Laws of chemical combination Questions in English

(B) According to Avogadro's Law,under the same conditions of temperature and pressure,equal volumes of all gases contain an equal number of molecules.

(C) Gay-Lussac's law of gaseous volumes states that when gases react together,they do so in volumes which bear a simple ratio to one another and to the volumes of the products if gaseous,provided that all gases are at the same temperature and pressure. This law was based on $Experimental \ observations$ made by Joseph Louis Gay-Lussac.

(B) The law of multiple proportions was proposed by John Dalton in $1803$ and was later verified by Jons Jacob Berzelius.

(D) Gay-Lussac's law of gaseous volumes states that when gases react together,they do so in volumes which bear a simple ratio to one another and to the volumes of the products,if gaseous,provided that the temperature and pressure remain constant.
In the reaction $N_2(g) + 3H_2(g) \rightarrow 2NH_3(g)$,the ratio of volumes of $N_2 : H_2 : NH_3$ is $1 : 3 : 2$,which is a simple whole-number ratio.

(C) The Law of Reciprocal Proportion states that when two different elements combine separately with a fixed mass of a third element,the ratio of the masses in which they do so is either the same or a simple multiple of the ratio in which they combine with each other.
Given:
$1 \text{ part of } A$ combines with $2 \text{ parts of } B$.
$6 \text{ parts of } C$ combine with $4 \text{ parts of } B$.
To compare $A$ and $C$ with a fixed mass of $B$ (let's fix $B$ at $4 \text{ parts}$):
$A$ combines with $B$ in ratio $1:2$,so $2 \text{ parts of } A$ combine with $4 \text{ parts of } B$.
$C$ combines with $B$ in ratio $6:4$,so $6 \text{ parts of } C$ combine with $4 \text{ parts of } B$.
The ratio of masses of $A$ and $C$ that combine with a fixed mass of $B$ is $2:6$ or $1:3$.
Since the ratio of weights of $A$ and $C$ is governed by their reaction with a third element $B$,this follows the Law of Reciprocal Proportion.

(A) Dalton's atomic theory,proposed in $1808$,stated that atoms are the ultimate,indivisible particles of matter. According to this theory,an atom cannot be subdivided into smaller particles.

(C) According to Dalton's atomic theory,atoms of the same element are identical in all respects,including their mass,shape,and chemical properties.
Therefore,the statement that atoms of an element are identical is the correct representation of his postulate.
Note: The existence of isotopes (atoms of the same element with different masses) is a limitation of Dalton's theory,as he originally proposed that all atoms of a given element are identical in every way.

(A) According to the law of conservation of mass,the total mass of the reactants must equal the total mass of the products in a balanced chemical equation.
In the reaction $4Fe_{(s)} + 3O_{2_{(g)}} \to 2Fe_{2}O_{3_{(s)}}$,the mass of $4$ moles of $Fe$ and $3$ moles of $O_{2}$ equals the mass of $2$ moles of $Fe_{2}O_{3}$.
Therefore,statement $A$ is correct as it correctly identifies that the reaction follows the law of conservation of mass.
Statement $B$ is incorrect because the law of multiple proportions applies to two elements forming more than one compound,not to a single balanced reaction.
Statements $C$ and $D$ are incorrect because the amount of product is determined by the limiting reagent,not by simply adding excess of one reactant.

(D) The law of multiple proportions states that when two elements combine to form more than one compound,the masses of one element that combine with a fixed mass of the other are in the ratio of small whole numbers.
In the pair $SnCl_2$ and $SnCl_4$,the same element tin $(Sn)$ combines with chlorine $(Cl)$ in different proportions.
For $SnCl_2$: $118.7 \ g$ of $Sn$ combines with $71 \ g$ of $Cl$.
For $SnCl_4$: $118.7 \ g$ of $Sn$ combines with $142 \ g$ of $Cl$.
The ratio of the masses of chlorine that combine with a fixed mass of tin is $142 : 71$,which simplifies to $2 : 1$.
Since this is a simple whole-number ratio,this pair illustrates the law of multiple proportions.

