Some Basic Concepts Of Chemistry

When it comes to understanding results of measurements, the terms precision and accuracy are used. Precision refers to the closeness of various measurements for the same quantity while accuracy is to show whether the particular value is true to the value of the result.

The average reading of Student A is 3.01 + 2.99/2 = 3.00

The average reading of Student B is 3.05 + 2.95/2 = 3.00

The average value of both students is close to the true value, hence both students have accurate results. However, the values of student A are close to each other as well as the average value, with the difference of the two results being 0.02. As for the values of student B the values are relatively farther, with the difference between the two values being 0.1.

Hence the results of student A are precise. The correct option is (ii).

Fahrenheit is converted to Celsius using this conversion:

°F = °C + 32

Therefore, 200°F = °C + 32

°C = (200 – 32) x = 93.3°C.

The correct answer is (iii).

The molarity of a solution is defined as the number of moles of a solute dissolved in 1 litre of a solution. The given solute is NaCl and its molar mass is 58.44 ~ 58.5 g. Therefore, a 1M solution of NaCl will contain 58.5g of NaCl dissolved in 1 litre of solvent.

The molarity of the given NaCl solution is given by the formula

= = 0.1/0.5 = 0.2M or 0.2 mol L^-1.

The correct answer is (iii).

The molarity M of a solution is inversely proportional to its volume V, if the mass of the solute is kept the same. Hence, the formula is established M₁V₁ = M₂V₂.

Using this formula, where M₁ is the initial molarity of the solution = 5M,

V₁ is the initial volume of the solution = 0.5L,

V₂ is the final volume of the solution = 1.5L

M₂ is the final volume of the solution =?

Substituting these values, 5 x 0.5 = M₂ x 1.5

Therefore, M₂ = 1.66M.

The correct answer is (ii).

The molecular weights of the given elements are as follows:

He = 4, Na = 23, Ca = 40.

To check which element has most atoms, we need to check the number of moles present in each option. The highest number of moles mean the most atoms present.

No. of moles = Given weight/molecular weight of the element

For 4g He, no. of moles are 4/4 = 1 mol.

For 46g Na, no. of moles are 46/23 = 2 mol.

For 0.40g Ca, no. of moles are 0.4/40 = 0.01 mol.

For 12g He, no. of moles are 12/4 = 3 mol.

Therefore, 12g He contains the most number of atoms.

The correct answer is (iv).

The concentration of a compound in the solution can be converted into molarity of the solution by the formula

The molar mass of glucose is 12x6 + 1x12 + 16x6 = 180.

Therefore,

Molarity = 0.9/180 = 0.005M.

The molar mass of HCl is 1x1 + 35.5x1 = 36.5. The given solution contains 18.25g of HCl gas. The number of moles is 18.25/36.5 = 0.5 mol. The molality is calculated by the formula

Molality = 0.5/0.5 = 1m.

The molality of the solution is 1 m. The correct answer is (iv).

1M of H₂SO₄ solution contains 6.022 × 10²³ molecules of H₂SO₄.

Hence, 0.02M of H₂SO₄ contains 0.02 × 6.022 × 10²³ = 12.044 × 10²⁰ molecules.

The correct answer is (i).

The molar mass of carbon dioxide CO₂ is 12x1 + 16x2 = 44. 1 g molecule of CO₂ contains 1 g atom of carbon. 44g of CO₂ will contain 12g of C. The mass percentage of carbon in CO₂ is given by the formula

= 12/44 x 100 = 27.27%

The correct answer is (ii).

The empirical formula of a compound represents the simplest whole number ratio of various atoms present in the molecule, while the molecular formula shows the exact number of different types of atoms present in a molecule of a compound.

The empirical formula mass of the compound is calculated to be 1x12 + 1x2 + 1x16 = 30.

The molecular mass of the compound is 180.

‘n’ is the factor to be multiplied with the empirical formula to give the molecular formula and it is given by

n = 180/30 = 6

Molecular formula = n(Empirical formula) = 6(CH₂O)

The molecular formula of the compound is C₆H₁₂O₆.

The correct answer is (iii).

Density is given by the formula

Density = mass/volume

By substituting the values, we get

3.12 = mass/1.5

Mass = 4.68g. Since the solution is asked in significant figures, the solution should be rounded up to two significant figures, i.e. 4.7g. The correct answer is (i).

