Writing Formulas, Molecular Mass and Moles

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Questions and Answers

A chemist wants to computationally predict the structure and stability of a novel polymorph of titanium dioxide ($TiO_2$) under high-pressure conditions. Which method would provide the most accurate and reliable results, balancing computational cost with the need to accurately describe the electronic structure and bonding environment of $TiO_2$?

  • Performing classical molecular dynamics simulations using empirical force fields optimized for oxides.
  • Using density functional theory (DFT) with a local density approximation (LDA) functional and a plane-wave basis set.
  • Using the Hartree-Fock method with a minimal basis set and applying corrections for electron correlation effects.
  • Employing the hybrid DFT method with a functional that includes a portion of Hartree-Fock exchange and a large, localized basis set. (correct)

A polymer chemist aims to synthesize a biodegradable polymer with precisely controlled molecular weight and narrow dispersity for biomedical applications. Which polymerization technique would be MOST suitable for achieving these goals, while also allowing for the incorporation of functional groups along the polymer backbone for targeted drug delivery?

  • Condensation polymerization of diacids and diamines using high-temperature and long reaction times.
  • Free radical polymerization using a conventional initiator and chain transfer agent.
  • Ring-opening polymerization (ROP) of cyclic esters or carbonates using a well-defined metal catalyst. (correct)
  • Emulsion polymerization of vinyl monomers in the presence of a surfactant and a water-soluble initiator.

How many atoms of each element are in a formula unit of Dinitrogen Tetroxide?

  • Three Oxygen atoms
  • Four Nitrogen atoms
  • Two Nitrogen atoms
  • Two Nitrogen atoms and Four Oxygen atoms (correct)

What distinguishes atomic mass, molecular mass, and formula mass from each other?

<p>Atomic mass refers to individual atoms, formula mass refers to ionic compounds, and molecular mass refers to covalent compounds. (D)</p> Signup and view all the answers

Calculate the formula mass of $2H_2O$

<p>36.04 u (C)</p> Signup and view all the answers

Define the term mole:

<p>Amount of any substance that contains the same number of units as the number of atoms in 12 g of carbon-12. (C)</p> Signup and view all the answers

A sample consists of 0.25 mole of ammonia. How many ammonia molecules is this?

<p>1.505 * 10^23 molecules (B)</p> Signup and view all the answers

A sample consists of 0.88 mole of Carbon Dioxide. How many Carbon Dioxide molecules is this?

<p>5.299 * 10^23 molecules (D)</p> Signup and view all the answers

A sample consists of 1.5 mole of Tetraiodine Nonoxide. How many Tetraiodine Nonoxide molecules is this?

<p>9.033 * 10^23 molecules (C)</p> Signup and view all the answers

Calculate the molar mass of calcium fluoride ($CaF_2$)

<p>78.07 g/mol (B)</p> Signup and view all the answers

You are carrying out a laboratory reaction that requires 0.0360 mole of barium chloride ($BaCl_2$). How many grams of compound do you measure out?

<p>7.43 g (C)</p> Signup and view all the answers

Determine the mass in grams of $3.2 × 10^{24}$ molecules of sulfur tetrafluoride

<p>529.23 grams (A)</p> Signup and view all the answers

Determine the mass in grams of $4 × 10^{24}$ molecules of Carbon Dioxide?

<p>292.27 grams (C)</p> Signup and view all the answers

What are the correct Formula Mass and Molar Mass units?

<p>Formula Mass: amu = Molar Mass: g/mol (A)</p> Signup and view all the answers

Under what circumstances is the subscript omitted from a chemical formula?

<p>The subscript is omitted when there is only one atom to an element. (B)</p> Signup and view all the answers

A chemist synthesizes a novel coordination complex where a transition metal is coordinated by a chiral ligand derived from a natural product. Spectroscopic analysis reveals a strong Cotton effect in the circular dichroism (CD) spectrum of the complex. What information does this Cotton effect provide about the stereochemistry and electronic structure of the complex?

<p>The sign of the Cotton effect reveals the configuration of metal-ligand chirality. The magnitude of the Cotton effect provides information on the ligand field splitting and the occupancy of d-orbitals. (B)</p> Signup and view all the answers

What term is used to describe individual components such as atoms or molecules when converting between moles and the number of those components?

<p>Particles (D)</p> Signup and view all the answers

If you have 2.5 moles of a substance, how would you calculate the number of individual particles (atoms or molecules) using the straightforward method?