(C) To verify the law,we fix the mass of dinitrogen $(N_2)$ to a constant value,say $14 \ g$.
$1$. For $14 \ g$ of $N_2$,the mass of dioxygen $(O_2)$ is $16 \ g$ and $32 \ g$. The ratio is $16:32 = 1:2$.
$2$. For $28 \ g$ of $N_2$,the mass of $O_2$ is $32 \ g$ and $80 \ g$. Normalizing to $14 \ g$ of $N_2$ (dividing by $2$),the masses of $O_2$ are $16 \ g$ and $40 \ g$. The ratio is $16:40 = 2:5$.
Since the masses of one element $(O_2)$ that combine with a fixed mass of another element $(N_2)$ are in the ratio of small whole numbers $(1:2:5)$,the data obeys the Law of Multiple Proportions.
Thus,option $C$ is correct.

(C) The Law of Multiple Proportions states that when two elements combine to form more than one compound,the masses of one element that combine with a fixed mass of the other are in the ratio of small whole numbers.
In $CuO$ and $Cu_2O$:
For $CuO$: $63.5 \ g$ of $Cu$ combines with $16 \ g$ of $O$.
For $Cu_2O$: $127 \ g$ of $Cu$ combines with $16 \ g$ of $O$,which means $63.5 \ g$ of $Cu$ combines with $8 \ g$ of $O$.
The ratio of the masses of oxygen combining with a fixed mass $(63.5 \ g)$ of copper is $16:8$,which simplifies to $2:1$,a simple whole number ratio.
Therefore,$CuO$ and $Cu_2O$ illustrate the Law of Multiple Proportions.

(A) The Law of Multiple Proportions states that when two elements combine to form more than one compound,the masses of one element that combine with a fixed mass of the other element are in the ratio of small whole numbers.
In $N_2O_3, N_2O_4$,and $N_2O_5$,the element nitrogen $(N)$ combines with oxygen $(O)$ to form different compounds.
For a fixed mass of nitrogen $(28 \ g)$,the masses of oxygen are $48 \ g, 64 \ g$,and $80 \ g$ respectively.
The ratio of these masses is $48:64:80$,which simplifies to $3:4:5$,a ratio of small whole numbers.
Thus,$N_2O_3, N_2O_4, N_2O_5$ illustrates the Law of Multiple Proportions.

(B) In the first compound,carbon = $42.9\%$ and oxygen = $(100 - 42.9)\% = 57.1\%$. The ratio of oxygen to carbon is $57.1 / 42.9 \approx 1.33$.
In the second compound,carbon = $27.3\%$ and oxygen = $(100 - 27.3)\% = 72.7\%$. The ratio of oxygen to carbon is $72.7 / 27.3 \approx 2.66$.
The ratio of the two ratios is $2.66 / 1.33 = 2:1$.
Since the ratio is a simple whole number,this illustrates the $Law$ $of$ $Multiple$ $Proportions$.

(A) For $SO_2$: The molar mass of $S$ is $32 \, g$ and $O_2$ is $32 \, g$.
Since $32 \, g$ of $S$ combines with $32 \, g$ of $O_2$,then $48 \, g$ of $S$ will combine with $(32 / 32) \times 48 = 48 \, g$ of $O_2$.
For $SO_3$: The molar mass of $S$ is $32 \, g$ and $O_3$ is $48 \, g$.
Since $32 \, g$ of $S$ combines with $48 \, g$ of $O_3$,then $48 \, g$ of $S$ will combine with $(48 / 32) \times 48 = 72 \, g$ of $O_3$.
Thus,the masses are $48 \, g$ and $72 \, g$.

(D) The Assertion is incorrect because,according to nuclear reactions,atoms can be created or destroyed (e.g.,in nuclear fission or fusion).
The Reason is also incorrect because,according to Avogadro's Law,equal volumes of all gases under the same conditions of temperature and pressure contain an equal number of molecules,and consequently,an equal number of atoms if the gases are monatomic.

