Mix Example - ATOMS AND MOLECULES Questions in English

(D) The chemical formula of the phosphate ion is $PO_{4}^{3-}$.
In one mole of $PO_{4}^{3-}$ ion,there is $1$ mole of phosphorus atom and $4$ moles of oxygen atoms.
Therefore,the number of moles of oxygen atoms present in $PO_{4}^{3-}$ is $4$.

(N/A) Initially,$1/16$th of the mass of a naturally occurring oxygen atom was chosen as the atomic mass unit because this standard allowed the atomic masses of most elements to be expressed as whole numbers or near-whole numbers,making calculations simpler.

(N/A) The molar mass of hydrogen $(H)$ is $1\,g/mol$.
Given mass of hydrogen $= 1\,g$.
Number of moles $= \frac{\text{Given mass}}{\text{Molar mass}} = \frac{1\,g}{1\,g/mol} = 1\,mol$.
Since $1\,mol$ of any substance contains $6.022 \times 10^{23}$ particles (Avogadro's number),the number of hydrogen atoms in $1\,g$ of hydrogen is $6.022 \times 10^{23}$ atoms.

(N/A) The relative atomic mass of an atom is defined as the average mass of the atom as compared to $1/12$th the mass of one carbon-$12$ atom.
Therefore,saying the relative atomic mass of oxygen is $16$ means that one atom of oxygen is $16$ times heavier than $1/12$th of the mass of a carbon-$12$ atom.

(C) John Dalton's atomic theory was primarily based on the laws of chemical combination, specifically the $Law$ $of$ $Conservation$ $of$ $Mass$ and the $Law$ $of$ $Definite$ $Proportions$.
These laws provided the empirical evidence needed to propose that matter is composed of indivisible particles called atoms, which combine in fixed ratios to form compounds.

(A) $(i)$ Element $A$ (Chlorine) has an atomic number of $17$,and its electronic configuration is $(2, 8, 7)$. It needs to gain $1$ electron to complete its octet.
$(ii)$ Element $B$ (Sulfur) has an atomic number of $16$,and its electronic configuration is $(2, 8, 6)$. It needs to gain $2$ electrons to complete its octet.
$(iii)$ Reactivity in non-metals is determined by the ease of gaining electrons. Since element $A$ requires only $1$ electron to achieve a stable noble gas configuration,it is more chemically reactive than element $B$,which requires $2$ electrons.

(B) $(i)$ $5$ moles of $CO_{2} = 5 \text{ mol} \times \text{molar mass of } CO_{2}$
$= 5 \text{ mol} \times 44 \text{ g/mol} = 220 \text{ g}$
$(ii)$ $5$ moles of $H_{2}O = 5 \text{ mol} \times \text{molar mass of } H_{2}O$
$= 5 \text{ mol} \times 18 \text{ g/mol} = 90 \text{ g}$
Thus,it can be seen that both have different masses.

(D) According to the law of definite proportion,carbon and oxygen combine in a fixed mass ratio of $3:8$.
This means that $3\,g$ of carbon reacts completely with $8\,g$ of oxygen.
Therefore,$1\,g$ of carbon reacts with $\frac{8}{3}\,g$ of oxygen.
For $15\,g$ of carbon,the mass of oxygen required is $\frac{8}{3} \times 15\,g = 8 \times 5\,g = 40\,g$.
Thus,$40\,g$ of oxygen gas is required to react completely with $15\,g$ of carbon.

(N/A) $Au$ represents Gold.
$(b)$ $Ag$ represents Silver.
$(c)$ $Hg$ represents Mercury.
$(d)$ $Sn$ represents Tin.

(D) The species $K$ (Potassium atom) is electrically neutral.
An atom is considered electrically neutral when the number of positively charged protons in its nucleus is exactly equal to the number of negatively charged electrons orbiting the nucleus.
In the case of $K^{+}$,$Cl^{-}$,$S^{2-}$,and $P^{3-}$,these are ions that have either lost or gained electrons,resulting in a net electrical charge.
Therefore,$K$ is the only neutral species among the given options.

