Stoichiometry

Question 1

Define:

mole

Answer 1

A mole is the number of particles of a substance that must be present in a sample such that the sample’s mass in grams is equal to the substance’s atomic weight in AMU.

One mole is equal to 6.02 x 10²³ particles, which is Avogadro’s number.

Question 2

What is the mass of one mole of helium atoms?

One helium atom has a mass of 4 AMU.

Answer 2

4 g

One mole of atoms or molecules is the exact number such that the entire sample will have a mass (in g) identical to the individual atom or molecule’s mass in AMU.

Question 3

Define:

atomic weight

Answer 3

Atomic weight is the mass, in grams, of one mole of a naturally occurring element.

To calculate atomic weight, one must take into account both the weight of all the naturally-occurring isotopes of that element and their proportional abundance.

For example, natural Cl appears as two significant isotopes, ³⁵Cl (75% abundance) and ³⁷Cl (25% abundance). The atomic weight of Cl is therefore:

(0.75 * 35) + (0.25 * 37) = 35.5

Question 4

Define:

atomic mass

Answer 4

Atomic mass is the mass, in atomic mass units (AMU), of one atom of a particular isotope of an element.

It also represents the mass in grams of one mole of the isotopes, and can be found by adding together the number of protons and neutrons in that particular isotope.

For example, the atomic mass of ²³⁵U, with 92 protons and 143 neutrons, is 235 AMU.

Question 5

Define:

molecular weight

Answer 5

Molecular weight is the weight of one mole of molecules of a substance.

It can also be calculated by adding together the atomic weights of all the atoms in the molecule.

Question 6

What is the molecular weight of glucose, C₆H₁₂O₆?

Answer 6

180.20 AMU

(6 * C) + (12 * H) + (6 * O) =
(6 * 12.01) + (12 * 1.01) + (6 * 16.00)

These 3 masses are worth memorizing. Remember, approximation is always good enough on the MCAT, so let C = 12, H = 1, and O = 16, for a total of 180 AMU.

Question 7

Define:

molecular formula

Answer 7

A molecular formula shows the total number and type of atoms in each molecule. This is the full, unsimplified formula.

For example, the molecular formula of glucose, with 6 carbon atoms, 12 hydrogen atoms, and 6 oxygen atoms, is C₆H₁₂O₆.

Question 8

Define:

empirical formula

Answer 8

An empirical formula is the simplified ratio of whole numbers for the different elements in a compound.

For example, the empirical formula of glucose, with 6 carbon atoms, 12 hydrogen atoms, and 6 oxygen atoms, is CH₂O.

Question 9

What is the molecular formula of this molecule?

Answer 9

C₄H₈

The molecular formula is the total of all the atoms present in a single molecule of the substance.

Question 10

What is the empirical formula of this molecule?

Answer 10

CH₂

The empirical formula is the ratio of the number of atoms in a substance, expressed as the lowest common denominator. In this case, take the molecular formula, C₄H₈, and divide both subscripts by 4 to get to the final answer.

Question 11

How do you calculate the mass of one mole of a substance?

Answer 11

1. Find the atomic weight of each element in the molecular formula.
2. Multiply that weight by the subscript (number of that atom present).
3. Add these numbers together to get the total sum.

For example, 1 mole of H₂O has a mass of 18 g.

(1 * 2) + (16 * 1) = 18

Question 12

What is the approximate weight of 1 mole of carbon dioxide, CO₂?

Answer 12

44 g

To calculate the weight of 1 mole of a substance, add the atomic weights of every atom in the molecular formula. Remember, approximation is almost always good enough on most chemistry tests, especially on the MCAT.

Weight (CO₂) = 12 + 2(16) = 44 g

Question 13

How many moles are in 32 g of SO₂?

Answer 13

1/2 of a mole

1 mole of SO₂ has a mass of:

32 + 2(16) = 64 g

Thus, 32 g is one half a mole.

Question 14

Define:

percent composition

Answer 14

Percent composition is a calculation of the proportion of a substance that a particular element makes up, by weight.

The formula for percent composition is:

Question 15

What is the percent composition of oxygen in glucose, C₆H₁₂O₆?

Answer 15

53.3%

Question 16

What is density, and in what units is it typically measured?

Answer 16

Density is a characteristic property of a substance. It describes the mass of a particular volume of that substance.

The SI units for density are kg/m³, though on the MCAT you may also see g/cm³ or g/mL.

Question 17

What is the density of water in:

1. g/cm³
2. g/mL
3. kg/m³
4. kg/L

Answer 17

1. 1 g/cm³
2. 1 g/mL
3. 1,000 kg/m³
4. 1 kg/L

Question 18

If the density of liquid sulfur is 1.819 g/cm³, what is the approximate mass of 500 mL of liquid sulfur?