The statements (i), (ii), and (iv) are correct as they are properties of compounds.

The statement (iii) is incorrect because a compound has physical properties different from that of its constituent elements.

For example, water is a compound of hydrogen and oxygen to make H₂O. Hydrogen and oxygen are gases are room temperature but H₂O is a liquid at room temperature.

The combination of elements to form compounds in a chemical reaction is governed by various basic laws. In option (i) the Law of Conservation of Mass states that matter cannot be created nor destroyed. In the given reaction, there is no net change in the mass, hence the first option is correct.

The second option mentions the Law of Multiple Proportions. The law 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.” This law does not apply here because there is only one product formed.

Considering the third and fourth option, the reaction does not create higher amount of product on excess or decreasing of one product as the reaction proceeds stoichiometrically.

The correct answer is (i).

Only in equation (ii), the reactants and products are not balanced.

The unbalanced equation goes against the law of conservation of mass.

The correct answer is (ii).

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.’

The first option does not follow the law because it is in regards to only carbon dioxide as a product of carbon and oxygen.

In the second option, the mass of oxygen in CO₂ is 16x2 = 32 and the mass in CO is 16x1 = 16. The ratio of the masses of oxygen is in the ratio 32:16 that is 2:1. Hence it follows the law of multiple proportions.

In the third option, the reaction of burning magnesium to magnesium oxide is given by 2Mg + O₂→ 2MgO. The amount of magnesium taken for the reaction is not equal to the amount of magnesium present in the molecule, hence it does not follow law of multiple proportions.

In the fourth option, the formation of water vapour does not follow law of multiple proportions but Gay-Lussac’s law which states ‘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.’

The correct option is (ii).

One mole of oxygen gas at STP contains Avogadro’s number of molecules. The question mentions oxygen gas so it will contain 6.022 × 10²³ molecules of oxygen, O₂ not atoms.

One mole of O₂ contains 16x2 = 32g of oxygen.

The correct options are →i) and →iv).

Sulphuric acid is H₂SO₄ and sodium hydroxide is NaOH. In the acid-base reaction, Na₂SO₄ is the salt formed as a product.

H₂SO₄ + 2NaOH → Na₂SO₄ + 2H₂O

H₂SO₄ and NaOH react in the ratio 1:2 for this reaction as H₂SO₄ is a dibasic acid. 1 mole of H₂SO₄ reacts with 2 moles of NaOH, so according to this reaction, 0.05 moles of H₂SO₄ reacts with 0.1 moles of NaOH. Since the reaction can go ahead only with the minimum amount of NaOH being 0.1 moles, NaOH is the limiting reagent. The limiting reagent is known as the reactant, which gets consumed first and limits the amount of product formed. The product formed will be equal to the amount of the other reactant used i.e. H₂SO₄ and it will be 0.05 moles. The mass of Na₂SO₄ formed will be 0.05x142 = 7.10g. The molarity of the solution formed will be

= 0.05/2 = 0.025M.

The correct answers are (ii) and (iii).

One mole of a substance is the mass of a substance which contains exactly 6.023 x 10²³ molecules or atoms of that substance. So if two different substances are one mole each, they contain the same number of atoms.

The atomic masses of the given substances are as follows: O = 16, H = 1, CO₂ = 44, N = 14, C = 12, Na = 23.

The number of atoms present in each mass is given by the formula

For option (i), No. of oxygen atoms = x 6.023 x 10²³

No. of hydrogen atoms = x 6.023 x 10²³

(ii) No. of oxygen atoms = x 6.023 x 10²³

No. of carbon dioxide atoms = x 6.023 x 10²³

(iii) No. of nitrogen atoms = x 6.023 x 10²³

No. of oxygen atoms = x 6.023 x 10²³

D. No. of carbon atoms = x 6.023 x 10²³

No. of sodium atoms = x 6.023 x 10²³

According to the calculation, the correct answers are (ii), (iii), and (iv).

The concentration of the given solutions can be calculated in terms of molarity. Molarity is given by the formula

For option (i) Molarity of NaOH = = 2.5M

(ii) Molarity of KCl = 0.5/0.2 = 2.5M

(iii) Molarity of NaOH = = 10M

(iv) Molarity of KOH = = 1.7M

The solutions (i) and (ii) have the same concentration.