<p>Multiply 2.5 by Avogadro's number ($6.022 \times 10^{23}$) (A)</p> Signup and view all the answers

What does 6.02E23 represent on a scientific calculator?

<p>6.02 multiplied by 10 to the power of 23 (A)</p> Signup and view all the answers

A calculation yields a result of $4.789 \times 10^{25}$ particles, but the initial data has only two significant figures. What is the correct way to express the final answer?

<p>$4.8 \times 10^{25}$ particles (D)</p> Signup and view all the answers

What is the primary purpose of using a conversion factor when converting between moles and atoms (or molecules)?

<p>To cancel out unwanted units and obtain the desired units (B)</p> Signup and view all the answers

Which conversion factor is correctly set up to convert from moles to number of atoms?

<p>$\frac{6.022 \times 10^{23} \text{ atoms}}{1 \text{ mole}}$ (D)</p> Signup and view all the answers

You have $1.2 \times 10^{25}$ molecules of a compound. Which calculation correctly converts this to moles using the conversion factor method?

<p>$1.2 \times 10^{25} \text{ molecules} \times \frac{1 \text{ mole}}{6.022 \times 10^{23} \text{ molecules}}$ (C)</p> Signup and view all the answers

What is the first step in converting from a given number of atoms to moles using the straightforward method?

<p>Divide the number of atoms by Avogadro's number ($6.022 \times 10^{23}$) (A)</p> Signup and view all the answers

If you calculate 3.14 moles from an atoms to moles conversion, but your initial number of atoms has only three significant figures, how should you report your final answer?

<p>3.14 moles (C)</p> Signup and view all the answers

Which of the following represents the correct setup for converting $9.0 \times 10^{22}$ atoms to moles using the conversion factor method?

<p>$9.0 \times 10^{22} \text{ atoms} \times \frac{1 \text{ mole}}{6.022 \times 10^{23} \text{ atoms}}$ (B)</p> Signup and view all the answers

You have 1.0 mole of NaCl. How many individual ions (Na+ and Cl-) are present?

<p>$1.2044 \times 10^{24}$ ions (A)</p> Signup and view all the answers

If a sample contains $1.8066 \times 10^{24}$ molecules of $H_2O$, how many moles of $H_2O$ are present?

<p>3.0 moles (C)</p> Signup and view all the answers

You want to determine the number of moles in a sample containing $3.011 \times 10^{22}$ atoms of gold (Au). Which calculation is correct?

<p>$(3.011 \times 10^{22}) / (6.022 \times 10^{23})$ (C)</p> Signup and view all the answers

A compound contains $6.022 \times 10^{24}$ molecules. How many moles of the compound are present?

<p>10.0 moles (C)</p> Signup and view all the answers

How many atoms are present in 0.5 moles of carbon?

<p>$3.011 \times 10^{23}$ atoms (D)</p> Signup and view all the answers

You have 0.25 moles of $O_2$ gas. How many molecules of $O_2$ are present?

<p>$1.5055 \times 10^{23}$ molecules (C)</p> Signup and view all the answers

You are given a sample of iron (Fe) containing $1.8 \times 10^{24}$ atoms. How many moles of iron are present in the sample, rounded to two significant figures?

<p>3.0 moles (B)</p> Signup and view all the answers

A chemist measures out 0.75 moles of glucose ($C_6H_{12}O_6$). How many molecules of glucose are present?

<p>$4.5165 \times 10^{23}$ molecules (D)</p> Signup and view all the answers

A reaction requires $2.4088 \times 10^{24}$ atoms of copper (Cu). How many moles of copper are needed for the reaction?

<p>4.0 moles (D)</p> Signup and view all the answers

What conversion factor should be used to convert $1.5 \times 10^{25}$ atoms of helium to moles?

<p>$\frac{1 \text{ mole}}{6.022 \times 10^{23} \text{ atoms}}$ (D)</p> Signup and view all the answers

If a sample contains $9.033 \times 10^{23}$ molecules of water ($H_2O$), how many moles of water are present?

<p>1.5 moles (B)</p> Signup and view all the answers

Which of the following correctly represents Avogadro's number?

<p>$6.022 \times 10^{23}$ (D)</p> Signup and view all the answers

To convert 3.0 moles of a substance to the number of molecules, which operation should you perform?

