Counting Particles By Mass: The Mole

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The Mole and Avogadro's Constant

The Avogadro constant (N_A or L) is the number of particles equivalent to the relative atomic mass (A_r) or molecular mass (M_r) of a substance in grams.
The value of the Avogadro constant is 6.02 × 10²³ mol⁻¹.
One mole of a substance contains the same number of fundamental units as there are atoms in exactly 12.00 g of carbon-12.
6.02 × 10²³ atoms of carbon-12 have a mass of exactly 12.00 g.
The Avogadro constant applies to atoms, molecules and ions.
The mass of a substance with this number of particles is called the molar mass.

Relative Atomic and Formula Mass

The relative atomic mass (A_r) of an element is the weighted average mass of one atom compared to one twelfth the mass of a carbon-12 atom.
The relative atomic mass is determined by using the weighted average mass of the isotopes of a particular element.
A_r has no units as it is a ratio and the units cancel out.
The relative formula mass (M_r) is used for compounds containing ions and is calculated in the same way as relative molecular mass.
M_r is the sum of the relative atomic masses of all atoms in the formula unit.

Molar Mass and Calculations

The molar mass of a substance is its relative atomic mass (A_r) or relative formula mass (M_r) expressed in grams.
Molar mass is given in units of g mol⁻¹.
The number of moles can be found using the formula: moles = mass (g) ÷ molar mass (g mol⁻¹).
The number of particles can be calculated using: number of particles = amount in moles × Avogadro constant.
To find the mass of a substance: mass = moles × molar mass.
Always show your workings in calculations as it is easier to check for errors and you may pick up credit if you get the final answer wrong.

Empirical and Molecular Formulas

The molecular formula shows the actual number and type of atoms in a molecule (e.g. ethanoic acid is C₂H₄O₂).
The empirical formula gives the simplest whole-number ratio of atoms of each element in a compound (e.g. ethanoic acid is CH₂O).
The empirical formula can be determined from percentage composition by mass data.
Organic compounds often have different empirical and molecular formulae.
The formula of an ionic compound is always written as an empirical formula.
To determine the molecular formula: divide the compound's relative molecular mass (M_r) by the relative mass of the empirical formula, then multiply the empirical formula by this whole number.

Molar Concentration

Concentration tells us how much solute is dissolved in a solvent to make a solution.
It is usually measured as the amount of solute in 1 dm³ of solution.
The solute is the substance being dissolved; the solvent is the liquid that does the dissolving.
A concentrated solution contains a large amount of solute per unit volume; a dilute solution contains a small amount.
Concentration can be expressed as moles per unit volume (mol dm⁻³), often written using square brackets, e.g. [NaCl] = 0.25 mol dm⁻³.
Concentration can also be expressed as mass per unit volume (g dm⁻³) or parts per million (ppm) for very low concentrations.
The formula for concentration in mol dm⁻³ is: concentration = moles of solute ÷ volume of solution (dm³).
You must convert cm³ to dm³ by dividing by 1000.

Concentration, moles and volume

Mass Concentration and ppm

The formula for mass concentration is: concentration (g dm⁻³) = mass of solute (g) ÷ volume of solution (dm³).
To convert from mol dm⁻³ to g dm⁻³: multiply the molar concentration by the molar mass.
To convert from g dm⁻³ to mol dm⁻³: divide the mass concentration by the molar mass.
Parts per million (ppm) is useful for expressing extremely low concentrations, such as pollutants in water or air.
1 ppm is defined as a mass of 1 mg dissolved in 1 dm³ of water (which weighs 1 kg), or 10⁻⁶ g in 10⁻³ g.
For concentration calculations, always check units: use g mol⁻¹ for molar mass, g for mass, and dm³ (not cm³) for volume.

Avogadro's Law and Gas Volumes

Avogadro's Law states that equal volumes of gases (under the same conditions of temperature and pressure) contain the same number of molecules.
This allows us to determine mole ratios from the volumes of reacting gases.
At standard temperature and pressure (STP), one mole of any gas occupies 22.7 dm³ (units: dm³ mol⁻¹).
STP conditions are defined as 0 °C (273 K) and 100 kPa pressure.
The volume ratio of gaseous reactants and products in a balanced chemical equation is the same as the mole ratio.
These gas volume relationships are only valid if all gases are measured under the same conditions of temperature and pressure.