The molar mass of oxygen is 32. Therefore, 32g of oxygen contains 6.023 x 10²³ molecules. 16g of oxygen contains x 6.023 x 10²³ = 0.5 x 6.023 x 10²³ molecules.

16g of CO contains x 6.023 x 10²³ = 0.57 x 6.023 x 10²³ molecules.

28g of N₂ contains x 6.023 x 10²³ = 6.023 x 10²³ molecules.

14g of N₂ contains x 6.023 x 10²³ = 0.5 x 6.023 x 10²³ molecules.

1.0g of H₂ contains x 6.023 x 10²³ = 0.5 x 6.023 x 10²³ molecules.

Hence oxygen has the same number of molecules as (iii) and (iv).

Molality is measured as and the unit is molal or moles per kg.

Molarity is measured as and the unit is Molar or moles per liter.

Mole fraction is calculated as and it does not have units as it is a fraction.

Mass Percent is calculated as and it is unitless as it is a ratio multiplied by 100.

The correct answers are (iii) and (iv).

The law of conservation of mass states that there is no net change in the mass in a physical or chemical reaction. It also means that the number of atoms of each element on both sides of a balanced chemical equation is the same.

The law of definite proportions states that a given compound contains exactly the same proportion of elements by weight.

The law of multiple proportions states that when 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.

The Avogadro law states that equal volumes of all gases at the same temperature and pressure should contain equal number of molecules.

Concluding from these laws, options (i) and (iv) are not related to the given Dalton’s law.

1 mole of carbon contains 12g of carbon and contains 6.023 x 10²³ atoms. Therefore the mass of 1 atom of carbon can be given by the calculation

Mass of 1 carbon atom = = 1.99 x 10^-23g.

The calculation of multiplication and division contains four numbers. The numbers 2.5 and 3.5 contain two significant figures.

The numbers 1.25 and 2.01 contain three significant figures. The least number of significant figures is two, hence the answer to the calculation should contain two significant figures.

The SI unit for mole is mol. The mole is defined as the amount of substance of a system, which contains as many elementary entities as there are atoms in 0.012 kilogram or 12 gram of carbon-12; the entities can be atoms, molecules, electrons and so on.

Molality is defined as the number of moles of a solute dissolved in 1 kg of a solution, while molarity is defined as the number of moles of solute dissolved in 1 litre of solution. The major difference is that molality is not dependent on temperature as it is a function of mass, while molarity of a solution is dependent on temperature.

The molar mass of Ca₃(PO₄)₂ is 40x3 + (31 + 16x4) x 2 = 310.

The mass percent is calculated by

Mass % of Ca = x 100 = 38.71%

Mass % of P = x 100 = 20%

Mass % of O = x 100 = 41.29%

Dinitrogen and dioxygen are N₂ and O₂, which are gases at STP. The reaction proceeds to form N₂O. The ratios of the reactant and products are 45.4:22.7:45.4, which is equal to 2:1:2.

The ratio has small whole numbers and is simple. Hence the experiment follows the Gay-Lussac’s law of gaseous volumes, which states that when gases combine or produced in a chemical reaction they do so in a simple ratio by volume, provided all gases are at the same temperature and pressure.

(a) Yes, the statement is true.

(b) This statement is the definition of the law of multiple proportions.

(c) An example of an application of this law is the reaction of hydrogen and oxygen to form water H₂O as well as hydrogen peroxide H₂O₂.

H₂ + 1/2O₂→ H₂O

2g 16g 18g

H₂ + O₂→ H₂O₂

2g 32g 34g

Experimentally, the masses of the reactants and products are given. The ratio of masses of oxygen with the fixed mass of hydrogen is 16:32 or 1:2 which is a simple whole-number ratio.

The average atomic mass of an element with isotopes is calculated taking into account the existence of these isotopes and their relative abundance. The formula to calculate this is given by

Average atomic mass of hydrogen =

= = 1.00015u.

The atomic mass of Zn is given to be 65.3. Hence 1 mole of Zn has 65.3g. 1 mole of hydrogen gas occupies 22.7L at STP.

The equation can be written as

Since 63.5g Zn gives 22.7L of H₂ gas, 32.65g of Zn will give 32.65 x 22.7/63.5 = 11.35L of H₂ gas.

The density of the given solution is 1.110g mL^-1.

