Mix Examples - ATOMS AND MOLECULES Questions in English

(A) Mass of the compound $= 0.24 \, g$
Mass of boron $= 0.096 \, g$
Mass of oxygen $= 0.144 \, g$
Percentage of boron $= \frac{\text{Mass of boron}}{\text{Mass of compound}} \times 100$
$= \frac{0.096 \, g}{0.24 \, g} \times 100 = 40\%$
Percentage of oxygen $= \frac{\text{Mass of oxygen}}{\text{Mass of compound}} \times 100$
$= \frac{0.144 \, g}{0.24 \, g} \times 100 = 60\%$
Alternative method:
Percentage of oxygen $= 100\% - \text{Percentage of boron}$
$= 100\% - 40\% = 60\%$

(A) The formula for the number of moles is: $\text{moles} = \frac{\text{mass}}{\text{molar mass}}$.
The molar mass of sucrose $(C_{12}H_{22}O_{11})$ is $342 \, g/mol$.
The number of moles of sucrose $= \frac{3.42 \, g}{342 \, g/mol} = 0.01 \, mol$.
Each molecule of sucrose contains $11$ oxygen atoms.
Therefore,the number of oxygen atoms from sucrose $= 0.01 \times 11 \times N_A = 0.11 \, N_A$.
The molar mass of water $(H_2O)$ is $18 \, g/mol$.
The number of moles of water $= \frac{18 \, g}{18 \, g/mol} = 1 \, mol$.
Each molecule of water contains $1$ oxygen atom.
Therefore,the number of oxygen atoms from water $= 1 \times 1 \times N_A = 1 \, N_A$.
Total number of oxygen atoms $= 0.11 \, N_A + 1 \, N_A = 1.11 \, N_A$.
Using $N_A = 6.022 \times 10^{23}$,the total number of oxygen atoms $= 1.11 \times 6.022 \times 10^{23} = 6.68442 \times 10^{23} \approx 6.68 \times 10^{23}$.

(A) The mass of one mole of screws is calculated by multiplying the mass of one screw by Avogadro's number $(N_A = 6.022 \times 10^{23})$.
Mass of $1 \text{ mole of screws} = 4.11 \, g \times 6.022 \times 10^{23} \approx 2.475 \times 10^{24} \, g$.
Converting this to kilograms: $2.475 \times 10^{24} \, g = 2.475 \times 10^{21} \, kg$.
Now,compare this with the mass of the Earth $(5.98 \times 10^{24} \, kg)$:
Ratio $= \frac{\text{Mass of the Earth}}{\text{Mass of 1 mole of screws}} = \frac{5.98 \times 10^{24} \, kg}{2.475 \times 10^{21} \, kg} \approx 2.416 \times 10^3 \approx 2400$.
Thus,the Earth is approximately $2400$ times heavier than one mole of steel screws.

(N/A) To solve this, we use the relations: $\text{Number of particles} = \text{moles} \times 6.022 \times 10^{23}$ and $\text{Mass} = \text{moles} \times \text{Molar mass}$.
$1$. For $CO_2$: Given particles = $3.011 \times 10^{23}$. Moles = $(3.011 \times 10^{23}) / (6.022 \times 10^{23}) = 0.5 \, \text{mol}$. Mass = $0.5 \times 44 \, \text{g/mol} = 22 \, \text{g}$.
$2$. For $Na$ atom: Given mass = $115 \, \text{g}$. Molar mass of $Na = 23 \, \text{g/mol}$. Moles = $115 / 23 = 5 \, \text{mol}$. Particles = $5 \times 6.022 \times 10^{23} = 3.011 \times 10^{24}$.
$3$. For $MgCl_2$: Given moles = $0.5$. Molar mass = $24 + (2 \times 35.5) = 95 \, \text{g/mol}$. Mass = $0.5 \times 95 = 47.5 \, \text{g}$. Particles = $0.5 \times 6.022 \times 10^{23} = 3.011 \times 10^{23}$.
$4$. For $H_2O$: Given moles = $2$. Particles = $2 \times 6.022 \times 10^{23} = 1.2044 \times 10^{24}$.

(N/A) Law of conservation of mass.
$(b)$ Polyatomic ion.
$(c)$ The formula unit mass of $Ca_3(PO_4)_2$ is calculated as: $(3 \times 40) + 2 \times (31 + 4 \times 16) = 120 + 2 \times (31 + 64) = 120 + 2 \times 95 = 120 + 190 = 310 \text{ u}$.
$(d)$ The formula of sodium carbonate is $Na_2CO_3$ and the formula of ammonium sulphate is $(NH_4)_2SO_4$.

