (c) \(\mathrm{Mg}(\mathrm{s}) ;\) (d) \(\mathrm{CO}(\mathrm{g})\). Use other common laboratory reactants as necessary, that is, water, acids or bases, metals, and so on.
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