<p>Multiply 3.0 by $6.022 \times 10^{23}$ (D)</p> Signup and view all the answers

How many moles are there in $1.2044 \times 10^{24}$ atoms of iron?

<p>2.0 moles (A)</p> Signup and view all the answers

Given that you have $3.011 \times 10^{23}$ molecules of $CO_2$, how many moles of $CO_2$ do you have?

<p>0.50 moles (D)</p> Signup and view all the answers

If you have 2.0 moles of water, how many water molecules do you have?

<p>$1.2044 \times 10^{24}$ molecules (A)</p> Signup and view all the answers

If you start with $2.0 \times 10^{24}$ atoms of gold, how many moles of gold do you have? (Round to two significant figures.)

<p>3.3 moles (B)</p> Signup and view all the answers

What is the number of carbon atoms in 0.75 moles of carbon?

<p>$4.5165 \times 10^{23}$ (C)</p> Signup and view all the answers

How many moles are in a sample containing $1.5055 \times 10^{23}$ atoms of neon?

<p>0.25 moles (B)</p> Signup and view all the answers

How many molecules are there in 2.5 moles of water?

<p>$1.5055 \times 10^{24}$ (D)</p> Signup and view all the answers

If you have $7.2264 \times 10^{23}$ atoms of carbon, how many moles of carbon do you have?

<p>1.2 moles (A)</p> Signup and view all the answers

What is the number of molecules in 0.3 moles of $CO_2$?

<p>$1.8066 \times 10^{23}$ (D)</p> Signup and view all the answers

Converting $3.6132 \times 10^{24}$ molecules of water ($H_2O$) to moles, how many moles do you have?

<p>6.0 moles (C)</p> Signup and view all the answers

If you have 4 moles of methane ($CH_4$), how many molecules of methane do you have?

<p>$2.4088 \times 10^{24}$ (D)</p> Signup and view all the answers

A sample contains $2.4088 \times 10^{23}$ atoms of helium. How many moles of helium are present?

<p>0.4 mole (C)</p> Signup and view all the answers

How many molecules are present in 1.25 moles of oxygen gas ($O_2$)?

<p>$7.5275 \times 10^{23}$ (C)</p> Signup and view all the answers

What is the number of molecules in 3.5 moles of water?

<p>$2.1077 \times 10^{24}$ (B)</p> Signup and view all the answers

How many moles are there in a sample containing $1.8066 \times 10^{23}$ atoms of iron?

<p>0.3 mole (B)</p> Signup and view all the answers

Flashcards

Subscripts in chemical formulas

Subscript numbers show the quantity of atoms or groups of atoms for an element in a formula unit. If there is only one atom, the subscript is omitted.

Molecular mass

The average mass of the molecules of a compound, expressed in atomic mass units (amu).

Formula mass

Expressed in atomic mass units (u) of one formula unit of a substance, equaling the sum of all atomic masses in the chemical formula.

Mole (mol)

The amount of a substance containing the same number of units as the number of atoms in 12 g of carbon-12.

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Avogadro's Number

6.02 x 10²³, representing the number of units in one mole of a substance.

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Molar mass

The mass of one mole of a substance, expressed in grams per mole (g/mol).

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Atomic mass/formula mass units (g/mol)

Atomic mass and Formula Mass units are equivalent to g/mol

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Importance of the Mole

Mole links the macroscopic and particulate worlds.

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Atomic Mass Units numerically equal to Molar Mass

Atomic Mass Units are numerically equal to Molar Mass

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Calculating Formula Mass, Molecular Mass, Molar Mass, Etc.

Get the Sum of all the elements in the compound, and designate units.

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Moles of a substance and you must determine the Molecules?

Multiple the quantity of moles by Avogadro's Number: 6.02 X 1023

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Moles of a substance and you must determine the Mass (grams)

Multiply the quantity of moles by the Molar Mass of the compound.

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Molecules of a substance and you must determine the Mass (grams)

Divide the quantity of molecules by Avogadro's Number: 6.02 X 1023 then multiply that number by the Molar Mass

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What is a 'particle'?

Atoms, molecules, jellybeans or any individual item.

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How to convert moles to atoms

Multiply the number of moles by Avogadro's number (6.02 x 10^23).

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How to convert atoms to moles

Divide the number of atoms by Avogadro's number (6.02 x 10^23).

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What is a conversion factor?

