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Chapter 21: Problem 62

When a \(0.200 \mathrm{g}\) sample of \(\mathrm{Mg}\) is heated in air, \(0.315 \mathrm{g}\) of product is obtained. Assume that all the Mg appears in the product. (a) If the product were pure \(\mathrm{MgO}\), what mass should have been obtained? (b) Show that the 0.315 g product could be a mixture of \(\mathrm{Mg} \mathrm{O}\) and \(\mathrm{Mg}_{3} \mathrm{N}_{2}.\) (c) What is the mass percent of \(\mathrm{MgO}\) in the \(\mathrm{MgO}-\mathrm{Mg}_{3} \mathrm{N}_{2}\) mixed product?

Short Answer

Expert verified
a) The mass of MgO, if the product were pure, should have been 0.332 g. b) Yes, the 0.315 g product could be a mixture of \(MgO\) and \(Mg_{3}N_{2}\). c) The mass percent of \(MgO\) in the mixed product is 94.88%.

Step by step solution

01

Calculation of moles of Mg

First, find the number of moles of Mg using its molar mass. To do this, divide the given mass of the Mg by its molar mass. Given, mass of Mg = 0.200 g, molar mass of Mg = 24.305 g/mol. Thus, moles of Mg = mass of Mg / molar mass of Mg = \(0.200 \, \mathrm{g} / 24.305 \, \mathrm{g/mol} = 0.00823 \, \mathrm{mol}\)
02

Theoretical calculation if the product were pure MgO

We then calculate the theoretical mass of MgO if all the magnesium would have been converted to magnesium oxide (MgO). The molar mass of MgO = 24.305 (Mg) + 15.999 (O) = 40.304 g/mol. The mass of MgO = moles of Mg * molar mass of MgO = \(0.00823 \, \mathrm{mol} * 40.304 \, \mathrm{g/mol} = 0.332 \, \mathrm{g}\)
03

Comparison of calculated MgO mass and actual mass

Showing that the product could be a mixture of \(MgO\) and \(Mg_{3}N_{2}\), we compare the calculated mass of MgO with the actual obtained mass. The obtained mass of the product is less than the calculated mass for the case of pure \(MgO\), implying that another product could also have been formed.
04

Calculation of the mass percent of MgO in the mixed product

The mass percent of a component in a mixture is the mass of that component divided by the total mass of the mixture, multiplied by 100. So, mass percent of \(MgO\) = (actual mass of \(MgO\)/total mass of the product) * 100 = \(0.315 \, \mathrm{g} / 0.332 \, \mathrm{g}) * 100 = 94.88 \%\)

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Molar Mass Calculation
Understanding the molar mass of a substance is crucial for solving stoichiometry problems in chemistry. Molar mass is the mass of one mole of a substance, usually expressed in grams per mole (g/mol), and it is the sum of the atomic masses of all the atoms in a molecule.

For instance, magnesium (Mg) has an atomic mass of approximately 24.305 g/mol. When you're given the mass of a substance, you divide it by the molar mass to find the number of moles. In our exercise, with a sample of magnesium weighing 0.200 g, the number of moles of Mg is calculated by dividing this mass by the molar mass of Mg, resulting in approximately 0.00823 moles.

Knowing how to calculate the molar mass and moles of a substance is foundational for subsequent calculations in stoichiometry, such as determining theoretical yields and mass percent compositions.
Theoretical Yield
Theoretical yield is a key concept in chemistry that refers to the maximum amount of product that can be generated from a given amount of reactants under perfect conditions. It is calculated by assuming that the reaction goes to completion and that there are no losses or side reactions.

In the exercise, to find the theoretical yield of MgO, we used the molar mass of MgO (40.304 g/mol) and the moles of Mg available to calculate that if all the Mg turned into MgO, 0.332 g of MgO would be formed. This theoretical yield is vital to compare with the actual yield, which is the amount of product actually obtained from the reaction. Any discrepancy between the two can help identify if other compounds, such as Mg3N2, might have also formed during the reaction.
Chemical Reactions
Chemical reactions involve the transformation of substances through the breaking and forming of chemical bonds. In a chemical reaction, the reactants interact to produce new substances, called products. For example, when magnesium is heated in air, it can react with oxygen to form magnesium oxide (MgO), or with nitrogen to form magnesium nitride (Mg3N2).

Understanding the reactants and the possible products is essential in stoichiometry. This knowledge allows us to perform calculations, like in our exercise, where we need to consider that a mixture of products might form. Recognizing that not all of the Mg might be converted into MgO is an example of how chemical knowledge informs our stoichiometric calculations.
Mass Percent Composition
Mass percent composition is a concept that reflects the concentration of a particular substance within a mixture. It is expressed as the mass of the component of interest divided by the total mass of the mixture, multiplied by 100 to get a percentage.

In our example, the use of the mass percent composition allowed us to determine the percentage of MgO in the final product. Given the actual mass of MgO as 0.315 g and the theoretical mass as 0.332 g, the percent composition calculation reveals that the product is approximately 94.88% MgO by mass. This figure can indicate the purity of the product or can help in identifying how much of another substance, like Mg3N2, might be present in a mixture.