(N/A) The completed crossword puzzle corresponds to the following elements:
$(1)$ Silver
$(2)$ Gold
$(3)$ Iron
$(4)$ Copper
$(5)$ Phosphorus
$(6)$ Mercury
$(7)$ Hydrogen
$(8)$ Lead

(A) The completed crossword puzzle reveals the names of the $11$ elements: Chlorine $(Cl)$,Hydrogen $(H)$,Argon $(Ar)$,Oxygen $(O)$,Xenon $(Xe)$,Nitrogen $(N)$,Helium $(He)$,Fluorine $(F)$,Krypton $(Kr)$,Radon $(Rn)$,and Neon $(Ne)$.
$(b)$ Inert gases (Noble gases) are elements that have a stable electron configuration. From the given crossword,there are $6$ inert gases present: Helium $(He)$,Neon $(Ne)$,Argon $(Ar)$,Krypton $(Kr)$,Xenon $(Xe)$,and Radon $(Rn)$.

(N/A) Caustic potash: $KOH$
Molecular mass: $39 + 16 + 1 = 56 \, g \, mol^{-1}$
$(b)$ Baking soda: $NaHCO_3$
Molecular mass: $23 + 1 + 12 + (3 \times 16) = 84 \, g \, mol^{-1}$
$(c)$ Limestone: $CaCO_3$
Molecular mass: $40 + 12 + (3 \times 16) = 100 \, g \, mol^{-1}$
$(d)$ Caustic soda: $NaOH$
Molecular mass: $23 + 16 + 1 = 40 \, g \, mol^{-1}$
$(e)$ Ethanol: $C_2H_5OH$
Molecular mass: $(2 \times 12) + (6 \times 1) + 16 = 46 \, g \, mol^{-1}$
$(f)$ Common salt: $NaCl$
Molecular mass: $23 + 35.5 = 58.5 \, g \, mol^{-1}$

(N/A) $(i)$ Molar mass: The mass of one mole of a substance in grams is called its molar mass.
$(ii)$ Valency: The combining capacity of an atom of an element is known as its valency. It represents the number of electrons an atom needs to lose,gain,or share to achieve a stable electronic configuration.

(N/A)

$(i)$ Molar mass	Avogadro's constant
It is the mass of one mole of a substance expressed in grams $(g/mol)$.	It is the number of particles (atoms,molecules,or ions) present in one mole of a substance,equal to $6.022 \times 10^{23} \text{ mol}^{-1}$.
$(ii)$ Molecular mass	Formula unit mass
It is the sum of the atomic masses of all atoms present in a molecule of a covalent compound.	It is the sum of the atomic masses of all atoms in a formula unit of an ionic compound.

(N/A) The chemical formula of sodium sulphate is $Na_{2}SO_{4}$.
$(b)$ $A$ diatomic molecule consists of two atoms of the same element. Examples include Oxygen $(O_{2})$,Hydrogen $(H_{2})$,or Nitrogen $(N_{2})$. Any one of these can be cited.
$A$ tetraatomic molecule consists of four atoms of the same element. Phosphorus $(P_{4})$ is a common example of a tetraatomic molecule.

(B) The postulate of Dalton's atomic theory that led to the law of conservation of mass is: $Atoms$ can neither be created nor destroyed in a chemical reaction.
To calculate the molecular mass of water $(H_2O)$:
Atomic mass of $H = 1 \text{ u}$
Atomic mass of $O = 16 \text{ u}$
Molecular mass of $H_2O = (2 \times \text{atomic mass of } H) + (1 \times \text{atomic mass of } O)$
$= (2 \times 1) + (1 \times 16) = 2 + 16 = 18 \text{ u}$.