(C) According to $Dalton's$ atomic theory,matter consists of indivisible atoms,chemical reactions involve the reorganization of atoms,and atoms are neither created nor destroyed.
The statement regarding the simple ratio of volumes of gases is known as $Gay-Lussac's$ Law of Gaseous Volumes,which was not part of $Dalton's$ atomic theory.

(N/A) If we fix the mass of dinitrogen at $28 \ g$, the masses of dioxygen that combine with the fixed mass of dinitrogen are $32 \ g, 64 \ g, 32 \ g,$ and $80 \ g$.
The ratio of these masses of dioxygen is $32:64:32:80$, which simplifies to $2:4:2:5$ (a whole number ratio).
Thus, the data obeys the Law of Multiple Proportions.
Statement: When two elements combine to form more than one compound, the masses of one element that combine with a fixed mass of the other are in the ratio of small whole numbers.
$(b) (i) \ 1 \ km = 10^{6} \ mm = 10^{15} \ pm$
$(ii) \ 1 \ mg = 10^{-6} \ kg = 10^{6} \ ng$
$(iii) \ 1 \ mL = 10^{-3} \ L = 10^{-3} \ dm^{3}$

(N/A) The atomic theory of matter was first proposed by John Dalton in $1808$.
$1$. Matter consists of indivisible atoms.
$2$. All the atoms of a given element have identical properties,including identical mass. Atoms of different elements differ in mass.
$3$. Compounds are formed when atoms of different elements combine in a fixed ratio.
$4$. Chemical reactions involve only the reorganization of atoms. Atoms are neither created nor destroyed in a chemical reaction.
This theory successfully explained the law of conservation of mass,the law of constant composition,and the law of multiple proportions. However,it failed to explain the existence of subatomic particles (like electrons,protons,and neutrons) and the phenomenon of static electricity generated by rubbing materials.

(N/A) The Law of Conservation of Mass states that matter can neither be created nor destroyed in a chemical reaction.
This law was put forth by Antoine Lavoisier in $1789$.
He performed careful experimental studies for combustion reactions to reach this conclusion.
This law formed the basis for several later developments in chemistry.
It is the result of exact measurements of the masses of reactants and products in carefully planned experiments.

(N/A) The Law of Definite Proportions was proposed by the French chemist $Joseph \ Proust$. He stated that a given chemical compound always contains exactly the same proportion of elements by weight,regardless of its source or method of preparation.
$Proust$ worked with two samples of cupric carbonate $(CuCO_3)$—one of natural origin and the other synthetic. He found that the composition of elements present in both samples was identical,as shown in the table below:

Sample Type	$\% \text{ of Copper}$	$\% \text{ of Carbon}$	$\% \text{ of Oxygen}$
Natural sample	$51.35$	$9.74$	$38.91$
Synthetic sample	$51.35$	$9.74$	$38.91$

Thus,irrespective of the source,a given compound always contains the same elements in the same proportion by mass. This law is also known as the Law of Definite Composition.

This law was proposed by Dalton in $1803$.
According to this law,if two elements can combine to form more than one compound,the masses of one element that combine with a fixed mass of the other element are in the ratio of small whole numbers.
For example,hydrogen combines with oxygen to form two compounds,namely,water $(H_2O)$ and hydrogen peroxide $(H_2O_2)$.
$1.$ Hydrogen $+$ Oxygen $\rightarrow$ Water $(H_2O)$
$2 \ g$ of Hydrogen combines with $16 \ g$ of Oxygen.
$2.$ Hydrogen $+$ Oxygen $\rightarrow$ Hydrogen Peroxide $(H_2O_2)$
$2 \ g$ of Hydrogen combines with $32 \ g$ of Oxygen.
Here,the masses of oxygen ($16 \ g$ and $32 \ g$) which combine with a fixed mass of hydrogen $(2 \ g)$ bear a simple ratio,i.e.,$16:32$ or $1:2$.