(N/A) The law of conservation of mass states that mass can neither be created nor destroyed in a system. This law holds true for physical changes as well,where the total mass of the substance remains constant before and after the physical transformation.
Examples:
$(i)$ Melting of wax: When a piece of wax melts,the mass of the solid wax is equal to the mass of the liquid wax formed.
$(ii)$ Melting of ice: When $100 \ g$ of ice melts into water,the mass of the resulting water is exactly $100 \ g$.

(N/A) $(i)$ $(a)$ One atomic mass unit ($1 \text{ amu}$ or $1 \text{ u}$) is a mass unit equal to exactly $\frac{1}{12}$th the mass of one $C-12$ atom.
$(b)$ The relative atomic mass of an element is defined as the average mass of one atom of the element compared to $\frac{1}{12}$th the mass of one $C-12$ atom.
$(ii)$ Atoms of most elements are highly reactive and cannot exist independently. However,they combine to form molecules and ions. These particles aggregate in large numbers to form matter,which we can see,feel,or touch,thereby confirming the presence of atoms.

(N/A) In a chlorine atom,the number of electrons is equal to the number of protons,which is $17$; hence,it is electrically neutral.
In a chloride ion,one electron is gained in the valence shell to attain a stable octet configuration. Consequently,the number of protons remains $17$,but the number of electrons becomes $18$ $(17 + 1)$. Since there is one excess electron compared to the number of protons,it carries a net charge of $-1$ and is thus negatively charged.

(A) $1$. To find the number of electrons:
- $Ca$ (atomic number $20$) has $20$ electrons. $Ca^{2+}$ has $20 - 2 = 18$ electrons.
- $K$ (atomic number $19$) has $19$ electrons. $K^{+}$ has $19 - 1 = 18$ electrons.
- $Na$ (atomic number $11$) has $11$ electrons.
- $Cl$ (atomic number $17$) has $17$ electrons. $Cl^{-}$ has $17 + 1 = 18$ electrons.
- $Ar$ (atomic number $18$) has $18$ electrons.
Thus,$Ca^{2+}, K^{+}, Cl^{-},$ and $Ar$ have $18$ electrons.
$2$. Isotopes of an element have the same atomic number,which means they have the same number of protons and electrons. Since chemical properties are determined by the electronic configuration (specifically valence electrons),all isotopes of an element exhibit similar chemical properties.

(N/A) Atomicity is defined as the total number of atoms present in one molecule of an element or a compound.
$(b)$ The atomicity of the given molecules is as follows:
$(i)$ Oxygen $(O_2)$: Diatomic (contains $2$ atoms).
$(ii)$ Phosphorus $(P_4)$: Tetra-atomic (contains $4$ atoms).
$(iii)$ Sulphur $(S_8)$: Polyatomic (contains $8$ atoms).
$(iv)$ Argon $(Ar)$: Monoatomic (contains $1$ atom).

(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) Nickel sulphide
$(b)$ Magnesium nitrate
$(c)$ Sodium sulphate
$(d)$ Aluminium nitrate
$(e)$ Potassium phosphate
$(f)$ Calcium nitride

(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) $K_{2}SO_{4}$ is Potassium sulphate.
$(b)$ $Mg_{3}(PO_{4})_{2}$ is Magnesium phosphate.
$(c)$ $NH_{4}Cl$ is Ammonium chloride.
$(d)$ $ZnS$ is Zinc sulphide.
$(e)$ $Na_{3}N$ is Sodium nitride.
$(f)$ $AgBr$ is Silver bromide.

(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 $(NH_{4})_{2}CO_{3}$.