(N/A) The number of atoms $= \frac{\text{Given mass}}{\text{Molar mass}} \times \text{Avogadro constant}$
$\Rightarrow N = \frac{m}{M} \times N_A = \frac{48}{24} \times 6.022 \times 10^{23} = 2 \times 6.022 \times 10^{23} = 12.044 \times 10^{23} \text{ atoms}$.
$(b)$ The number of molecules $= \frac{\text{Given mass}}{\text{Molar mass}} \times \text{Avogadro constant}$
$\Rightarrow N = \frac{8}{32} \times 6.022 \times 10^{23} = 0.25 \times 6.022 \times 10^{23} = 1.5055 \times 10^{23} \text{ molecules}$.
$(c)$ The number of particles (atoms) $= \text{Number of moles} \times \text{Avogadro constant}$
$\Rightarrow N = 0.1 \times 6.022 \times 10^{23} = 6.022 \times 10^{22} \text{ atoms}$.

(N/A) The molar mass of $CO_2$ is $44 \, g/mol$ and the molar mass of $H_2O$ is $18 \, g/mol$.
Mass of $5$ moles of $CO_2 = 5 \times 44 = 220 \, g$.
Mass of $5$ moles of $H_2O = 5 \times 18 = 90 \, g$.
Since $220 \, g > 90 \, g$, it is verified that $5$ moles of $CO_2$ has a higher mass.
$(b)$ Molar mass of $Ca = 40 \, g/mol$ and $Mg = 24 \, g/mol$.
Moles of $120 \, g$ of $Ca = 120 / 40 = 3 \, moles$.
Moles of $120 \, g$ of $Mg = 120 / 24 = 5 \, moles$.
Therefore, the mole ratio of $Ca$ to $Mg = 3:5$.

(N/A) Mass $=$ Molar mass $\times$ Number of moles
$m = M \times n$
$m = 16 \ g/mol \times 0.5 \ mol = 8 \ g$
$(b)$ Number of moles $(n) = \frac{\text{Given mass } (m)}{\text{Molar mass } (M)}$
$n = \frac{90 \ g}{180 \ g/mol} = 0.5 \ mol$
Since $1 \ mol$ contains $6.022 \times 10^{23}$ molecules,
Therefore,$0.5 \ mol$ will contain $0.5 \times 6.022 \times 10^{23} = 3.011 \times 10^{23}$ molecules.
$(c)$ Number of moles $(n) = \frac{\text{Given mass } (m)}{\text{Molar mass } (M)}$
Given mass of water $= 2 \ g$,Molar mass of water $(H_2O) = (2 \times 1) + 16 = 18 \ g/mol$
$n = \frac{2}{18} = \frac{1}{9} \approx 0.11 \ mol$

(N/A) Molar mass of $H_{2}O_{2} = (2 \times 1) + (2 \times 16) = 34 \, g/mol$. Percentage of oxygen $= (32 / 34) \times 100 = 94.12 \%$.
$(b)$ Molar mass of $N_{2} = 2 \times 14 = 28 \, g/mol$. Number of moles $= 56 \, g / 28 \, g/mol = 2 \, moles$.
$(c)$ Mass of $Ca = \text{moles} \times \text{atomic mass} = 0.50 \times 40 = 20 \, g$.
$(d)(i)$ Number of molecules $= \text{moles} \times N_{A} = 5 \times 6.022 \times 10^{23} = 30.110 \times 10^{23}$ particles.
$(d)(ii)$ Number of atoms $= (\text{given mass} / \text{atomic mass}) \times N_{A} = (92 / 23) \times 6.022 \times 10^{23} = 4 \times 6.022 \times 10^{23} = 24.088 \times 10^{23}$ particles.

(N/A) $(i)$ $2O$ represents two separate atoms of oxygen.
$(ii)$ $O_{2}$ represents one molecule of diatomic oxygen.
$(iii)$ $O_{3}$ represents one molecule of triatomic oxygen (ozone).
$(iv)$ $H_{2}O$ represents one molecule of water, consisting of two atoms of hydrogen and one atom of oxygen.
$(b)$ $(i)$ Potassium carbonate: $K_{2}CO_{3}$
$(ii)$ Calcium chloride: $CaCl_{2}$
$(c)$ Formula unit mass of $Al_{2}(SO_{4})_{3}$:
$= (2 \times \text{atomic mass of } Al) + (3 \times \text{atomic mass of } S) + (12 \times \text{atomic mass of } O)$
$= (2 \times 27) + (3 \times 32) + (12 \times 16)$
$= 54 + 96 + 192 = 342 \, u$.