This law was proposed by Gay-Lussac in $1808$.
He observed that when gases combine or are produced in a chemical reaction,they do so in a simple ratio by volume,provided all gases are at the same temperature and pressure.
For example,$100 \ mL$ of hydrogen combines with $50 \ mL$ of oxygen to give $100 \ mL$ of water vapour.
$\text{Hydrogen} + \text{Oxygen} \rightarrow \text{Water vapour}$
$100 \ mL$ $50 \ mL$ $100 \ mL$
Thus,the volumes of hydrogen and oxygen which combine together (i.e.,$100 \ mL$ and $50 \ mL$) bear a simple ratio of $2:1$.
Gay-Lussac's discovery of an integer ratio in volume relationships is essentially the law of definite proportions by volume,whereas the earlier law was with respect to mass.

(N/A) In $1811$,Avogadro proposed that equal volumes of gases at the same temperature and pressure should contain an equal number of molecules.
Avogadro made a distinction between atoms and molecules,which is well-understood in modern times.
If we consider the reaction of hydrogen and oxygen to produce water,we observe that two volumes of hydrogen combine with one volume of oxygen to yield two volumes of water vapor without leaving any unreacted oxygen.
In the figure,each box contains an equal number of molecules. Avogadro explained this result by considering the molecules to be polyatomic. Specifically,he proposed that hydrogen and oxygen exist as diatomic molecules.
At that time,Dalton and others believed that atoms of the same kind could not combine,and thus molecules of oxygen or hydrogen containing two atoms did not exist. However,Avogadro's hypothesis successfully explained the experimental observations.

(N/A) The first atomic theory was proposed by John Dalton in $1808$.
According to this theory:
$(i)$ Matter consists of indivisible atoms.
$(ii)$ All atoms of a given element have identical properties,including identical mass. Atoms of different elements differ in mass.
$(iii)$ Compounds are formed when atoms of different elements combine in a fixed ratio.
$(iv)$ Chemical reactions involve the reorganization of atoms. Atoms are neither created nor destroyed in a chemical reaction.

(A) The given reaction is: $2N_{2(g)} + O_{2(g)} \to 2N_2O_{(g)}$
Stoichiometric volumes: $2 \ V \quad 1 \ V \quad 2 \ V$
Given volumes: $45.4 \ L \quad 22.7 \ L \quad 45.4 \ L$
Dividing by $22.7 \ L$: $2 : 1 : 2$
Since the volumes of reactants and products bear a simple whole-number ratio $(2:1:2)$,this reaction follows Gay-Lussac's Law of Gaseous Volumes.
Gay-Lussac's Law states: "When gases react together,they do so in volumes which bear a simple ratio to one another and to the volume of the products,if gaseous,provided that all gases are at the same temperature and pressure."

(N/A) Yes,the statement is correct.
$(b)$ It follows the Law of Multiple Proportions.
$(c)$ Example: Hydrogen and oxygen combine to form water $(H_2O)$ and hydrogen peroxide $(H_2O_2)$.
For $H_2O$: $2 \ g$ of $H$ combines with $16 \ g$ of $O$.
For $H_2O_2$: $2 \ g$ of $H$ combines with $32 \ g$ of $O$.
The masses of oxygen ($16 \ g$ and $32 \ g$) that combine with a fixed mass of hydrogen $(2 \ g)$ bear a simple ratio of $16:32$,which is $1:2$.

The 'Law of Multiple Proportions' was proposed by Dalton in $1803$. It states that when two elements combine to form more than one compound,the masses of one element that combine with a fixed mass of the other are in the ratio of small whole numbers.
Example $1$: Hydrogen and oxygen form water $(H_2O)$ and hydrogen peroxide $(H_2O_2)$.
In $H_2O$,$2 \ g$ of hydrogen combines with $16 \ g$ of oxygen.
In $H_2O_2$,$2 \ g$ of hydrogen combines with $32 \ g$ of oxygen.
The ratio of the masses of oxygen $(16:32)$ is $1:2$,which is a simple whole number ratio.
Example $2$: Carbon and oxygen form carbon monoxide $(CO)$ and carbon dioxide $(CO_2)$.
In $CO$,$12 \ g$ of carbon combines with $16 \ g$ of oxygen.
In $CO_2$,$12 \ g$ of carbon combines with $32 \ g$ of oxygen.
The ratio of the masses of oxygen $(16:32)$ is $1:2$.
This law supports the existence of atoms because it implies that elements combine in discrete,fixed units (atoms) rather than in arbitrary amounts,leading to fixed ratios of mass.