Stoichiometry and Limiting Reactants in Gases

In a balanced equation, the coefficients give the mole ratio, which can be directly applied to gas volumes.
Example: C₃H₈(g) + 5O₂(g) → 3CO₂(g) + 4H₂O(l). If 50 cm³ of propane is burned, volume of O₂ needed = 5 × 50 = 250 cm³, and volume of CO₂ formed = 3 × 50 = 150 cm³.
If gases are not in the same ratio as the balanced equation, use limiting reactant principles to determine the actual amount of product formed.
To identify the limiting reactant, divide the volumes of the gases by their coefficients; the lowest number indicates the limiting reactant.
In limiting reactant problems involving gas volumes, use the 'lowest is limiting' technique.
For example, in the reaction 4NH₃(g) + 5O₂(g) → 4NO(g) + 6H₂O(l), if 70 cm³ NH₃ and 50 cm³ O₂ are used, O₂ is limiting because 50/5 = 10 is lower than 70/4 = 17.5.

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1.Which of the following is the value of the Avogadro constant?
Easy
- A6.02 × 10²³ mol⁻¹
- B6.02 × 10²² mol⁻¹
- C6.02 × 10²⁴ mol⁻¹
- D6.02 × 10⁻²³ mol⁻¹
2.Which of the following is the standard reference used for the relative atomic mass scale?
Easy
- Athe mass of an electron
- B1/12 the mass of a carbon-12 atom
- Cthe mass of a hydrogen-1 atom
- Dthe mass of a proton
3.Which of the following shows the relative formula mass of ammonium sulfate, (NH₄)₂SO₄?
Easy
- A70.00
- B132.17
- C114.09
- D132.00
4.Shown below are four molecular formulas. Which one is also an empirical formula?
Medium
- APCl₅
- BCH₃COOH
- CH₂O₂
- DC₆H₁₂O₆
5.Ethane has the formula C₂H₆. What is the mass in grams of one molecule of ethane?
Medium
- A1.8 × 10²⁵
- B3.0 × 10⁻²³
- C30.0
- D5.0 × 10⁻²³
6.A compound has an empirical formula of C₂H₆O and a molar mass of 92.16 g mol⁻¹. What is the molecular formula of this compound?
Medium
- AC₂H₆O
- BC₄H₁₂O₂
- CC₆H₁₈O₃
- DC₈H₂₄O₄
7.Which amount of the following substances contains the smallest quantity of ions?
Medium
- A2 mol of KOH
- B1 mol of NH₄Br
- C2 mol of MgCl₂
- D1 mol of Fe₂O₃
8.A sample of hydrated calcium sulfate, CaSO₄·xH₂O, has a relative formula mass of 172.19. What is the value of x?
Medium
- A1
- B2
- C3
- D4