(N/A) The international organization that approves the names of elements is the International Union of Pure and Applied Chemistry $(IUPAC)$.
$(b)$ The melting of ice into water is a physical change. To demonstrate the Law of Conservation of Mass,take a piece of ice in a small flask,cork it,and weigh it (let this be $W_{\text{ice}} \text{ g}$). Heat the flask gently so that the ice (solid) melts into water (liquid). Weigh the flask again (let this be $W_{\text{water}} \text{ g}$). It is observed that there is no change in the total mass of the system.
i.e.,$W_{\text{ice}} = W_{\text{water}}$
$\text{Ice (solid)} \xrightarrow{\text{Heat}} \text{Water (liquid)}$
This process represents a physical change. Since the mass remains constant before and after the change,it proves that the Law of Conservation of Mass holds true for physical changes.

(N/A) The number of atoms present in one molecule of a substance is called its atomicity.
Depending on the number of atoms present in a molecule,the following types of molecules are known:
$(i)$ Monoatomic molecules: These consist of a single atom. Noble gases like $He$,$Ne$,and $Ar$ exist as monoatomic molecules.
$(ii)$ Diatomic molecules: These consist of two atoms,e.g.,$O_{2}$,$N_{2}$,$Cl_{2}$,$H_{2}$,$Br_{2}$,and $I_{2}$.
$(iii)$ Triatomic molecules: These consist of three atoms,e.g.,$O_{3}$ (Ozone molecule).
$(iv)$ Tetratomic molecules: These consist of four atoms,e.g.,$P_{4}$ (Phosphorus molecule).
$(v)$ Polyatomic molecules: These consist of more than four atoms,e.g.,$S_{8}$ (Sulphur molecule).
Note: All the above types represent molecules of an element,where atoms of the same element exist together as a single species in a free state.

(N/A) $(i)$ $NH_{4}NO_{3} = 14 + (1 \times 4) + 14 + (16 \times 3) = 14 + 4 + 14 + 48 = 80 \ u$
$(ii)$ $H_{2}SO_{4} = (2 \times 1) + 32 + (4 \times 16) = 2 + 32 + 64 = 98 \ u$
$(iii)$ $Na_{2}CO_{3} = (2 \times 23) + 12 + (3 \times 16) = 46 + 12 + 48 = 106 \ u$
$(iv)$ $NaOH = 23 + 16 + 1 = 40 \ u$
$(v)$ $HNO_{3} = 1 + 14 + (3 \times 16) = 1 + 14 + 48 = 63 \ u$
$(vi)$ $Al_{2}(SO_{4})_{3} = (2 \times 27) + 3 \times [32 + (4 \times 16)] = 54 + 3 \times [32 + 64] = 54 + 3 \times 96 = 54 + 288 = 342 \ u$

(N/A) mole of particles (atoms,ions,or molecules) is defined as the amount of a substance that contains the same number of particles as there are in $12 \ g$ of the $C-12$ isotope.
Experimentally,it has been found that $0.012 \ kg$ of carbon-$12$ contains $6.022 \times 10^{23}$ atoms. This number is called Avogadro's number or Avogadro's constant and is represented by the symbol $N_A$ or $N_0$.
The symbol for the unit of mole is $mol$.
Advantage of the Mole Concept:
The mole concept allows for the convenient selection of a specific number of atoms and molecules by relating them to the mass and volume of a chemical substance,making stoichiometric calculations easier.

(N/A) $(i)$ We know that $1$ mole of atoms contains $6.022 \times 10^{23}$ atoms.
Therefore,$0.02$ moles of carbon atoms $= 6.022 \times 10^{23} \times 0.02 = 1.2044 \times 10^{22}$ atoms.
$(ii)$ We know that the molar mass of carbon is $12 \text{ g/mol}$.
Number of moles $= \frac{\text{Given mass}}{\text{Molar mass}} = \frac{30 \text{ g}}{12 \text{ g/mol}} = 2.5$ moles.
Number of atoms $= 2.5 \times 6.022 \times 10^{23} = 1.5055 \times 10^{24}$ atoms.
$(iii)$ We know that $1$ mole of ions contains $6.022 \times 10^{23}$ ions.
Therefore,$6$ moles of aluminium ions $= 6 \times 6.022 \times 10^{23} = 3.6132 \times 10^{24}$ atoms.