(N/A) To verify the law of multiple proportions,we calculate the mass of $B$ that combines with a fixed mass of $A$ $(4 \ g)$:

Combination	Mass of $B$ combined with $4 \ g$ of $A$
$AB$	$10 \ g$
$AB_2$	$20 \ g$
$A_2B$	$5 \ g$
$A_2B_3$	$15 \ g$

The masses of $B$ that combine with a fixed mass of $4 \ g$ of $A$ are $10 \ g, 20 \ g, 5 \ g$ and $15 \ g$.
The ratio of these masses is $10:20:5:15$,which simplifies to $2:4:1:3$.
Since this is a simple whole-number ratio,the law of multiple proportions is applicable.

(D) Dalton's atomic theory provides a theoretical basis for the laws of chemical combination. These include:
$1$. The Law of Conservation of Mass.
$2$. The Law of Definite Proportions.
$3$. The Law of Multiple Proportions.
$4$. Gay-Lussac's Law of Gaseous Volumes and Avogadro's Law are also consistent with the atomic theory.

The Law of Multiple Proportions states that if two elements can combine to form more than one compound,the masses of one element that combine with a fixed mass of the other element are in the ratio of small whole numbers.
For example,carbon and oxygen can combine to form $CO$ and $CO_2$.
In $CO$,$12 \ g$ of carbon combines with $16 \ g$ of oxygen.
In $CO_2$,$12 \ g$ of carbon combines with $32 \ g$ of oxygen.
The ratio of the masses of oxygen that combine with a fixed mass $(12 \ g)$ of carbon is $16:32$,which simplifies to $1:2$,a simple whole number ratio.

(A) The correct matches are:
$(1)$ Law of Multiple Proportions was proposed by John Dalton.
$(2)$ Law of Conservation of Mass was proposed by Antoine Lavoisier.
$(3)$ Law of Definite Proportions was proposed by Joseph Proust.
Therefore,the correct sequence is $(1-A, 2-C, 3-B)$.

(A) According to Dalton's Atomic Theory,atoms of different elements combine in a fixed ratio by mass to form compounds. Therefore,the statement that they combine in 'any' ratio is incorrect.

(D) For option $(A)$:
Let atomic mass of $P$ be $M_P$ and atomic mass of $Q$ be $M_Q$. Molar ratio of atoms $P:Q$ in compound $3$ is $\frac{40}{M_P} : \frac{60}{M_Q} = 3:4$.
$\frac{40 M_Q}{60 M_P} = \frac{3}{4}$ $\Rightarrow \frac{2 M_Q}{3 M_P} = \frac{3}{4}$ $\Rightarrow 9 M_P = 8 M_Q$.
For compound $2$,molar ratio is $\frac{44.4}{M_P} : \frac{55.6}{M_Q} = 44.4 M_Q : 55.6 M_P = 44.4 M_Q : 55.6 \times (\frac{8 M_Q}{9}) = 44.4 : 49.42 \approx 9:10$. Empirical formula is $P_9 Q_{10}$. Option $(A)$ is incorrect.
For option $(B)$:
Molar ratio of atoms $P:Q$ in compound $3$ is $\frac{40}{M_P} : \frac{60}{M_Q} = 3:2$.
$\frac{40 M_Q}{60 M_P} = \frac{3}{2}$ $\Rightarrow \frac{2 M_Q}{3 M_P} = \frac{3}{2}$ $\Rightarrow 9 M_P = 4 M_Q$.
If $M_P = 20$,then $M_Q = \frac{9 \times 20}{4} = 45$. Option $(B)$ is correct.
For option $(C)$:
Molar ratio of atoms $P:Q$ in compound $2$ is $\frac{44.4}{M_P} : \frac{55.6}{M_Q} = 1:1 \Rightarrow \frac{M_P}{M_Q} = \frac{44.4}{55.6}$.
Molar ratio of atoms $P:Q$ in compound $1$ is $\frac{50}{M_P} : \frac{50}{M_Q} = M_Q : M_P = 55.6 : 44.4 \approx 5:4$. Empirical formula is $P_5 Q_4$. Option $(C)$ is correct.
For option $(D)$:
Molar ratio of atoms $P:Q$ in compound $1$ is $\frac{50}{M_P} : \frac{50}{M_Q} = M_Q : M_P = 35 : 70 = 1:2$. Empirical formula is $PQ_2$. Option $(D)$ is incorrect.