A ratio that converts one unit to another (e.g., 6.02 x 10^23 atoms / 1 mole).

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What number is equal to one mole?

6.02 x 10^23, it represents the number of particles in one mole.

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Scientific notation

A way of writing very large or small numbers. For example, 3.3 x 10^24.

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Significant Figures

Digits in a number that contribute to its precision. Non-zero digits are always significant.

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Study Notes

Writing Formulas for Substances

  • Subscripts indicate atom count or groups of atoms of each element in a formula unit.
  • Subscripts are omitted when there is only one atom of that element.
  • Dinitrogen trioxide, N2O3, contains two nitrogen atoms and three oxygen atoms.

Molecular Mass and Formula Mass

  • Molecular mass is the average mass of a compound's molecules, expressed in atomic mass units.
  • Formula mass applies to one formula unit of a substance, also expressed in atomic mass units.
  • Formula mass is the sum of all the atomic masses in a chemical formula.
  • Carbon dioxide's molecular mass is the sum of one carbon atom and two oxygen atoms, equaling 44.01 u.

Mole (mol)

  • A mole is the amount of any substance containing the same number of units as the number of atoms in 12 g of carbon-12.
  • One mole of a substance contains 6.02 X10^23 units of that substance.
  • Avogadro's number or Avogadro's constant (NA) is 6.02 X10^23.

Molar Mass

  • Molar mass is the mass of one mole of any substance, expressed in grams per mole (g/mol).
  • The molar mass (g/mol) of a substance is numerically equivalent to the atomic, molecular, or formula mass of that substance in atomic mass units.
  • Carbon-12 has an atomic mass of 12 atomic mass units and a molar mass of 12 g per mole.
  • Atomic mass units and formula mass units are equivalent to g/mol.

Mass, Moles, and Number of Units

  • Moles connect the macroscopic and particulate worlds.
  • NA stands for the Avagadro constant.
  • MM stands for molar mass in g/mol.
  • Atomic Mass Units are numerically equal to Molar Mass
  • Amu & u = g/mol

Converting Between Moles and Number of Atoms/Molecules

  • Atoms and molecules are referred to as "particles" in conversions.
  • A particle refers to any individual item like an atom, molecule, jellybean, or coin.
  • Problems convert moles to atoms or atoms back to moles.

Moles to Atoms - Straightforward Method

  • A mole contains 6.02 x 10^23 items (602 hexillion).
  • To find the number of atoms in a given quantity of moles, multiply the number of moles by 6.02 x 10^23.
  • In calculators, 6.02 x 10^23 can be written as 6.02E23.
  • Account for significant figures in the final answer.

Moles to Atoms - Conversion Factor Method

  • Multiply the quantity of moles by a ratio to cancel out moles and end up with atoms.
  • One mole equals 6.02 x 10^23 atoms; this relationship produces conversion factors.
  • Conversion factors can be written as 1 mole / 6.02 x 10^23 atoms or 6.02 x 10^23 atoms / 1 mole.
  • To cancel out moles, use the conversion factor with moles on the bottom: 6.02 x 10^23 atoms / 1 mole.

Atoms to Moles - Straightforward Method

  • To find how many moles are in a given quantity of atoms, divide by 6.02 x 10^23.
  • Round the answer to the appropriate number of significant figures.

Atoms to Moles - Conversion Factor Method

  • Multiply the quantity of atoms by a ratio to cancel out atoms and end up with moles.
  • Use the relationship 1 mole = 6.02 x 10^23 atoms to create conversion factors.
  • Conversion factors are expressed as 1 mole / 6.02 x 10^23 atoms or 6.02 x 10^23 atoms / 1 mole.
  • To cancel out atoms, use the conversion factor with atoms on the bottom: 1 mole / 6.02 x 10^23 atoms.

Key Takeaways

  • To calculate formula mass, molecular mass, and molar mass, one must sum all the elements in the compound and designate the units.
    • Formula Mass: amu, Molecular Mass: u, Molar Mass: g/mol
  • To determine the number of molecules, multiply the quantity of moles by Avogadro's Number (6.02 X 1023) when given the moles of a substance.
  • To determine mass (grams) when given moles of a substance, multiply the quantity of moles by the molar mass of the compound.
  • To determine the mass (grams) when given the molecules of a substance, divide the quantity of molecules by Avogadro's Number (6.02 X 1023), then multiply that number by the molar mass.

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