더 많은 문제

9.Analysis of a 46.0 g sample of a compound with a molar mass of 92.0 g mol⁻¹ showed it contained 12.0 g of carbon, 2.0 g of hydrogen, and 32.0 g of oxygen. What is the molecular formula of the compound?
Medium
- ACH₂O₂
- BCH₂O
- CC₂H₄O₂
- DC₂H₄O₄
10.Ethanoic acid has the formula CH₃COOH. How many carbon atoms are present in 0.1 mol of ethanoic acid?
Medium
- A6.0 × 10²²
- B1.2 × 10²³
- C6.0 × 10²³
- D1.2 × 10²⁴
11.A compound contains carbon and hydrogen only. The amount of carbon is 80% by mass. What is the empirical formula of the compound?
Medium
- ACH
- BCH₂
- CCH₃
- DCH₄
12.A hydrated carbonate of an unknown Group 1 metal has the formula X₂CO₃·10H₂O and is found to have a relative formula mass of 286.19. What is the Group 1 metal?
Medium
- ARb
- BK
- CNa
- DLi
13.Phenazine has the molecular formula C₁₂H₈N₂. What is the empirical formula of phenazine?
Medium
- AC₆H₆N
- BC₁₂H₈N₂
- CC₆H₄N
- DC₁₂H₁₂N₂
14.A coin contains 5.869% nickel by mass. If the coin weighs 10.00 g, how many nickel atoms are in the coin?
Medium
- A4.30 × 10²²
- B3.01 × 10²³
- C6.02 × 10²⁵
- D6.02 × 10²¹
15.10 cm³ of methane and 10 cm³ of ethane were sparked with an excess of oxygen. Once cooled, the remaining gas was passed through aqueous potassium hydroxide, which absorbs carbon dioxide. Assume all measurements were taken at 25°C and 1 atm pressure. What volume of gas is absorbed by the alkali?
Hard
- A45 cm³
- B30 cm³
- C20 cm³
- D10 cm³
16.Which sample contains the largest amount, in mol, of atoms?
Hard
- A0.30 mol of P₂O₅
- B0.40 mol of CuSO₄·5H₂O
- C0.50 mol of CH₃COOH
- D0.90 mol of H₂O
17.How many ions are present in 0.02 mol of (NH₄)₃PO₄?
Hard
- A8.0 × 10⁻²
- B1.2 × 10²²
- C4.8 × 10²²
- D2.4 × 10²³
18.Which of the following statements about the mole are correct? (select all that apply)
Medium
- AOne mole of any substance contains 6.02 × 10²³ particles.
- BThe molar mass of a substance is its relative atomic or formula mass in grams.
- COne mole of oxygen gas contains 6.02 × 10²³ atoms.
- DThe Avogadro constant applies only to atoms, not molecules or ions.
- EOne mole of carbon-12 has a mass of exactly 12.00 g.
19.Which of the following are true about empirical and molecular formulas? (select all that apply)
Medium
- AThe empirical formula shows the simplest whole-number ratio of atoms.
- BThe molecular formula shows the actual number of atoms in a molecule.
- CThe empirical formula mass is always equal to the molecular mass.
- DFor ionic compounds, the formula is always written as an empirical formula.
- EThe molecular formula is always a whole-number multiple of the empirical formula.
20.The relative atomic mass of an element is the weighted average mass of one atom compared to one twelfth the mass of a carbon-12 atom.
Easy
True or false?
21.One mole of any gas at STP occupies 22.7 dm³.
Easy
True or false?
22.The empirical formula of ethanoic acid is C₂H₄O₂.
Easy
True or false?
23.Match the term with its correct definition.
Medium
- Mole
- Avogadro constant
- Molar mass
- Empirical formula
- The amount of substance containing 6.02 × 10²³ particles
- The number of particles in one mole, 6.02 × 10²³ mol⁻¹
- The mass of one mole of a substance in grams
- The simplest whole-number ratio of atoms in a compound
24.Place the steps for determining the molecular formula from percentage composition in the correct order.
Medium
- Divide the percentage by the atomic mass to get moles.
- Divide by the smallest number of moles to get the simplest ratio.
- Write the empirical formula.
- Divide the relative molecular mass by the empirical formula mass.
- Multiply the empirical formula by the whole number.
25.Which of the following correctly states Avogadro's Law?
Medium
- AEqual volumes of gases at the same temperature and pressure contain the same number of molecules
- BEqual masses of gases at the same temperature and pressure contain the same number of molecules
- COne mole of any gas occupies 22.7 dm³ at any temperature and pressure
- DThe volume of a gas is directly proportional to its molar mass at constant temperature and pressure