(N/A) $(a) (i)$ Examples include Carbon $(C)$ and Nitrogen $(N)$.
$(ii)$ Examples include Sodium ($Na$,from Natrium) and Iron ($Fe$,from Ferrum).
$(b)$ Avogadro's constant: The value $6.022 \times 10^{23}$ is defined as Avogadro's constant $(N_A)$. It represents the number of particles (atoms,molecules,or ions) present in one mole of any substance.
Molar mass: The mass of $1$ mole of a substance in grams is called its molar mass.
Relationship: One mole of any species (atoms,molecules,or ions) contains $6.022 \times 10^{23}$ number of particles,and its mass is equal to its relative atomic or molecular mass expressed in grams.

$1$ mole of particles

Number of particles = $6.022 \times 10^{23}$

Mass = Molar mass in grams

(N/A) group of atoms carrying a charge is known as a polyatomic ion.
Example: $NH_{4}^{+}, PO_{4}^{3-}, SO_{4}^{2-}$.
$(b)$ Formula unit mass of $CaCO_{3} = (1 \times \text{Atomic mass of } Ca) + (1 \times \text{Atomic mass of } C) + (3 \times \text{Atomic mass of } O)$
$= 40 \ u + 12 \ u + (3 \times 16 \ u) = 40 + 12 + 48 = 100 \ u$.
$(c)$ $(i)$ Molecular mass of $HNO_{3} = (1 \times \text{Atomic mass of } H) + (1 \times \text{Atomic mass of } N) + (3 \times \text{Atomic mass of } O)$
$= 1 \ u + 14 \ u + (3 \times 16 \ u) = 1 + 14 + 48 = 63 \ u$.
$(ii)$ Molecular mass of $CH_{3}COOH = (2 \times \text{Atomic mass of } C) + (4 \times \text{Atomic mass of } H) + (2 \times \text{Atomic mass of } O)$
$= (2 \times 12 \ u) + (4 \times 1 \ u) + (2 \times 16 \ u) = 24 + 4 + 32 = 60 \ u$.

(N/A)

Atom	Molecule
$(i)$ An atom is the smallest particle of an element that takes part in a chemical reaction.	$(i)$ $A$ molecule is the smallest particle of an element or a compound that is capable of independent existence.
$(ii)$ An atom is usually not stable by itself.	$(ii)$ $A$ molecule is usually stable by itself.
$(iii)$ Similar atoms can combine in varying numbers to form different molecules with different properties. e.g.,$O_2$ and $O_3$.	$(iii)$ When similar molecules combine in any number,the nature of the substance remains the same. e.g.,$5$ water molecules combined with $50$ water molecules still represent water.

(N/A) molecule is defined as the smallest particle of an element or a compound that is capable of independent existence and exhibits all the properties of that substance.
The molecule of an element is constituted by the same type of atoms, e.g., $O_{2}$, while the molecule of a compound is constituted by different types of atoms, e.g., $CO_{2}$.
$(b)$ To derive the chemical formula, we cross the valencies of the ions:
$(i)$ For $Al^{3+}$ and $SO_{4}^{2-}$:

Symbol	$Al$	$SO_{4}$
Charge	$3+$	$2-$
Formula	$Al_{2}(SO_{4})_{3}$

$(ii)$ For $Ba^{2+}$ and $NO_{3}^{-}$:

Symbol	$Ba$	$NO_{3}$
Charge	$2+$	$1-$
Formula	$Ba(NO_{3})_{2}$

(N/A) Since $6.022 \times 10^{23}$ oxygen atoms are present in $1$ mole of oxygen atoms,the number of moles in $2.58 \times 10^{24}$ oxygen atoms is calculated as:
$\text{Moles} = \frac{2.58 \times 10^{24}}{6.022 \times 10^{23}} \approx 4.284 \text{ moles}$.
$(b)$ $(i)$ Law of conservation of mass.
$(ii)$ Polyatomic ion.
$(c)$ $(i)$ The formula for Sodium phosphate is $Na_{3}PO_{4}$.
$(ii)$ The formula for Ammonium carbonate is $(NH_{4})_{2}CO_{3}$.