Answer 18

About 900 g

Mass = Density * Volume

1.819 g/cm³ * 500 mL ≈ 900 g

Remember that 1 mL = 1 cm³. Also, remember that you won’t have a calculator on the MCAT, so approximations will be necessary.

Question 19

Define:

oxidation state

Answer 19

Oxidation state is the formal charge left on an atom if it is assumed that every bond in a molecule is perfectly ionic.

For example, in H₂O, assume that the more electronegative O atom takes all the electrons in both bonds, giving it an oxidation state of -2 and leaving each H with a +1 oxidation state.

Question 20

Define:

oxidation

Answer 20

Oxidation is the process in which a chemical species loses electrons.

When a species is oxidized, its oxidation state increases. For example, Co²⁺ (aq) ⇒ Co³⁺ (aq) + e^-.

Question 21

Define:

reduction

Answer 21

Reduction is the process in which a chemical species gains electrons.

When a species is reduced, its oxidation state decreases. For example, Cu²⁺ (aq) + e^- ⇒ Cu⁺(aq).

Question 22

Identify the oxidizing agent and reducing agent in the following reaction:

Na(s) + Co³⁺ ⇒ Na⁺ + Co²⁺

Answer 22

Co³⁺ is the oxidizing agent, Na is the reducing agent.

In a redox reaction, the oxidizing agent is the species which receives electrons and is reduced, while the reducing agent is the species which donates electrons and is oxidized.

Question 23

Is each of the following an oxidizing agent or a reducing agent?

1. MnO₄^-
2. NaBH₄
3. Cr₂O₇
4. O₂
5. LiAlH₄

Answer 23

1. MnO₄^- is an oxidizing agent
2. NaBH₄ is a reducing agent
3. Cr₂O₇ is an oxidizing agent
4. O₂ is an oxidizing agent
5. LiAlH₄ is a reducing agent

Most common oxidizing agents contain oxygen atoms, particularly in the presence of metal atoms. Most common reducing agents contain hydrogen atoms in the presence of metal atoms.

Question 24

This reaction is a disproportionation reaction. What does that mean?

Hg₂Cl₂ → HgCl₂ + Hg

Answer 24

Disproportionation reactions are a subset of redox reactions in which one species (in this case, the Hg atom) acts as both the oxidizing agent and the reducing agent.

Question 25

What is the oxidation state assigned to any element in its standard state?

Answer 25

The oxidation state is zero.

For example, in O₂, the oxygen atoms share electrons perfectly, and so each has an oxidation state of zero.

Question 26

What oxidation states are commonly assigned to the following when not in their standard states?

1. oxygen
2. hydrogen

Answer 26

1. oxygen = -2
2. hydrogen = +1

Remember these notable exceptions: oxygen is -1 in peroxides (such as H₂O₂), while hydrogen is -1 in hydrides (such as NaH).

Question 27

Knowing that the oxidation state of the oxygen atoms in NO₃^- is -2, what is the oxidation state of nitrogen?

Answer 27

In this example, the oxidation state of nitrogen is +5.

1) Add up the total oxidation for all the molecule’s known atoms:
* *(-2) * 3 = -6**

2) Subtract that amount from the molecule’s net charge:
* *(-1) - (-6) = +5**

The remaining amount is the unknown atom’s oxidation state.

Question 28

What oxidation state is usually assigned to the following?

1. alkali metals
2. alkali earth metals
3. halogens

Answer 28

1. alkali metals = +1
2. alkali earth metals = +2
3. halogens = -1

Elements in these groups will typically give up or accept a standard number of electrons when making bonds in compounds.

Question 29

What is the oxidation state of the oxygen atom(s) in the following?

• O₂
• H₂O
• H₂O₂

Answer 29

• In O₂, O = 0

The oxidation number for every element in its standard state is zero.

• In H₂O, O = -2

This is oxygen’s typical oxidation state in compounds.

• In H₂O₂, O = -1

Peroxides are the one compound where oxygen has this oxidation state.

Question 30

What is the oxidation state of the nitrogen atom in the following?

• NO
• NO₂
• HNO₃

Answer 30

• In NO, N = +2

Oxygen’s oxidation state is -2, and the molecule is neutrally charged, so the nitrogen must be +2.

• In NO₂, N = +4

Oxygen’s oxidation state is -2 (total of -4 for both), and the molecule is neutrally charged, so the nitrogen must be +4.

• In HNO₃, N = +5

Oxygen’s oxidation state is -2 (total of -6 for all 3), hydrogen’s oxidation state is +1, and the molecule is neutrally charged, so the nitrogen must be +5.

Question 31

What is the oxidation state of the sulfur atom in the following?

• H₂S
• S₈
• SO_{<span>2</span>}

Answer 31

• In H₂S, S = -2

H₂=2(+1)=2, S must be -2 to compensate.

• In S₈, S = 0

This is sulfur’s standard state, all atoms are zero oxidation in their standard state.