26.What is the total volume of gases remaining when 70 cm³ of ammonia is combusted completely with 50 cm³ of oxygen according to the equation: 4NH₃(g) + 5O₂(g) → 4NO(g) + 6H₂O(l)?
Medium
- A70 cm³
- B40 cm³
- C30 cm³
- D120 cm³
27.Which of the following statements about the mole and the Avogadro constant are correct? (select all that apply)
Medium
- AThe Avogadro constant is 6.02 × 10²³ mol⁻¹
- BOne mole of any substance contains 6.02 × 10²³ fundamental units
- CThe mass of one mole of a substance is its relative atomic or formula mass in grams
- DOne mole of oxygen gas, O₂, contains 6.02 × 10²³ atoms
- EThe Avogadro constant applies only to atoms, not to molecules or ions
28.Which of the following statements about empirical and molecular formulas is correct?
Medium
- AThe empirical formula shows the simplest whole-number ratio of atoms in a compound
- BThe molecular formula is always the same as the empirical formula for organic compounds
- CThe empirical formula gives the actual number of atoms in a molecule
- DThe molecular formula of ethanoic acid is CH₂O
29.The relative formula mass is used for compounds containing ions.
Easy
True or false?
30.Match each term with its correct definition.
Medium
- Mole
- Molar mass
- Avogadro constant
- Empirical formula
- The number of particles in one mole of a substance, 6.02 × 10²³ mol⁻¹
- The simplest whole-number ratio of atoms of each element in a compound
- The amount of substance that contains the same number of particles as there are atoms in 12.00 g of carbon-12
- The mass of one mole of a substance, in g mol⁻¹
31.Which of the following statements about Avogadro's Law and gas volumes are correct? (select all that apply)
Medium
- AEqual volumes of gases at the same temperature and pressure contain the same number of molecules.
- BAt STP, one mole of any gas occupies 22.7 dm³.
- CThe volume ratio of gaseous reactants and products in a balanced equation is the same as the mole ratio.
- DThe molar volume of a gas is independent of temperature and pressure.
- EIf gases are not in the same ratio as the balanced equation, the limiting reactant determines the amount of product.
32.A gaseous hydrocarbon burns in excess oxygen. 20 cm³ of the hydrocarbon produces 60 cm³ of carbon dioxide and 80 cm³ of water vapour, all volumes measured at the same temperature and pressure. What is the molecular formula of the hydrocarbon?
Medium
- AC₃H₈
- BC₃H₄
- CC₆H₈
- DC₂H₆
33.25.0 cm³ of a 0.100 mol dm⁻³ solution of a metal chloride, MCl₂, is found to contain 0.00250 mol of chloride ions. What is the concentration of the metal chloride solution in mol dm⁻³?
Medium
- A0.100
- B0.200
- C0.050
- D0.025
34.A 2.00 g sample of an impure sample of calcium carbonate is reacted with excess dilute hydrochloric acid. The carbon dioxide produced occupies 400 cm³ at STP (molar volume 22.7 dm³ mol⁻¹). What is the percentage purity of the calcium carbonate? (Mᵣ CaCO₃ = 100.09)
Hard
- A88.2%
- B44.1%
- C17.6%
- D100%
35.Which of the following statements about the mole and Avogadro's constant are correct? (select all that apply)
Medium
- AOne mole of any substance contains 6.02 × 10²³ particles.
- BThe Avogadro constant has units of mol⁻¹.
- COne mole of oxygen gas, O₂, contains 6.02 × 10²³ atoms.
- DThe mass of one mole of a substance in grams is numerically equal to its relative atomic or formula mass.
- EOne mole of any gas occupies 22.7 dm³ at any temperature and pressure.
36.At the same temperature and pressure, 1 dm³ of nitrogen gas contains the same number of molecules as 1 dm³ of carbon dioxide gas.
Easy
True or false?
37.A student heats a sample of hydrated copper(II) sulfate, CuSO₄·5H₂O, in a crucible until constant mass. Which experimental technique is most suitable for ensuring all the water of crystallisation has been removed?
Medium
- AHeating to constant mass
- BFiltering the residue
- CTitrating against a standard solution
- DMeasuring the volume of gas evolved
38.A 1.00 g sample of an impure carbonate is reacted with excess dilute hydrochloric acid. The carbon dioxide produced is collected and its volume measured at STP. Which additional measurement is essential to calculate the percentage purity of the carbonate?
Medium
- AThe molar mass of the carbonate