$(a)$ 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 $H_{2}O = \frac{18 \text{ g}}{6.022 \times 10^{23}} \approx 2.99 \times 10^{-23} \text{ g}$.

(B) Given mass of carbon $= 60 \text{ g}$.
Gram atomic mass of carbon $(C)$ $= 12 \text{ g/mol}$.
We know that,the number of moles is calculated by the formula:
$\text{Number of moles} = \frac{\text{Given mass (in grams)}}{\text{Gram atomic mass}}$.
Substituting the values:
$\text{Number of moles} = \frac{60 \text{ g}}{12 \text{ g/mol}} = 5 \text{ moles}$.
Therefore,there are $5 \text{ moles}$ in $60 \text{ g}$ of carbon.

(B) Given mass of water $= 90 \text{ g}$.
The molar mass of water $(H_2O)$ is calculated as follows:
$H_2O = (2 \times 1) + 16 = 18 \text{ g/mol}$.
We know that the number of moles is calculated by the formula:
$\text{Number of moles} = \frac{\text{Given mass}}{\text{Molar mass}}$.
Substituting the values:
$\text{Number of moles} = \frac{90 \text{ g}}{18 \text{ g/mol}} = 5 \text{ moles}$.
Therefore,there are $5 \text{ moles}$ in $90 \text{ g}$ of water.

(B) $(i)$ The atomic mass of carbon is $12 \text{ g/mol}$.
$(ii)$ The number of moles in $60 \text{ g}$ of carbon is calculated as: $\text{Moles} = \frac{\text{Given mass}}{\text{Molar mass}} = \frac{60}{12} = 5 \text{ moles}$.
$(iii)$ The number of atoms is calculated by multiplying the number of moles by Avogadro's number $(N_A = 6.022 \times 10^{23} \text{ atoms/mol})$:
$\text{Number of atoms} = 5 \times 6.022 \times 10^{23} = 3.011 \times 10^{24} \text{ atoms}$.

(C) $(i)$ The molar mass of water $(H_2O)$ is $(2 \times 1) + 16 = 18 \text{ g/mol}$.
$(ii)$ Number of moles in $90 \text{ g}$ of water $= \frac{\text{Given mass}}{\text{Molar mass}} = \frac{90}{18} = 5 \text{ moles}$.
$(iii)$ Number of molecules $=$ Number of moles $\times$ Avogadro's number $(N_A)$.
$= 5 \times 6.022 \times 10^{23} \text{ molecules/mol}$.
$= 3.011 \times 10^{24} \text{ molecules}$.

(A) The number of atoms in a substance is calculated by multiplying the number of moles by Avogadro's constant $(N_A = 6.022 \times 10^{23} \text{ atoms/mol})$.
Number of atoms $= \text{Number of moles} \times N_A$
Number of atoms $= 0.02 \times 6.022 \times 10^{23}$
Number of atoms $= 1.2044 \times 10^{22} \text{ atoms}$.

(A) To find the number of molecules in a given amount of substance,we use Avogadro's number $(N_A = 6.022 \times 10^{23} \text{ molecules/mole})$.
The formula is: $\text{Number of molecules} = \text{Number of moles} \times N_A$.
Given,number of moles = $0.5$.
Therefore,$\text{Number of molecules} = 0.5 \times 6.022 \times 10^{23}$.
$= 3.011 \times 10^{23} \text{ molecules}$.