• In SO₂, S = +4

The two oxygens (-2 each) have a total charge of -4, S must be +4 to compensate.

Question 32

Balance this chemical equation:

H₂SO₄ + NaOH → Na₂SO₄ + H₂O

Answer 32

H₂SO₄ + 2 NaOH → Na₂SO₄ + 2 H₂O

The first step in balancing any reaction is finding an atom which exists in a single molecule on each side (Na, in this case), and changing coefficients to have equal numbers on both sides. H₂O also needs to be doubled, to equate the total number of H’s and O’s on both sides.

Question 33

Balance this chemical equation:

AgNO₃ + Cu → Cu(NO₃)₂ + Ag

Answer 33

2 AgNO₃ + Cu → Cu(NO₃)₂ + 2 Ag

The first step to balancing this reaction is to balance the NO₃ groups by doubling AgNO₃ on the left. But doing so unbalances the equation in Ag, making it necessary to double Ag on the right to restore balance.

Question 34

Balance this chemical equation:

CrO₃ → Cr₂O₃ + O₂

Answer 34

4 CrO₃ → 2 Cr₂O₃ + 3 O₂

The first step in this reaction is to balance Cr atoms by doubling the CrO₃. To balance O atoms at this point requires a coefficient of 3/2 in front of the O_2. However, the rules of equation-balancing require all coefficients to be whole numbers. Doubling every coefficient, however, allows you to balance the equation using whole numbers.

Question 35

Define:

limiting reactant

Answer 35

The limiting reactant (or limiting reagent) is the reactant which is totally consumed when a chemical reaction is complete.

The amount of limiting reactant present defines the amount of product which can be created.

Question 36

What process can be used to find the limiting reactant of a reaction?

Answer 36

1. If necessary, balance the reaction.
2. If given amounts of molecules in grams, convert to moles.
3. Take the number of moles of the substance, and divide into that the coefficient in front of that substance in the balanced equation.
4. Do this for all reactants.
5. Whichever reactant has the lowest final value from that calculation is the limiting reactant.

Question 37

What is the limiting reactant in the reaction

AgNO₃ + NaCl ⇒ AgCl + NaNO₃

if there is 1 mole of AgNO₃ and 2 moles of NaCl present?

Answer 37

AgNO₃ is the limiting reactant.

1 mole of AgNO₃ will react completely with 1 mole of NaCl, since the equation shows that they react in a 1:1 ratio. Thus, there will be 1 mole of NaCl left over (in excess).

Question 38

What is the limiting reactant in the reaction

HCl + NaOH ⇒ NaCl + H₂O

if there are 37 g HCl and 60 g NaOH present?

Answer 38

HCl is the limiting reactant.

After converting grams to moles, there is one mole of HCl and 1.5 moles of NaOH. Since these combine in a 1:1 ratio, when all the HCl has been consumed, there will be 0.5 moles of excess NaOH remaining.

Question 39

What is the limiting reactant in the reaction

CH₄ + 2 O₂ ⇒ CO₂ + 2 H₂O

if there are 24g CH₄ and 64g O₂ present?

Answer 39

O₂ is the limiting reactant.

Converting grams to moles, there are 2 moles of O₂ and 1.5 moles of CH₄. Due to the 2:1 ratio in the equation, two moles of O₂ are needed for every mole of CH₄ consumed.

The 2 moles of O₂ will react completely with 1 mole CH₄, leaving 0.5 moles of excess CH₄ remaining.

Question 40

What is the theoretical yield of a reaction?

Answer 40

Theoretical yield (or expected product) is the maximum amount of product that the given amount of reactants are capable of producing.

This amount can be in number of moles or weight in grams, and assumes ideal reactivity, with 100% efficiency and no experimental error.

Question 41

What is the theoretical yield of NaCl for the equation

NaOH + HCl ⇒ H₂O + NaCl

if there are 1.5 moles NaOH and 1 mole HCl present?

Answer 41

The theoretical yield is 1 mole of NaCl.

1.5 moles of NaOH could support the formation of 1.5 moles of NaCl. In contrast, 1 mole of HCl could support the formation of 1.0 moles of NaCl. However, the limiting reagent is HCl, so 1 mole is the maximum product that is possible from this system.

Question 42

What does the Δ sign indicate in the below reaction?

Answer 42

It indicates that heat was added.

The Δ sign indicates that heat is necessary for the reaction to occur. In the case of this reaction, one could find in a table that 172.5 kJ per mole are required.

Question 43

What is the difference between the arrows in these two equations?

2 H₂O ⇔ H₃O⁺ + OH^-

NaCl (s) ⇒ Na⁺(aq) + Cl^-(aq)

Answer 43

The two-sided arrow ⇔ implies a reaction which reaches an equlibrium between reactants and products.

The single-sided arrow ⇒ indicates a reaction which goes to completion, leaving only products.