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Chapter 4: Problem 14

A 3.104 g sample of an oxide of manganese contains 1.142 grams of oxygen. Write a balanced chemical equation for the reaction that produces the compound from \(\mathrm{Mn}(\mathrm{s})\) and \(\mathrm{O}_{2}(\mathrm{g})\)

Short Answer

Expert verified
The balanced chemical reaction is \(\mathrm{2Mn(s)} + \mathrm{O_{2}(g)} \rightarrow \mathrm{2MnO(s)}\)

Step by step solution

01

Calculation of moles

The first step is to convert the given masses of Mn and O into moles. The molar mass of manganese (Mn) is approximately 54.94 g/mol, and for oxygen (O), it is 16.00 g/mol. To calculate the moles, divide the given mass by the molar mass. Hence, the moles of Mn = 3.104g/54.94 g/mol = 0.056 moles (approx) and the moles of O = 1.142g/16.00 g/mol = 0.071 moles (approx).
02

Determining the empirical formula

To ascertain the empirical formula of manganese oxide, find the simplest whole number ratio of moles of Mn to moles of O. This is done by dividing each by the smallest quantity of moles. So, Mn:O = 0.056/0.056 : 0.071/0.056 = 1:1.27. Rounding to the nearest whole number gives Mn:O = 1:1 (Approximately). Hence, the empirical formula of the oxide is MnO.
03

Writing the chemical equation

Considering the empirical formula obtained in Step 2, the balanced chemical equation for the reaction that produces manganese oxide from \(\mathrm{Mn}(\mathrm{s})\) and \(\mathrm{O}_{2}(\mathrm{g})\) is:\[\mathrm{2Mn(s)} + \mathrm{O_{2}(g)} \rightarrow \mathrm{2MnO(s)}\]

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Most popular questions from this chapter

An essentially \(100 \%\) yield is necessary for a chemical reaction used to analyze a compound, but it is almost never expected for a reaction that is used to synthesize a compound. Explain this difference.

A method for eliminating oxides of nitrogen (e.g., \(\mathrm{NO}_{2}\) ) from automobile exhaust gases is to pass the exhaust gases over solid cyanuric acid, \(\mathrm{C}_{3} \mathrm{N}_{3}(\mathrm{OH})_{3}\) When the hot exhaust gases come in contact with cyanuric acid, solid \(\mathrm{C}_{3} \mathrm{N}_{3}(\mathrm{OH})_{3}\) decomposes into isocyanic acid vapor, HNCO(g), which then reacts with \(\mathrm{NO}_{2}\) in the exhaust gases to give \(\mathrm{N}_{2}, \mathrm{CO}_{2^{\prime}}\) and \(\mathrm{H}_{2} \mathrm{O}\) How many grams of \(\mathrm{C}_{3} \mathrm{N}_{3}(\mathrm{OH})_{3}\) are needed per gram of \(\mathrm{NO}_{2}\) in this method? [Hint: To balance the equation for reaction between HNCO and \(\mathrm{NO}_{2}\), balance with respect to each kind of atom in this order: \(\mathrm{H}, \mathrm{C}, \mathrm{O}, \text { and } \mathrm{N} .]\)

A 99.8 mL sample of a solution that is \(120 \%\) KI by mass \((d=1.093 \mathrm{g} / \mathrm{mL})\) is added to \(96.7 \mathrm{mL}\) of another solution that is \(14.0 \% \mathrm{Pb}\left(\mathrm{NO}_{3}\right)_{2}\) by mass \((d=1.134 \mathrm{g} / \mathrm{mL})\) How many grams of \(\mathrm{PbI}_{2}\) should form? \(\mathrm{Pb}\left(\mathrm{NO}_{3}\right)_{2}(\mathrm{aq})+2 \mathrm{KI}(\mathrm{aq}) \longrightarrow \mathrm{PbI}_{2}(\mathrm{s})+2 \mathrm{KNO}_{3}(\mathrm{aq})\)

Water and ethanol, \(\mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{OH}(\mathrm{l}),\) are miscible, that is, they can be mixed in all proportions. However, when these liquids are mixed, the total volume of the resulting solution is not equal to the sum of the pure liquid volumes, and we say that the volumes are not additive. For example, when \(50.0 \mathrm{mL}\) of water and \(50.0 \mathrm{mL}\) of \(\mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{OH}(\mathrm{l}),\) are mixed at \(20^{\circ} \mathrm{C},\) the total volume of the solution is \(96.5 \mathrm{mL}\), not \(100.0 \mathrm{mL}\). (The volumes are not additive because the interactions and packing of water molecules are slightly different from the interactions and packing of \(\mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{OH}\) molecules.) Calculate the molarity of \(\mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{OH}\) in a solution prepared by mixing \(50.0 \mathrm{mL}\) of water and \(50.0 \mathrm{mL}\) of \(\mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{OH}(\mathrm{l})\) at \(20^{\circ} \mathrm{C} .\) At this temperature, the densities of water and ethanol are 0.99821 \(\mathrm{g} / \mathrm{mL}\) and \(0.7893 \mathrm{g} / \mathrm{mL},\) respectively.

The minerals calcite, \(\mathrm{CaCO}_{3},\) magnesite, \(\mathrm{MgCO}_{3}\) and dolomite, \(\mathrm{CaCO}_{3} \cdot \mathrm{MgCO}_{3},\) decompose when strongly heated to form the corresponding metal oxide(s) and carbon dioxide gas. A 1.000 -g sample known to be one of the three minerals was strongly heated and \(0.477 \mathrm{g} \mathrm{CO}_{2}\) was obtained. Which of the three minerals was it?
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