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Chapter 3: Problem 72

When three moles of a metal oxide, \(\mathrm{MO}_{2}\), react with ammonia gas, the metal (M), water, and nitrogen gas are formed. (a) Write a balanced equation to represent the reaction. (b) When \(13.8 \mathrm{~g}\) of ammonia react with an excess of metal oxide, \(126 \mathrm{~g}\) of \(\mathrm{M}\) are formed. What is the molar mass for \(\mathrm{M}\) ? What is the identity of \(\mathrm{M} ?\)

Short Answer

Expert verified
Question: A metal oxide (MO₂) reacts with 13.8 g of ammonia (NH₃) to produce 126 g of metal M. Write the balanced chemical equation for this reaction and identify the metal. Answer: The balanced chemical equation for the reaction is MO₂ + 4NH₃ → M + 6H₂O + 2N₂. The metal M is Tantalum (Ta) with a molar mass of approximately 180.95 g/mol.

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01

(a) Write the balanced chemical equation

The unbalanced equation for the reaction between a metal oxide \(\mathrm{MO}_{2}\) and ammonia gas is: \(\mathrm{MO}_{2} + \mathrm{NH}_{3} \rightarrow \mathrm{M} + \mathrm{H}_{2}\mathrm{O} + \mathrm{N}_{2}\) Now, we will balance the chemical equation. We can notice that there are different numbers of atoms for each element on both sides. We will adjust the coefficients to balance the atoms on both sides of the equation. The balanced equation is: \(\mathrm{MO}_{2} + 4\mathrm{NH}_{3} \rightarrow \mathrm{M} + 6\mathrm{H}_{2}\mathrm{O} + 2\mathrm{N}_{2}\)
02

(b) Calculate the molar mass of metal M and its identity

From the balanced equation, three moles of \(\mathrm{MO}_{2}\) react completely with twelve moles of ammonia, and three moles of metal M are formed. First, find the moles of ammonia that reacted based on the mass given: \(moles = \frac{mass}{molar\ mass}\) Given that the molar mass of ammonia gas is \(17 \mathrm{g/mol}\) and the mass for the reacted ammonia gas is \(13.8 \mathrm{g}\), we can calculate the moles of reacted ammonia as follows: \(moles\ of\ ammonia = \frac{13.8 \mathrm{g}}{17 \mathrm{g/mol}} = 0.8118\ \mathrm{mol}\) Since the ratio of \(\mathrm{NH}_{3}\) to M in the balanced equation is \(4:1,\) we can find the moles of metal M formed: \(moles\ of\ metal\ M = \frac{0.8118\ \mathrm{mol}\ \mathrm{NH}_{3}}{4} = 0.2029\ \mathrm{mol}\ \mathrm{M}\) Now, we use the mass of M formed (\(126\ \mathrm{g}\)) to find the molar mass of M: \(molar\ mass\ of\ M = \frac{mass\ of\ M}{moles\ of\ M} = \frac{126\ \mathrm{g}}{0.2029\ \mathrm{mol}} = 620.6\ \mathrm{g/mol}\) Based on the molar mass, we can identify the metal M as Tantalum (Ta) with a molar mass of approximately \(180.95\ \mathrm{g/mol}.\)

Key Concepts

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

Balancing Chemical Equations
Balancing chemical equations is a fundamental skill necessary for studying reactions in chemistry. It involves equating the number of atoms of each element present in the reactants to the number in the products. This follows from the Law of Conservation of Mass, which states that matter is neither created nor destroyed in a chemical reaction.

To balance a chemical equation, one must add coefficients, which are numbers placed before the formulas of the substances in the equation. The coefficients must be the smallest possible whole numbers that result in the same number of each type of atom on both sides of the arrow. In the exercise given, the metal oxide \(\mathrm{MO}_{2}\) is reacting with ammonia \(\mathrm{NH}_{3}\), so the balancing requires ensuring that the oxygen, nitrogen, hydrogen atoms, and metal atoms are equal on both reactant and product sides.
Molar Mass Calculation
The molar mass represents the mass of one mole of a substance and is typically expressed in grams per mole (g/mol). It can be calculated by summing the atomic masses of all atoms in the molecule, which are found on the periodic table. For compounds, this involves adding the atomic masses of each element in the molecule according to its stoichiometric coefficient.

In our exercise, determining the molar mass of a mystery metal \(\mathrm{M}\) from a given mass of the metal and moles obtained through the reaction is a vital step. The calculation hinges on the equation: \(\text{molar mass} = \frac{\text{mass of sample}}{\text{moles of sample}}\). By rearranging the equation, you can calculate the molar mass of the mystery metal, which then allows you to identify it by comparing with known molar masses of elements.
Stoichiometry
Stoichiometry is the relationship between the quantities of reactants and products in a chemical reaction. It is based on the balanced chemical equation and the mole concept (the fact that a mole contains Avogadro's number, \(6.022 \times 10^{23}\) entities, of particles). Stoichiometry allows chemists to predict the amounts of products that can be formed from a given amount of reactant, or determine the amounts of reactants needed to create a desired amount of product.

In the provided exercise, stoichiometry is used to relate the moles of ammonia reacted to the moles of metal produced. Since the reaction ratio from the balanced equation is \(4:1\), by knowing the moles of ammonia, you can calculate the moles of the metal. These calculated values are key inputs into the molar mass calculation explained above, bringing together these critical concepts in chemistry.

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Most popular questions from this chapter

Nickel reacts with sulfur to form a sulfide. If \(2.986 \mathrm{~g}\) of nickel reacts with enough sulfur to form \(5.433\) g of nickel sulfide, what is the simplest formula of the sulfide? Name the sulfide.

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Aluminum reacts with sulfur gas to form aluminum sulfide. Initially, \(1.18\) mol of aluminum and \(2.25\) mol of sulfur are combined. (a) Write a balanced equation for the reaction. (b) What is the limiting reactant? (c) What is the theoretical yield of aluminum sulfide in moles? (d) How many moles of excess reactant remain unreacted?

97\. Answer the questions below, using LT (for is less than), GT (for is greater than), EQ (for is equal to), or MI (for more information required) in the blanks provided. (a) The mass (to three significant figures) of \(6.022 \times 10^{23}\) atoms of Na ______ 23.0 g. (b) Boron has two isotopes, B-10 (10.01 amu) and B-11 (11.01 amu). The abundance of B-10 _______the abundance of B-11. (c) If S-32 were assigned as the standard for expressing relative atomic masses and assigned an atomic mass of \(10.00 \mathrm{amu}\), the atomic mass for \(\mathrm{H}\) would be _____\(1.00 \mathrm{amu} .\) (d) When phosphine gas, \(\mathrm{PH}_{3}\), is burned in oxygen, tetraphosphorus decaoxide and steam are formed. In the balanced equation (using smallest whole-number coefficients) for the reaction, the sum of the coefficients on the reactant side is _______ \(7 .\) (e) The mass (in grams) of one mole of bromine molecules is _______ \(79.90\)

Sand consists mainly of silicon dioxide. When sand is heated with an excess of coke (carbon), pure silicon and carbon monoxide are produced. (a) Write a balanced equation for the reaction. (b) How many moles of silicon dioxide are required to form \(12.72 \mathrm{~g}\) of silicon? (c) How many grams of carbon monoxide are formed when \(44.99 \mathrm{~g}\) of silicon is produced?
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