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Chapter 2: Problem 92

A 7.12 g sample of magnesium is heated with 1.80 g of bromine, All the bromine is used up, and 2.07 g of magnesium bromide is produced. What mass of magnesium remains unreacted?

Short Answer

Expert verified
6.847 g of magnesium remains unreacted.

Step by step solution

01

Identify the Initial Masses

We start by identifying the initial masses given in the problem. We have 7.12 grams of magnesium and 1.80 grams of bromine.
02

Write the Balanced Chemical Equation

The balanced chemical reaction for magnesium combining with bromine to form magnesium bromide is: \[ \text{Mg} + \text{Br}_2 \rightarrow \text{MgBr}_2 \] which shows that 1 mole of Mg reacts with 1 mole of Br\(_2\) to produce 1 mole of MgBr\(_2\).
03

Calculate Moles of Bromine

The molar mass of bromine (Br\(_2\)) is approximately 159.8 g/mol. Calculate the moles of bromine: \[ \text{Moles of Br}_2 = \frac{1.80 \, \text{g}}{159.8 \, \text{g/mol}} \approx 0.01127 \, \text{mol} \]
04

Calculate Moles of Magnesium Bromide Produced

Now calculate the moles of magnesium bromide (MgBr\(_2\)) produced using its given mass and molar mass (184.1 g/mol): \[ \text{Moles of MgBr}_2 = \frac{2.07 \, \text{g}}{184.1 \, \text{g/mol}} \approx 0.01125 \, \text{mol} \]
05

Calculate Moles of Magnesium That Reacted

Since 1 mole of Mg reacts to form 1 mole of MgBr\(_2\), 0.01125 moles of Mg must have reacted (same as moles of MgBr\(_2\)). The molar mass of Mg is 24.3 g/mol, so: \[ \text{Mass of Mg that reacted} = 0.01125 \, \text{mol} \times 24.3 \, \text{g/mol} = 0.273 \text{g} \]
06

Calculate Mass of Magnesium Remaining

Subtract the mass of magnesium that reacted from the initial mass to find the remaining magnesium: \[ 7.12 \, \text{g} - 0.273 \, \text{g} = 6.847 \, \text{g} \]
07

Conclusion

The mass of magnesium that remains unreacted is 6.847 g.

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Key Concepts

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

Chemical Reactions
Chemical reactions are processes that transform substances into different substances. In these reactions, bonds between atoms are broken and new ones are formed.
This rearrangement allows atoms to combine in new ways.
In the example of magnesium reacting with bromine, we witness such a transformation: magnesium (Mg) and bromine (Br\(_2\)) combine to create magnesium bromide (MgBr\(_2\)).Chemical reactions:
- Start with reactants. Here, the reactants are magnesium and bromine.
- End with products. The reaction yields magnesium bromide as the product.
Reactants' atoms do not disappear; instead, they just form new products.
This concept is foundational in chemistry, as observed in our example where each atom of magnesium bonds with an atom pair of bromine to form magnesium bromide.
Moles and Molar Mass
Moles and molar mass are essential in understanding chemical reactions. The mole is a unit that measures the amount of substance.
It's one of the seven base SI units and is utilized in quantifying atoms and molecules.
One mole corresponds to approximately 6.022 x 10\(^{23}\) particles of a substance, a number known as Avogadro's constant.Molar mass, on the other hand, is the mass of one mole of a substance.
Expressed in grams per mole (g/mol), it enables the conversion between grams and moles, which is critical for stoichiometric calculations.
In the problem, knowing the molar masses of bromine (Br\(_2\), 159.8 g/mol) and magnesium bromide (MgBr\(_2\), 184.1 g/mol) allows us to determine how many moles of each are involved in the reaction.
This understanding helps chemists predict amounts of substances consumed and produced in chemical reactions.
Balanced Chemical Equations
Balanced chemical equations are crucial tools in chemistry. These equations ensure that the same number of each type of atom appears on both the reactant and product sides, maintaining the law of conservation of mass.
In essence, no atoms are lost or gained during a chemical reaction.To balance the equation for the reaction of magnesium and bromine to form magnesium bromide, we write:\[ \text{Mg} + \text{Br}_2 \rightarrow \text{MgBr}_2 \]This balanced equation indicates that one mole of magnesium reacts with one mole of bromine (Br\(_2\)) to produce one mole of magnesium bromide.
By doing these calculations, chemists can determine precisely how much of each substance is needed or produced, which was crucial in solving the problem of magnesium and bromine's reaction to form magnesium bromide.

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Most popular questions from this chapter

Answer true or false. (a) To say that "energy is quantized" means that only certain energy values are allowed. (b) Bohr discovered that the energy of an electron in an atom is quantized. (c) Electrons in atoms are confined to regions of space called "principal energy levels." (d) Each principal energy level can hold a maximum of two electrons. (e) An electron in a 1 s orbital is held closer to the nucleus than an electron in a \(2 s\) orbital. (f) An electron in a 2s orbital is harder to remove from an atom than an electron in a 1 s orbital. (g) An sorbital has the shape of a sphere, with the nucleus at the center of the sphere. (h) Each \(2 p\) orbital has the shape of a dumbbell, with the nucleus at the midpoint of the dumbbell. (i) The three \(2 p\) orbitals in an atom are aligned parallel to each other. (j) An orbital is a region of space that can hold two electrons. (k) The second shell contains one \(s\) orbital and three \(p\) orbitals. (1) In the ground-state electron configuration of an atom, only the lowest- energy orbitals are occupied. \((\mathrm{m}) \mathrm{A}\) spinning electron behaves as a tiny bar magnet, with a North Pole and a South Pole. (n) An orbital can hold a maximum of two electrons with their spins paired. (o) Paired electron spins means that the two electrons are aligned with their spins North Pole to North Pole and South Pole to South Pole. (p) \(A n\) orbital box diagram puts all of the electrons of an atom in one box with their spins aligned. (q) An orbital box diagram of a carbon atom shows two unpaired electrons. (r) A Lewis dot structure shows only the electrons in the valence shell of an atom of the element. (s) A characteristic of Group 1A elements is that each has one unpaired electron in its outermost occupied (valence) shell. (t) A characteristic of Group 6A elements is that each has six unpaired electrons in its valence shell.

Americium-241 is used in household smoke detectors. This element has 11 known isotopes, none of which occurs in nature, but must be made in the laboratory. Give the number of protons, neutrons, and electrons in an atom of americium- 241.

Name these elements (try not to look at a Periodic Table): (a) 0 (b) \(\mathrm{Pb}\) (c) \(\mathrm{Ca}\) (d) \(\mathrm{Na}\) (e) \(\mathbf{C}\) (f) \(\mathrm{Ti}\) \((g) S\) (h) Fe (i) \(\mathrm{H}\) (j) \(\mathrm{K}\) (k) \(\mathrm{Ag}\) (1) \(\mathrm{Au}\)

Consider the Period 3 elements of the Periodic Table and identify the one that matches each of the following descriptions: (a) largest ionization energy (b) three valence electrons (c) a metalloid (d) smallest atomic radius (e) an alkaline earth metal (f) electron configuration \(1 s^{2} 2 s^{2} 2 p^{6} 3 s^{2} 3 p^{3}\) (g) a noble gas (h) six valence electrons

Determine the number of protons, electrons, and neutrons present in: (a) \(32 \mathrm{P}\) (b) \(95 \mathrm{Mo}\) (c) \(44 \mathrm{Ca}\) (d) \(^{3} \mathrm{H}\) (e) \(158 \mathrm{Gd}\) (f) \(212 \mathrm{Bi}\)
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