(D) Dalton's atomic theory was based on the concept of atoms as indivisible particles and could explain the laws of chemical combination like the law of conservation of mass,law of constant proportions,and law of multiple proportions.
However,it failed to explain the law of gaseous volume,which was later explained by Avogadro's hypothesis.

(D) The law of multiple proportions states that when two elements combine to form more than one compound,the masses of one element that combine with a fixed mass of the other are in the ratio of small whole numbers.
In the pair $D_2O$ and $D_2O_2$,the element $D$ (deuterium) has a fixed mass,while the mass of $O$ (oxygen) in $D_2O$ is $16 \ g$ and in $D_2O_2$ is $32 \ g$.
The ratio of the masses of oxygen is $16:32$,which simplifies to $1:2$,a simple whole number ratio.
Therefore,$D_2O$ and $D_2O_2$ illustrate the law of multiple proportions.

(B) The law of multiple proportions states that when two elements combine to form more than one compound,the masses of one element that combine with a fixed mass of the other are in the ratio of small whole numbers.
$CuO$ and $Cu_2O$ consist of $Cu$ and $O$.
$CO$ and $CO_2$ consist of $C$ and $O$.
$N_2O_4$ and $N_2O_5$ consist of $N$ and $O$.
$NaNO_3$ and $CaCO_3$ are different compounds containing different sets of elements ($Na, N, O$ vs $Ca, C, O$).
Therefore,they do not satisfy the criteria for the law of multiple proportions.

(D) The statement "$A$ given compound always contains the same proportion of elements by mass" refers to the $Law \ of \ definite \ proportions$.
This law states that a chemical compound always consists of the same elements combined together in the same fixed proportion by mass,regardless of its source or method of preparation.
For example,water $(H_2O)$ always contains hydrogen and oxygen in a mass ratio of $1:8$.

(C) The correct answer is $C$ (Law of Multiple Proportions).
Explanation:
The Law of Multiple Proportions states that when two elements combine to form more than one compound,the different masses of one element that combine with a fixed mass of the other element are in simple whole number ratios.
- In $H_2O$,$2 \ g$ of hydrogen combines with $16 \ g$ of oxygen.
- In $H_2O_2$,$2 \ g$ of hydrogen combines with $32 \ g$ of oxygen.
- The masses of oxygen ($16 \ g$ and $32 \ g$) that combine with a fixed mass of hydrogen $(2 \ g)$ are in the ratio $16:32$,which simplifies to $1:2$,a simple whole number ratio.
- Therefore,these compounds illustrate the Law of Multiple Proportions.

(D) The law of multiple proportions states that when two elements combine to form two or more compounds,the masses of one element that combine with a fixed mass of the other are in the ratio of small whole numbers.
This law is applicable only when the same two elements form different compounds.
In the pair $Na_2S$ and $NaF$,the elements involved are different ($S$ and $F$),so they cannot demonstrate the law of multiple proportions.