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Most popular questions from this chapter

Mono Lake in eastern California is a rather unusual salt lake. The lake has no outlets; water leaves only by evaporation. The rate of evaporation is great enough that the lake level would be lowered by three meters per year if not for fresh water entering through underwater springs and streams originating in the nearby Sierra Nevada mountains. The principal salts in the lake are the chlorides, bicarbonates, and sulfates of sodium. An approximate "recipe" for simulating the lake water is to dissolve 18 tablespoons of sodium bicarbonate, 10 tablespoons of sodium chloride, and 8 teaspoons of Epsom salt (magnesium sulfate heptahydrate) in 4.5 liters of water (although the lake water actually contains only trace amounts of magnesium ion). Assume that 1 tablespoon of any of the salts weighs about \(10 \mathrm{g} .(1 \text { tablespoon }=3\) teaspoons.) (a) Expressed as grams of salt per liter, what is the approximate salinity of Mono Lake? How does this salinity compare with seawater, which is approximately 0.438 M NaCl and 0.0512 M MgCl_? (b) Estimate an approximate pH for Mono Lake water. How does your estimate compare with the observed \(\mathrm{pH}\) of about \(9.8 ?\) Actually, the recipe for the lake water also calls for a pinch of borax. How would its presence affect the pH? [Borax is a sodium salt, \(\mathrm{Na}_{2} \mathrm{B}_{4} \mathrm{O}_{7} \cdot 10 \mathrm{H}_{2} \mathrm{O},\) related to the weak monoprotic boric acid \(\left(\mathrm{pK}_{\mathrm{a}}=9.25\right) \cdot\) (c) Mono Lake has some unusual limestone formations called \(t u f\). They form at the site of underwater springs and grow only underwater, although some project above water, having formed at a time when the lake level was higher. Explain how the tufa form. [Hint: What chemical reaction(s) is(are) involved?]

Describe what is meant by the terms silane and silanol. What is their role in the preparation of silicones?

Write chemical equations for the reactions you would expect to occur when (a) \(\operatorname{Mg}\left(\mathrm{HCO}_{3}\right)_{2}(\mathrm{s})\) is heated to a high temperature (b) \(\mathrm{BaCl}_{2}(1)\) is electrolyzed (c) \(\operatorname{Sr}(\text { s) is added to cold dilute } \operatorname{HBr}( \text { aq) }\) (d) \(\mathrm{Ca}(\mathrm{OH})_{2}(\mathrm{aq})\) is added to \(\mathrm{H}_{2} \mathrm{SO}_{4}(\mathrm{aq})\) (e) \(\mathrm{CaSO}_{4} \cdot 2 \mathrm{H}_{2} \mathrm{O}(\mathrm{s})\) is heated

Handbooks and lists of chemicals do not contain entries under the formulas \(\mathrm{Al}\left(\mathrm{HCO}_{3}\right)_{3}\) and \(\mathrm{Al}_{2}\left(\mathrm{CO}_{3}\right)_{2} .\) Explain why these compounds do not exist.

Lithium superoxide, \(\mathrm{LiO}_{2}(\mathrm{s}),\) has never been isolated. Use ideas from Chapter \(12,\) together with data from this chapter and Appendix \(D\), to estimate \(\Delta H_{f}\) for \(\mathrm{LiO}_{2}(\mathrm{s})\) and assess whether \(\mathrm{LiO}_{2}(\mathrm{s})\) is thermodynamically stable with respect to \(\mathrm{Li}_{2} \mathrm{O}(\mathrm{s})\) and \(\mathrm{O}_{2}(\mathrm{g}).\) (a) Use the Kapustinskii equation, along with appropriate data below, to estimate the lattice energy, \(U,\) for \(\left.\mathrm{LiO}_{2}(\mathrm{s}) . \text { (See exercise } 126 \text { in Chapter } 12 .\right)\) The ionic radii for \(L\) i \(^{+}\) and \(O_{2}^{-}\) are \(73 \mathrm{pm}\) and \(144 \mathrm{pm},\) respectively. (b) Use your result from part (a) in the BornFajans-Haber cycle to estimate \(\Delta H_{\mathrm{f}}^{2}\) for \(\mathrm{LiO}_{2}(\mathrm{s})\) [Hint: For the process \(\mathrm{O}_{2}(\mathrm{g})+\mathrm{e}^{-} \rightarrow \mathrm{O}_{2}^{-}(\mathrm{g}), \Delta H^{\circ}=.\) \(-43 \mathrm{kJ} \mathrm{mol}^{-1} .\) See Table 21.2 and Appendix \(\mathrm{D}\) for the other data that are required.] (c) Use your result from part (b) to calculate the enthalpy change for the decomposition of \(\mathrm{LiO}_{2}(\mathrm{s})\) to \(\mathrm{Li}_{2} \mathrm{O}(\mathrm{s})\) and \(\mathrm{O}_{2}(\mathrm{g}) .\) For \(\mathrm{Li}_{2} \mathrm{O}(\mathrm{s}), \Delta H_{\mathrm{f}}^{\circ}=-598.73\) \(\mathrm{kJmol}^{-1}.\) (d) Use your result from part (c) to decide whether \(\mathrm{LiO}_{2}(\mathrm{s})\) is thermodynamically stable with respect to \(\mathrm{Li}_{2} \mathrm{O}(\mathrm{s})\) and \(\mathrm{O}_{2}(\mathrm{g}) .\) Assume that entropy effects can be neglected.
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