(N/A) We know that the gram atomic mass of carbon is $12 \text{ g}$.
Further,the mass of $1$ carbon atom is calculated as:
$\text{Mass of 1 atom} = \frac{\text{Gram atomic mass}}{\text{Avogadro's number}} = \frac{12 \text{ g}}{6.022 \times 10^{23}}$
$= 1.99 \times 10^{-23} \text{ g}$
Therefore,the mass of $10$ carbon atoms is:
$= 10 \times 1.99 \times 10^{-23} \text{ g}$
$= 1.99 \times 10^{-22} \text{ g}$

(A) The molar mass (gram molecular mass) of water $(H_2O)$ is $18 \text{ g/mol}$.
One mole of water contains $6.022 \times 10^{23}$ molecules (Avogadro's number).
Therefore,the mass of $1$ water molecule is calculated as:
$\text{Mass of } 1 \text{ molecule} = \frac{\text{Molar mass}}{\text{Avogadro's number}} = \frac{18 \text{ g}}{6.022 \times 10^{23}} \approx 2.99 \times 10^{-23} \text{ g}$.
To find the mass of $20$ water molecules,we multiply the mass of one molecule by $20$:
$\text{Mass of } 20 \text{ molecules} = 20 \times 2.99 \times 10^{-23} \text{ g} = 5.98 \times 10^{-22} \text{ g}$.

(17 G) The law of conservation of mass states that mass can neither be created nor destroyed in a chemical reaction.
$(b)$ The balanced chemical equation is:
$AgNO_{3}(aq) + NaCl(aq) \rightarrow AgCl(s) + NaNO_{3}(aq)$
According to the law of conservation of mass:
Total mass of reactants = Total mass of products
Let the mass of $AgNO_{3}$ be $x$.
Mass of reactants = $x + 5.85 \, g$
Mass of products = $14.35 \, g + 8.5 \, g = 22.85 \, g$
Equating the two:
$x + 5.85 \, g = 22.85 \, g$
$x = 22.85 \, g - 5.85 \, g$
$x = 17 \, g$
Therefore,$17 \, g$ of silver nitrate will react.

$(a)$ 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.

(A) Step $1$: Calculate the number of moles in $16\, g$ of sulphur.
Atomic mass of sulphur $(S)$ = $32\, g/mol$.
Moles of $S = \frac{\text{Given mass}}{\text{Atomic mass}} = \frac{16\, g}{32\, g/mol} = 0.5\, mol$.
Step $2$: Determine the number of atoms.
Since $1\, mol$ of any element contains $6.022 \times 10^{23}$ atoms (Avogadro's number),$0.5\, mol$ of $S$ contains $0.5 \times 6.022 \times 10^{23} = 3.011 \times 10^{23}$ atoms.
Step $3$: Calculate the mass of sodium $(Na)$ containing the same number of atoms.
Atomic mass of sodium $(Na)$ = $23\, g/mol$.
To have the same number of atoms $(3.011 \times 10^{23})$,we need $0.5\, mol$ of sodium.
Mass of $Na = \text{Moles} \times \text{Atomic mass} = 0.5\, mol \times 23\, g/mol = 11.5\, g$.
Therefore,$11.5\, g$ of sodium contains the same number of atoms as $16\, g$ of sulphur.

(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 $= 2 \times 1.5055 \times 10^{23} = 3.011 \times 10^{23} \, atoms$.

(C) The molar mass of oxygen atoms $(O)$ is $16 \, g/mol$.
By definition,$1 \, mole$ of any substance contains $6.022 \times 10^{23}$ particles (Avogadro's number).
Therefore,the mass of $6.022 \times 10^{23}$ atoms of oxygen is $16 \, g$.
The mass of one atom of oxygen is calculated by dividing the molar mass by Avogadro's number:
$\text{Mass of one atom} = \frac{\text{Molar mass}}{\text{Avogadro's number}} = \frac{16}{6.023 \times 10^{23}} \, g$.

