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Chapter 22: Problem 78

How many grams of \(\mathrm{CaH}_{2}(\mathrm{s})\) are required to generate sufficient \(\mathrm{H}_{2}(\mathrm{g})\) to fill a \(235 \mathrm{L}\) weather observation balloon at \(722 \mathrm{mmHg}\) and \(19.7^{\circ} \mathrm{C} ?\) \(\mathrm{CaH}_{2}(\mathrm{s})+2 \mathrm{H}_{2} \mathrm{O}(1) \longrightarrow \mathrm{Ca}(\mathrm{OH})_{2}(\mathrm{aq})+2 \mathrm{H}_{2}(\mathrm{g})\).

Short Answer

Expert verified
Approximately 191.5 grams of \(CaH2\) is required.

Step by step solution

01

Convert given conditions to moles of \(H2\)

First, convert the given conditions to moles of \(H2\) using the Ideal Gas Law, \(PV = nRT\). Here, pressure P = 722mmHg which is 0.95 atmospheres, V is volume = 235L, R is the gas constant =0.0821 L.atm/K.mol, and T is the temperature = 19.7°C which is 292.85 K when converted. Solve for n, the number of moles of \(H_2\), thus: \(n = PV/RT = (0.95 * 235) / (0.0821 * 292.85) ≈ 9.1 mol\).
02

Convert moles of \(H2\) to moles of \(CaH2\)

Once the number of moles of \(H2\) is found, convert the moles of \(H2\) to moles of \(CaH2\) by the stoichiometry of the balanced equation. This is done because for every 1 mole of \(CaH2\), 2 moles of \(H2\) gas are produced. Therefore, the number of moles of \(CaH2\) = 9.1 mol / 2 ≈ 4.55 mol.
03

Convert moles to grams

The final step is to convert moles of \(CaH2\) to grams. Using the molecular weight of \(CaH2\) which is 42.094 g/mol, the mass of \(CaH2\) required = 4.55 mol * 42.094 g/mol ≈ 191.5 g.

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Most popular questions from this chapter

The so-called pyroanions, \(\mathrm{X}_{2} \mathrm{O}_{7}^{n-},\) form a series of structurally similar polyatomic anions for the elements Si, P, and S. (a) Draw the Lewis structures of these anions, and predict the geometry of the anions. What is the maximum number of atoms that can lie in a plane? (b) Each pyroanion in part (a) corresponds to a pyroacid, \(\mathrm{X}_{2} \mathrm{O}_{7} \mathrm{H}_{n} .\) Compare each pyroacid to the acid containing only one atom of the element in its maximum oxidation state. From this comparison, suggest a strategy for the preparation of these pyroacids. (c) What is the chlorine analogue of the pyroanions? For which acid is this species the anhydride?

The structure of \(\mathrm{N}\left(\mathrm{SiH}_{3}\right)_{3}\) involves a planar arrangement of \(\mathrm{N}\) and \(\mathrm{Si}\) atoms, whereas that of the related compound \(\mathrm{N}\left(\mathrm{CH}_{3}\right)_{3}\) has a pyramidal arrangement of N and \(\mathrm{C}\) atoms. Propose bonding schemes for these molecules that are consistent with this observation.

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.

In water, \(\mathrm{O}^{2-}\) is a strong base. If \(50.0 \mathrm{mg}\) of \(\mathrm{Li}_{2} \mathrm{O}\) is dissolved in \(750.0 \mathrm{mL}\) of aqueous solution, what will be the pH of the solution?

Various thermochemical cycles are being explored as possible sources of \(\mathrm{H}_{2}(\mathrm{g}) .\) The object is to find a series of reactions that can be conducted at moderate temperatures (about \(500^{\circ} \mathrm{C}\) ) and that results in the decomposition of water into \(\mathrm{H}_{2}\) and \(\mathrm{O}_{2} .\) Show that the following series of reactions meets these requirements. $$\begin{aligned}\mathrm{FeCl}_{2}+\mathrm{H}_{2} \mathrm{O} \longrightarrow \mathrm{Fe}_{3} \mathrm{O}_{4}+\mathrm{HCl}+\mathrm{H}_{2} \\\\\mathrm{Fe}_{3} \mathrm{O}_{4}+\mathrm{HCl}+\mathrm{Cl}_{2} & \longrightarrow \mathrm{FeCl}_{3}+\mathrm{H}_{2} \mathrm{O}+\mathrm{O}_{2} \\\\\mathrm{FeCl}_{3} \longrightarrow & \mathrm{FeCl}_{2}+\mathrm{Cl}_{2}\end{aligned}$$
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