- BThe concentration of the acid
- CThe temperature of the room
- DThe mass of the empty flask
39.Which of the following precautions are important when carrying out a titration to determine the concentration of an unknown acid? (select all that apply)
Medium
- ARinse the burette with the solution it will contain
- BUse a measuring cylinder to measure the acid into the conical flask
- CAdd the indicator near the end point
- DRead the burette at eye level, taking the bottom of the meniscus
- EPerform a rough titration first to estimate the end point
40.When determining the empirical formula from combustion data, the mass of oxygen in the compound is found by subtracting the masses of carbon and hydrogen from the original mass of the compound.
Easy
True or false?
41.Calculate the molar mass of urea, CO(NH₂)₂, in g mol⁻¹. Give your answer to two decimal places.
Medium
42.Calculate the percentage of nitrogen in urea, CO(NH₂)₂. Give your answer to two decimal places.
Medium
43.How many atoms are present in 0.200 mol of P₂O₅? Give your answer in standard form to 3 significant figures.
Medium
44.How many moles are in 2.35 × 10²⁴ molecules of oxygen gas? Give your answer to 3 significant figures.
Medium
45.How many atoms are in 4.00 g of hydrogen gas, H₂? Give your answer in standard form to 3 significant figures.
Hard
46.Complete the sentence about the mole.
Medium
One mole of a substance contains ____ particles, where the number is known as the ____ constant.
47.Complete the definition of molar mass.
Medium
Molar mass is the mass of one mole of a substance, expressed in units of ____.
48.Calculate the molecular formula of the compound.
Hard
49.How many ions are present in 0.02 mol of (NH₄)₃PO₄? Give your answer in standard form to 2 significant figures.
Medium
50.Complete the sentence about molar concentration.
Easy
Molar concentration is the amount of solute in moles dissolved in 1 ____ of solution.
51.Calculate the mass of sodium hydroxide, NaOH, required to prepare 250 cm³ of a 0.200 mol dm⁻³ solution. (Mᵣ NaOH = 40.00) Give your answer in grams to 3 significant figures.
Medium
52.Calculate the molar mass of potassium carbonate, K₂CO₃, in g mol⁻¹. Give your answer to two decimal places.
Easy
53.State the meaning of the term empirical formula.
Medium
54.Define the term one mole in chemistry.
Hard
55.Explain why the relative atomic mass of an element has no units.
Hard
56.Calculate its empirical formula.
Hard
57.A student heats a hydrated salt to constant mass. Explain why heating to constant mass is necessary and how it affects the accuracy of the calculated value of x in the formula MCl₂·xH₂O.
Hard
58.Calculate the molar mass of urea, CO(NH₂)₂, in g mol⁻¹. Give your answer to two decimal places.
Medium
- A66.07 g mol⁻¹
- B60.06 g mol⁻¹
- C72.08 g mol⁻¹
- D54.05 g mol⁻¹
59.Calculate the percentage of nitrogen in urea, CO(NH₂)₂. Give your answer to two decimal places.
Medium
- A51.32 %
- B46.65 %
- C55.99 %
- D41.98 %
60.How many atoms are present in 0.200 mol of P₂O₅? Give your answer in standard form to 3 significant figures.
Medium
- A9.273e+23 atoms
- B8.43e+23 atoms
- C7.587e+23 atoms
- D1.0115999999999999e+24 atoms
61.How many moles are in 2.35 × 10²⁴ molecules of oxygen gas? Give your answer to 3 significant figures.
Medium
- A2.9 mol
- B3.9 mol
- C4.9 mol
- D5.9 mol
62.How many atoms are in 4.00 g of hydrogen gas, H₂? Give your answer in standard form to 3 significant figures.
Hard
- A2.629e+24 atoms
- B2.1510000000000002e+24 atoms
- C2.39e+24 atoms
- D2.868e+24 atoms
63.How many ions are present in 0.02 mol of (NH₄)₃PO₄? Give your answer in standard form to 2 significant figures.
Medium
- A4.32e+22 ions
- B4.8e+22 ions
- C5.28e+22 ions
- D5.76e+22 ions
64.Calculate the mass of sodium hydroxide, NaOH, required to prepare 250 cm³ of a 0.200 mol dm⁻³ solution. (Mᵣ NaOH = 40.00) Give your answer in grams to 3 significant figures.
Medium
- A4 g
- B1 g
- C2 g
- D3 g
65.Calculate the molar mass of potassium carbonate, K₂CO₃, in g mol⁻¹. Give your answer to two decimal places.
Easy
- A152.03 g mol⁻¹
- B138.21 g mol⁻¹
- C165.85 g mol⁻¹
- D124.39 g mol⁻¹

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