(A) $1$. Molar mass of sucrose $(C_{12}H_{22}O_{11})$ = $(12 \times 12) + (22 \times 1) + (11 \times 16) = 144 + 22 + 176 = 342 \, g/mol$.
$2$. Moles of sucrose = $\frac{3.42 \, g}{342 \, g/mol} = 0.01 \, mol$.
$3$. Oxygen atoms from sucrose = $0.01 \times 11 \times N_A = 0.11 \times 6.022 \times 10^{23} = 6.6242 \times 10^{22}$ atoms.
$4$. Moles of water $(H_2O)$ = $\frac{18 \, g}{18 \, g/mol} = 1 \, mol$.
$5$. Oxygen atoms from water = $1 \times 1 \times N_A = 6.022 \times 10^{23}$ atoms.
$6$. Total oxygen atoms = $(0.066242 \times 10^{23}) + (6.022 \times 10^{23}) = 6.088242 \times 10^{23} \approx 6.09 \times 10^{23}$ atoms. (Note: The provided option $A$ is $6.09 \times 10^{22}$,which appears to be a typo in the question's options; however,based on standard calculation,the result is $6.09 \times 10^{23}$).

(A) The physical state of matter (solid,liquid,or gas) is determined by the kinetic energy of its particles and the intermolecular forces of attraction.
To change the physical state,one must either increase the kinetic energy (by heating/supplying energy) to overcome intermolecular forces or decrease the kinetic energy (by cooling/removing energy) to allow particles to come closer.
Therefore,a change in physical state requires an exchange of energy with the surroundings,either by adding or removing it.

(B) In water,$(H_2O)$,hydrogen and oxygen are always present in a fixed ratio by mass.
The atomic mass of hydrogen is $1 \text{ u}$ and the atomic mass of oxygen is $16 \text{ u}$.
In one molecule of water $(H_2O)$,there are $2$ atoms of hydrogen and $1$ atom of oxygen.
Total mass of hydrogen $= 2 \times 1 = 2 \text{ u}$.
Total mass of oxygen $= 1 \times 16 = 16 \text{ u}$.
The ratio of the mass of hydrogen to the mass of oxygen is $2: 16$,which simplifies to $1: 8$.

(B) Dalton's atomic theory stated that atoms are indivisible particles. However,later scientific discoveries revealed that atoms are composed of subatomic particles such as protons,neutrons,and electrons,which means they are divisible. Additionally,the existence of isotopes challenges the postulate that atoms of the same element are identical in mass,as isotopes have the same atomic number but different mass numbers. Among the given options,the concept of indivisibility (Option $B$) and the concept of identical mass (Option $C$) were challenged. However,the most fundamental challenge to the 'indivisibility' of the atom is widely cited as the primary limitation of Dalton's theory.

(D) The atomic mass unit $(u)$ is defined as a mass unit equal to exactly one-twelfth $(1/12)$ of the mass of one carbon-$12$ atom.
This standard was adopted by the $IUPAC$ to provide a consistent reference for measuring the masses of atoms.
Therefore,$1 \, u = (1/12) \times \text{mass of one } C-12 \text{ atom}$.

(A) The chemical symbol for calcium is $Ca$.
The chemical symbol for carbon is $C$.
The chemical symbol for copper is $Cu$.
Therefore,the correct sequence of symbols for calcium,carbon,and copper is $Ca, C, Cu$.

(D) The mass of an atom or a molecule is extremely small. To express these masses conveniently,a standard unit is required.
Historically,the 'atomic mass unit' $(amu)$ was used,which is now represented by the unified mass unit $(u)$.
This unit is defined as exactly $1/12$th of the mass of one carbon-$12$ atom.
Therefore,the accepted unit for measuring the mass of an atom and a molecule is the atomic mass unit ($amu$ or $u$).