(A) The law of reciprocal proportions states that if two different elements combine separately with a fixed mass of a third element,the ratio of the masses in which they do so is either the same or a simple multiple of the ratio of the masses in which they combine with each other.
In the set $P_2O_3, PH_3$ and $H_2O$:
$1$. $P$ combines with $H$ to form $PH_3$ ($31 \ g$ of $P$ with $3 \ g$ of $H$).
$2$. $P$ combines with $O$ to form $P_2O_3$ ($62 \ g$ of $P$ with $48 \ g$ of $O$).
$3$. For a fixed mass of $P$ $(62 \ g)$,the mass of $H$ is $6 \ g$ and the mass of $O$ is $48 \ g$. The ratio is $6:48 = 1:8$.
$4$. In $H_2O$,$H$ and $O$ combine in the ratio $2:16 = 1:8$.
Since the ratios are the same,this set illustrates the law.

(C) The law of multiple proportions states that when two elements combine to form more than one compound,the masses of one element that combine with a fixed mass of the other are in the ratio of small whole numbers.
In the pair $CO$ and $CO_2$,carbon $(C)$ and oxygen $(O)$ combine to form two different compounds.
In $CO$,$12 \ g$ of carbon combines with $16 \ g$ of oxygen.
In $CO_2$,$12 \ g$ of carbon combines with $32 \ g$ of oxygen.
The ratio of the masses of oxygen that combine with a fixed mass of carbon $(12 \ g)$ is $16:32$,which simplifies to $1:2$,a simple whole number ratio.
Therefore,$CO$ and $CO_2$ demonstrate the law of multiple proportions.

(C) The statement "Mass can neither be created nor destroyed" is the fundamental definition of the $Law \ of \ conservation \ of \ mass$.
This law was proposed by $Antoine \ Lavoisier$ in $1789$.
It states that in any chemical reaction, the total mass of the reactants is equal to the total mass of the products.

(B) The correct answer is $(B)$.
According to $\text{Dalton's}$ atomic theory,the symbols for elements and compounds were represented by specific pictorial symbols.
The symbol for water was represented by two circles,one containing a dot (representing hydrogen) and the other empty (representing oxygen),placed side by side.

(B) According to the law of definite proportion,the percentage composition of a compound remains constant regardless of its source.
Given that $Ca$ constitutes $40 \%$ of the sample by mass.
Therefore,in a $4 \ g$ sample of calcium carbonate,the mass of calcium is calculated as:
$\text{Mass of } Ca = \frac{40}{100} \times 4 \ g = 1.6 \ g$.

(D) The Law of Definite Proportions (also known as the Law of Constant Composition) states that a given chemical compound always contains its component elements in a fixed ratio by mass,regardless of its source or method of preparation.
Since the samples of copper carbonate from both the laboratory and natural sources contain the same percentage composition by weight ($51.35 \%$ copper,$38.91 \%$ carbon,and $9.74 \%$ oxygen),it confirms the Law of Definite Proportions.

(D) The combining ratios of hydrogen and oxygen in water $(H_2O)$ and hydrogen peroxide $(H_2O_2)$ are $1: 8$ and $1: 16$ respectively.
This is an example of the law of multiple proportions.
According to this law,if two elements combine to form more than one compound,the masses of one element that combine with a fixed mass of the other are in the ratio of small whole numbers.
Here,for a fixed mass of hydrogen $(1 \ g)$,the masses of oxygen are $8 \ g$ and $16 \ g$,which are in the ratio $8:16$ or $1:2$.

(B) The law of definite proportions states that every chemical compound contains fixed and constant proportions (by mass) of its constituent elements.
The statement that the $\%$ of oxygen in $H_2O$ is constant irrespective of the source is in accordance with the law of definite proportions.
The ratio of oxygen in $H_2O$ and $H_2O_2$ with respect to a fixed mass of Hydrogen is related to the law of multiple proportions.
The statement regarding equal volumes of gases containing equal molecules is Avogadro's law.
The statement that matter can neither be created nor destroyed is the law of conservation of mass.

(B) The given statement is $Avogadro's \ law$,because according to $Avogadro's \ law$.
$Equal \ volume \ of \ all \ gases \ under \ similar \ conditions \ of \ temperature \ and \ pressure \ contain \ equal \ number \ of \ molecules$,i.e.,volume of gas $V \propto N$ (number of molecules).
Or $V \propto n$ (number of moles) [at constant temperature and pressure].