Since the solute is NaOH, the molar mass is 40. Since the solution is 3 molal, it means 3 moles of NaOH is dissolved in 1000g of water, or 120g of NaOH in 1000g of water. The total mass of the solution should therefore be 1120g. Since the mass and density is given, the volume is calculated by

1.110 = 1120/Volume

Volume = 1009mL = 1.009L

Molarity of the solution can now be calculated

M = 3 moles/1.009L = 2.97M.

Molality of a solution is defined as the number of moles of solute in 1 kilogram of solution.

Since molality depends on mass and not the volume of the solution, the mass is unaffected by temperature and molality of the solution is not affected by temperature.

There are two components in the NaOH solution, NaOH and H₂O. The mole fraction of a component is given by the formula

Number of moles of H₂O = Mass/Molar mass = 36/18 = 2 moles

Number of moles of NaOH = 4/40 = 0.1 moles.

Total number of moles = 2 + 0.1 = 2.1 moles.

Mole fraction of H₂O = 2/2.1 = 0.952

Mole fraction of NaOH = 0.1/2.1 = 0.048

Specific gravity is the density of a substance divided by density of water. Here, the density is 1g mL^-1. Mass of the solution is the sum of mass of NaOH and mass of H₂O = 4 + 36 = 40g.

Volume of solution = Mass/density

Volume of solution = 40mL.

Molarity = 0.1 moles/0.04L = 2.5M.

The equation in terms of moles of reactants and products is given as

Considering the definition of limiting reagent, we consider two cases where each reactant is completely consumed.

Case (I): Reactant A is completely consumed.

5 moles of A and 6 moles of B are given.

If 2 mol of A gives 3 mol of C, then 5 mol of A will give 3 x 5/2 = 7.5 mol of C.

Case (II): Reactant B is completely consumed.

5 moles of A and 6 moles of B are given.

If 4 mol of B gives 3 mol of C, then 6 mol of B gives 6 x 3/4 = 4.5 mol of C.

If reactant B is completely consumed, lesser amount of product C is formed, hence the limiting reagent is B.

(i) The limiting reagent is B

(ii) The amount of C formed is 4.5 moles.

(i) 44g of CO₂ constitutes 1 mol of CO₂. Therefore, 88g of CO₂ is 2 mol of CO₂. The correct answer is (b).

(ii) 1 mol of any compound contains 6.022 x 10²³ molecules of the compound. Hence 6.022 x 10²³ molecules of H₂O constitute 1 mol of H₂O. The correct answer is (c).

(iii) At STP, 22.4L of O₂ makes 1 mol of O₂. Hence, 5.6L of O₂ constitutes 5.6/22.4 = 0.25mol of O₂. The correct answer is (a).

(iv) 1 mol of O₂ contains 32g of O₂. Hence 96g of O₂ makes 96/32 = 3 mol of O₂. The correct answer is (e).

(v) 1 mol of any gas contains 6.023 x 10²³ molecules. Hence, the correct answer is (d).

The units of the physical quantities are as follows:

(i) – (e)

As we all know that Molarity is defined as;

So, SI unit of Molarity is mole/litre.

(ii) – (d)

As we all know that Mole fraction is defined as given below;

Mole fraction of A =

And, both of the nominator and denominator and have same SI unit. Thus, the SI unit of mole fraction is unitless.

(iii) – (b)

SI unit of Mole is simply mol.

(iv) – (g)

Molality =

So, from the above formula we can conclude that the SI unit of Molality is molekg^-1.

(v) – (c)

SI unit of Pressure is Pascal.

Although, it is defined as given below;

Pressure = .

Although, the SI unit of the above formula is . Which is also known as Pascal.

(vi) – (f)

In photometry, luminous intensity is a measure of the wavelength-weighted power emitted by a light source in a particular direction per unit solid angle, based on the luminous function, a standardized model of the sensitivity of the human eye.

The SI unit of luminous intensity is the candela(cd).

(vii) – (a)

The formula of density is given below;

So, from the above formula, we can conclude that SI unit of Density is gml^-1.

(viii) – (i)

As we all know that mass is measured in Kg and the SI unit of Mass is Kg.

The molecular formula of ethene is C₂H₄ and the empirical formula is CH₂. The molecular mass of ethene is 28 and the empirical mass is 14. The empirical mass is half of its molecular mass. The empirical formula shows that the ratio of C:H is 1:2.