$(a)$ We know that,$1$ mole of carbon atoms $= 12 \text{ g}$.
Also,$1$ mole of carbon atoms $= 6.022 \times 10^{23}$ atoms.
Therefore,the mass of $1$ atom of carbon $= \frac{12 \text{ g}}{6.022 \times 10^{23}} \approx 1.99 \times 10^{-23} \text{ g}$.
$(b)$ We know that,$1$ mole of sodium atoms $= 23 \text{ g}$.
Therefore,the mass of $0.02$ mole of sodium $= 0.02 \times 23 \text{ g} = 0.46 \text{ g}$.
$(c)$ The molar mass of $H_{2}O = (2 \times 1) + 16 = 18 \text{ g/mol}$.
Since $1$ mole of $H_{2}O$ contains $6.022 \times 10^{23}$ molecules,the mass of $1$ molecule of $H_{2}O = \frac{18 \text{ g}}{6.022 \times 10^{23}} \approx 2.99 \times 10^{-23} \text{ g}$.

$(a)$ We know that $1$ molecule of $O_2$ contains $2$ oxygen atoms.
$1 \, mole$ of $O_2 = 32 \, g$.
$32 \, g$ of $O_2 = 1 \, mole = 6.022 \times 10^{23}$ oxygen molecules.
$16 \, g$ of $O_2 = \frac{1 \, mole}{32 \, g} \times 16 \, g = 0.5 \, mole$.
Number of $O_2$ molecules in $0.5 \, mole = 0.5 \times 6.022 \times 10^{23} = 3.011 \times 10^{23}$ molecules.
Since $1$ molecule of $O_2$ contains $2$ atoms,the number of oxygen atoms $= 3.011 \times 10^{23} \times 2 = 6.022 \times 10^{23}$ atoms.
$(b)$ $1 \, mole$ of carbon atoms contains $6.022 \times 10^{23}$ atoms.
Therefore,$0.1 \, mole$ of carbon atoms contains $= 0.1 \times 6.022 \times 10^{23} = 6.022 \times 10^{22}$ atoms.

(N/A) Gram atomic mass of $Fe = 56 \, g/mol$.
Number of moles $= \frac{\text{Given mass}}{\text{Molar mass}} = \frac{112 \, g}{56 \, g/mol} = 2 \, moles$.
$(b)$ Molecular mass of sugar $(C_{12}H_{22}O_{11}) = (12 \times 12) + (22 \times 1) + (11 \times 16) = 144 + 22 + 176 = 342 \, u$.
Mass of $0.5 \, mole = 0.5 \, mol \times 342 \, g/mol = 171 \, g$.
$(c)$ Molar mass of $O_2 = 32 \, g/mol$.
Number of moles in $8 \, g$ of $O_2 = \frac{8 \, g}{32 \, g/mol} = 0.25 \, moles$.
Number of molecules $= 0.25 \times 6.022 \times 10^{23} = 1.5055 \times 10^{23} \, molecules$.
Since $1$ molecule of $O_2$ contains $2$ atoms, total atoms $= 2 \times 1.5055 \times 10^{23} = 3.011 \times 10^{23} \, atoms$.

(B) The molar mass of water $(H_2O)$ is calculated as: $(2 \times 1) + 16 = 18 \, g/mol$.
To find the number of moles in $360 \, g$ of water,we use the formula: $\text{Number of moles} = \frac{\text{Given mass}}{\text{Molar mass}} = \frac{360 \, g}{18 \, g/mol} = 20 \, \text{moles}$.
Thus,statement $(ii)$ is correct.
To find the number of molecules,we multiply the number of moles by Avogadro's constant $(N_A = 6.022 \times 10^{23} \, \text{molecules/mol})$:
$\text{Number of molecules} = 20 \times 6.022 \times 10^{23} = 1.2044 \times 10^{25} \, \text{molecules}$.
Thus,statement $(iv)$ is also correct.
Therefore,the correct representation is $(ii)$ and $(iv)$.

(A) molecule is defined as the smallest particle of an element or a compound that is capable of an independent existence and exhibits all the properties of that substance.
It consists of two or more atoms that are chemically bonded together.
These atoms can be of the same element (e.g.,$O_2$) or different elements (e.g.,$H_2O$).
Therefore,all the given statements correctly describe a molecule.

(A) All living organisms are composed of organic molecules that form the structural and functional basis of life.
These essential biomolecules include proteins,carbohydrates,fats (lipids),nucleic acids ($DNA$ and $RNA$),and vitamins.
While carbon dioxide,carbonates,and hydrogen carbonates are carbon-containing compounds,they are generally considered inorganic and are not the fundamental building blocks of life forms in the same way as organic macromolecules.
Therefore,the correct group of carbon-containing molecules found in all life forms is proteins,carbohydrates,fats,nucleic acids,and vitamins.