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Chapter 3: Problem 13

Calculate each of the following quantities: (a) Amount (mol) of Mn atoms in \(62.0 \mathrm{mg}\) of Mn (b) Amount (mol) for \(1.36 \times 10^{22}\) atoms of \(\mathrm{Cu}\) (c) Mass (g) of \(8.05 \times 10^{24} \mathrm{Li}\) atoms

Short Answer

Expert verified
a) 0.00113 mol, b) 0.0226 mol, c) 92.81 g

Step by step solution

01

Convert Mass of Mn to Moles

To find the amount of Mn atoms in 62.0 mg of Mn, first convert the mass from mg to grams. \[ 62.0 \text{ mg} = 0.0620 \text{ g} \]Next, use the molar mass of Mn, which is approximately 54.94 g/mol, to convert grams to moles. \[ \text{moles of Mn} = \frac{0.0620 \text{ g}}{54.94 \text{ g/mol}} \]Calculate the result. \[ \text{moles of Mn} 鈮� 0.00113 \text{ mol} \]
02

Convert Number of Cu Atoms to Moles

To find the amount of moles for 1.36 脳 10^{22} atoms of Cu, use Avogadro's number, which is \(6.022 \times 10^{23}\) atoms/mol.\[ \text{moles of Cu} = \frac{1.36 \times 10^{22} \text{ atoms}}{6.022 \times 10^{23} \text{ atoms/mol}} \]Calculate the result. \[ \text{moles of Cu} 鈮� 0.0226 \text{ mol} \]
03

Convert Number of Li Atoms to Mass

To find the mass of 8.05 脳 10^{24} Li atoms, first convert the number of atoms to moles using Avogadro's number.\[ \text{moles of Li} = \frac{8.05 \times 10^{24} \text{ atoms}}{6.022 \times 10^{23} \text{ atoms/mol}} \]Calculate the moles. \[ \text{moles of Li} 鈮� 13.37 \text{ mol} \]Next, use the molar mass of Li, which is approximately 6.94 g/mol, to convert moles to grams.\[ \text{mass of Li} = 13.37 \text{ mol} \times 6.94 \text{ g/mol} \]Calculate the result. \[ \text{mass of Li} 鈮� 92.81 \text{ g} \]

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Key Concepts

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

molar mass
Molar mass is a fundamental concept in chemistry. It allows us to convert between the mass of a substance and the amount (in moles) of that substance. The molar mass of an element is the mass of one mole of its atoms, typically measured in grams per mole (g/mol). It is equivalent to the atomic or molecular weight of the element or compound, scaled up to Avogadro's number of particles.

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Most popular questions from this chapter

Which of the following sets of information allows you to obtain the molecular formula of a covalent compound? In each case that allows it, explain how you would proceed (draw a road map and write a plan for a solution). (a) Number of moles of each type of atom in a given sample of the compound (b) Mass \% of each element and the total number of atoms in a molecule of the compound (c) Mass \% of each element and the number of atoms of one element in a molecule of the compound (d) Empirical formula and mass \(\%\) of each element (e) Structural formula

Calculate each of the following: (a) Mass \% of I in strontium periodate (b) Mass \% of Mn in potassium permanganate

Calculate each of the following quantities: (a) Total number of ions in \(38.1 \mathrm{~g}\) of \(\mathrm{SrF}_{2}\) (b) Mass (kg) of \(3.58 \mathrm{~mol}\) of \(\mathrm{CuCl}_{2} \cdot 2 \mathrm{H}_{2} \mathrm{O}\) (c) Mass (mg) of \(2.88 \times 10^{22}\) formula units of \(\mathrm{Bi}\left(\mathrm{NO}_{3}\right)_{3} \cdot 5 \mathrm{H}_{2} \mathrm{O}\)

Menthol \((\mathscr{A} \ell=156.3 \mathrm{~g} / \mathrm{mol}),\) the strong- smelling substance in many cough drops, is a compound of carbon, hydrogen, and oxygen. When \(0.1595 \mathrm{~g}\) of menthol was burned in a combustion apparatus, \(0.449 \mathrm{~g}\) of \(\mathrm{CO}_{2}\) and \(0.184 \mathrm{~g}\) of \(\mathrm{H}_{2} \mathrm{O}\) formed. What is menthol's molecular formula?

When powdered zinc is heated with sulfur, a violent reaction occurs, and zinc sulfide forms: $$ \mathrm{Zn}(s)+\mathrm{S}_{8}(s) \longrightarrow \mathrm{ZnS}(s)[\text { unbalanced }] $$ Some of the reactants also combine with oxygen in air to form zinc oxide and sulfur dioxide. When \(83.2 \mathrm{~g}\) of Zn reacts with \(52.4 \mathrm{~g}\) of \(\mathrm{S}_{8}\), \(104.4 \mathrm{~g}\) of \(\mathrm{ZnS}\) forms. (a) What is the percent yield of \(\mathrm{ZnS}\) ? (b) If all the remaining reactants combine with oxygen, how many grams of each of the two oxides form?
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