One atomic mass unit is defined as one twelfth of the mass of one C-12 atom but it is taken as standard not because of the abundance of C-12. It is taken because this isotope of carbon, C-12 has a whole number as a measure of atomic mass hence it is simpler to carry out measurements of other elements.

Zeros at the end of a number or on the right side of a decimal point may or may not be a significant figure.

Thus,

Combustion of methane is given by the reaction

CH₄(g) + 2O₂(g) → CO₂(g) + 2H₂O(g)

If 1 mol of methane is combusted completely, it will give 2 mol of H₂O. Hence, 16g of methane on combustion gives 36g of H₂O not 18g.

So, from the above reaction we can conclude that H₂O is a product.

(i) The given vessel contains 1.6g of dioxygen i.e. O₂ gas at STP. Therefore it contains 1.6/32 = 0.05mol of O₂. At STP, 1 mol of O₂ has 22.4L of volume, hence at 0.05mol, O₂ has 0.05 x 22.4 = 1.12L volume.

We consider Boyle’s Law, where pressure is inversely proportional to volume of the gas. Therefore, P₁V₁ = P₂V₂.

Here, V₁ = 1.12L, V₂ = ?, P₁ = 1 atm, P₂ = 0.5 atm.

V₂ = 1 x 1.12/0.5 = 2.24L.

Hence, volume of the new vessel is 2.24L.

(ii) No. of molecules in 1 mol of O₂ = 6.023 x 10²³

Therefore, no. of molecules in 0.05 mol of O₂ = 0.05 x 6.023 x 10²³

= 3.011 x 10²².

We need to compute (i) What mass of CaCl₂ will be formed when 250 mL of 0.76 M HCl reacts with 1000 g of CaCO₃?

(ii) Name the limiting reagent

(iii) Number of moles of CaCl₂ formed in the reaction.

Number of moles of HCl are not known. 0.76M in a 250mL solution gives 0.76M x 0.25L = 0.19 mol of HCl.

Molecular mass of CaCO₃ is 100. Number of moles present in 1000g of CaCO₃ is 1000/100 = 10 mol.

The limiting reagent is defined as the reactant which is entirely consumed in reaction.

The reaction is

CaCO₃(s) + 2HCl(aq) → CaCl₂(aq) + CO₂(g) + H₂O(l)

1 mol 2 mol 1 mol

To find the limiting reagent, we consider the case of both reactants being completely consumed.

Case (I): Let CaCO₃ be completely consumed.

1 mol of CaCO₃ will give 1 mol of CaCl₂

Hence 10 mol of CaCO₃ will give 10 mol of CaCl₂.

Case (II): Let HCl be completely consumed.

2 mol of HCl will give 1 mol of CaCl₂

Hence, 0.19 mol of HCl will give 0.19/2 = 0.095 mol of CaCl₂.

Since the product formed in Case (II) is lesser, HCl is the limiting reagent, and the number of moles of CaCl₂ formed in the reaction is 0.095 mol. Mass of CaCl₂ formed will be 0.095 x Molar mass of CaCl₂ = 0.095 x 110 = 10.45g.

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.

Examples of this law include (i) Hydrogen combines with oxygen to form two compounds, water and hydrogen peroxide.

2H₂ + O₂→ 2H₂O

H₂ + O₂→ H₂O₂

In this example, the ratio of masses of oxygen which combine with the fixed mass of hydrogen is 16:32 or 1:2, which is a simple whole number ratio.

(ii) Carbon and oxygen combine to form carbon dioxide and carbon monoxide.

C + O₂→ CO₂

2C + O₂→ 2CO

In this example, the ratio of masses of oxygen which combine with the fixed mass of carbon is 16:32 or 1:2, which is a simple whole number ratio.

The law and the examples of the law show that in the formation of a compound, there are constituents which combine in a fixed proportion. The constituents may be atoms. Thus this law confirms the existence of atoms which combine to form molecules and compounds.

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.

The given data is tabulated as follows:

Consider the first two examples AB and AB₂ where the mass of A is fixed and the mass of B is not. The ratio of masses of B with the fixed mass of A is 5:10 or 1:2 which is a simple whole number ratio. Here the law of multiple proportions is applicable.

In the second two examples, A₂B and A₂B₃, the ratio of masses of B with the fixed mass of A is 5:15 or 1:3, which is also a simple whole number ratio.