(C) To find the substance with the highest weight, we calculate the mass of each option using the formula: $\text{Mass} = \text{Number of moles} \times \text{Molar mass}$.
$A$. $0.2$ mole of sucrose $(C_{12}H_{22}O_{11})$:
$\text{Molar mass} = (12 \times 12) + (22 \times 1) + (11 \times 16) = 144 + 22 + 176 = 342 \text{ g/mol}$.
$\text{Mass} = 0.2 \times 342 = 68.4 \text{ g}$.
$B$. $2$ moles of $CO_2$:
$\text{Molar mass} = 12 + (2 \times 16) = 44 \text{ g/mol}$.
$\text{Mass} = 2 \times 44 = 88 \text{ g}$.
$C$. $2$ moles of $CaCO_3$:
$\text{Molar mass} = 40 + 12 + (3 \times 16) = 100 \text{ g/mol}$.
$\text{Mass} = 2 \times 100 = 200 \text{ g}$.
$D$. $10$ moles of $H_2O$:
$\text{Molar mass} = (2 \times 1) + 16 = 18 \text{ g/mol}$.
$\text{Mass} = 10 \times 18 = 180 \text{ g}$.
Comparing the masses: $68.4 \text{ g} < 88 \text{ g} < 180 \text{ g} < 200 \text{ g}$.
Thus, $2$ moles of $CaCO_3$ weigh the highest.

(D) To find the number of atoms,we first calculate the number of moles $(n = \text{mass} / \text{molar mass})$ and then multiply by the number of atoms per molecule and Avogadro's number $(N_A)$.
$A) \, 18 \, g$ of $H_2O$: Molar mass = $18 \, g/mol$. Moles = $18/18 = 1 \, mol$. Atoms per molecule = $3$ $(2H + 1O)$. Total atoms = $1 \times 3 \times N_A = 3N_A$.
$B) \, 18 \, g$ of $O_2$: Molar mass = $32 \, g/mol$. Moles = $18/32 = 0.5625 \, mol$. Atoms per molecule = $2$. Total atoms = $0.5625 \times 2 \times N_A = 1.125N_A$.
$C) \, 18 \, g$ of $CO_2$: Molar mass = $44 \, g/mol$. Moles = $18/44 \approx 0.409 \, mol$. Atoms per molecule = $3$ $(1C + 2O)$. Total atoms = $0.409 \times 3 \times N_A \approx 1.227N_A$.
$D) \, 18 \, g$ of $CH_4$: Molar mass = $16 \, g/mol$. Moles = $18/16 = 1.125 \, mol$. Atoms per molecule = $5$ $(1C + 4H)$. Total atoms = $1.125 \times 5 \times N_A = 5.625N_A$.
Comparing the values,$CH_4$ has the maximum number of atoms.

(A) The number of molecules in a substance is calculated by the formula: $\text{Number of molecules} = \frac{\text{Given mass}}{\text{Molar mass}} \times N_A$,where $N_A$ is Avogadro's number $(6.022 \times 10^{23})$.
Since the given mass is $1\, g$ for all options,the number of molecules is inversely proportional to the molar mass.
$1$. Molar mass of $H_2 = 2 \times 1 = 2\, g/mol$. Number of molecules $\propto 1/2 = 0.5$.
$2$. Molar mass of $CO_2 = 12 + (2 \times 16) = 44\, g/mol$. Number of molecules $\propto 1/44 \approx 0.0227$.
$3$. Molar mass of $N_2 = 2 \times 14 = 28\, g/mol$. Number of molecules $\propto 1/28 \approx 0.0357$.
$4$. Molar mass of $CH_4 = 12 + (4 \times 1) = 16\, g/mol$. Number of molecules $\propto 1/16 = 0.0625$.
Comparing the values,$H_2$ has the smallest molar mass,therefore it contains the maximum number of molecules.

(B) Atomicity is defined as the total number of atoms present in one molecule of an element or compound.
$1$. Sulphur $(S_8)$ has an atomicity of $8$.
$2$. Phosphorus $(P_4)$ has an atomicity of $4$.
$3$. Ozone $(O_3)$ has an atomicity of $3$.
$4$. Methane $(CH_4)$ has an atomicity of $5$ ($1$ carbon atom + $4$ hydrogen atoms).
Therefore,the molecule with an atomicity of $4$ is the Phosphorus molecule.