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Q1.8:
Determine the molecular formula of an oxide of iron, in which the mass per cent of iron and oxygen are 69.9 and 30.1, respectively.
Solution :
Step 1: Establishing Atomic Data and Empirical Basis
To determine the empirical formula, we must convert the mass percentages of the constituent elements into their molar ratios. The given data is as follows:
- Mass % of Iron ($Fe$) = $69.9\%$
- Mass % of Oxygen ($O$) = $30.1\%$
- Atomic mass of $Fe$ = $55.85\text{ g/mol}$
- Atomic mass of $O$ = $16.00\text{ g/mol}$
Step 2: Calculating Moles of Constituent Elements
Assuming a sample mass of $100\text{ g}$, the mass of each element corresponds numerically to its percentage. The number of moles ($n$) is calculated as $n = \frac{\text{mass}}{\text{molar mass}}$.
For Iron ($Fe$):
$n_{Fe} = \frac{69.9\text{ g}}{55.85\text{ g/mol}} \approx 1.2515\text{ mol}$
For Oxygen ($O$):
$n_{O} = \frac{30.1\text{ g}}{16.00\text{ g/mol}} \approx 1.8812\text{ mol}$
Step 3: Determining the Simplest Molar Ratio
To find the simplest whole-number ratio, we divide the molar amounts by the smallest value calculated in Step 2 ($1.2515$). [Per the Law of Definite Proportions]
| Element | Molar Ratio | Division by $1.2515$ |
|---|---|---|
| $Fe$ | $1.2515$ | $1.00$ |
| $O$ | $1.8812$ | $1.50$ |
Step 4: Deriving the Empirical Formula
The ratio $Fe:O$ is $1:1.5$. Since empirical formulas must contain integer subscripts, we multiply the ratio by $2$ to obtain the smallest whole-number stoichiometry:
$Fe : O = (1 \times 2) : (1.5 \times 2) = 2 : 3$
Thus, the empirical formula is $Fe_{2}O_{3}$.
Step 5: Visual Representation of the Oxide Structure ($Fe_2O_3$)
Final Solution: The molecular formula of the iron oxide is $Fe_{2}O_{3}$ (Iron(III) oxide).
More Questions from Class 11 Chemistry Some Basic Concepts of Chemistry EXERCISES
- Q1.1(i): Calculate the molar mass of the following: (i) $H_2O$
- Q1.1(ii): Calculate the molar mass of the following: (ii) $CO_2$
- Q1.1(iii): Calculate the molar mass of the following: (iii) $CH_4$
- Q1.10(i): In three moles of ethane ($C_2H_6$), calculate the following: (i) Number of moles of carbon atoms.
- Q1.10(ii): In three moles of ethane ($C_2H_6$), calculate the following: (ii) Number of moles of hydrogen atoms.
- Q1.10(iii): In three moles of ethane ($C_2H_6$), calculate the following: (iii) Number of molecules of ethane.
- Q1.11: What is the concentration of sugar ($C_{12}H_{22}O_{11}$) in $mol L^{-1}$ if its 20 g are dissolved in enough water to make a final volume up to 2L?
- Q1.12: If the density of methanol is 0.793 kg $L^{-1}$, what is its volume needed for making 2.5 L of its 0.25 M solution?
- Q1.13: Pressure is determined as force per unit area of the surface. The SI unit of pressure, pascal is as shown below: $1Pa = 1N m^{-2}$ If mass of air at sea level is 1034 g $cm^{-2}$, calculate the pressure in pascal.
- Q1.14: What is the SI unit of mass? How is it defined?
- Q1.15: Match the following prefixes with their multiples: Prefixes Multiples (i) micro $10^6$ (ii) deca $10^9$ (iii) mega $10^{-6}$ (iv) giga $10^{-15}$ (v) femto $10$
- Q1.16: What do you mean by significant figures?
- Q1.17(i): A sample of drinking water was found to be severely contaminated with chloroform, $CHCl_3$, supposed to be carcinogenic in nature. The level of contamination was 15 ppm (by mass). (i) Express this in per cent by mass.
- Q1.17(ii): A sample of drinking water was found to be severely contaminated with chloroform, $CHCl_3$, supposed to be carcinogenic in nature. The level of contamination was 15 ppm (by mass). (ii) Determine the molality of chloroform in the water sample.
- Q1.18(i): Express the following in the scientific notation: (i) 0.0048
- Q1.18(ii): Express the following in the scientific notation: (ii) 234,000
- Q1.18(iii): Express the following in the scientific notation: (iii) 8008
- Q1.18(iv): Express the following in the scientific notation: (iv) 500.0
- Q1.18(v): Express the following in the scientific notation: (v) 6.0012
- Q1.19(i): How many significant figures are present in the following? (i) 0.0025
- Q1.19(ii): How many significant figures are present in the following? (ii) 208
- Q1.19(iii): How many significant figures are present in the following? (iii) 5005
- Q1.19(iv): How many significant figures are present in the following? (iv) 126,000
- Q1.19(v): How many significant figures are present in the following? (v) 500.0
- Q1.19(vi): How many significant figures are present in the following? (vi) 2.0034
- Q1.2: Calculate the mass per cent of different elements present in sodium sulphate ($Na_2SO_4$).
- Q1.20(i): Round up the following upto three significant figures: (i) 34.216
- Q1.20(ii): Round up the following upto three significant figures: (ii) 10.4107
- Q1.20(iii): Round up the following upto three significant figures: (iii) 0.04597
- Q1.20(iv): Round up the following upto three significant figures: (iv) 2808
- Q1.21(a): The following data are obtained when dinitrogen and dioxygen react together to form different compounds: Mass of dinitrogen Mass of dioxygen (i) 14 g 16 g (ii) 14 g 32 g (iii) 28 g 32 g (iv) 28 g 80 g (a) Which law of chemical combination is obeyed by the above experimental data? Give its statement.
- Q1.21(b)(i): Fill in the blanks in the following conversions: (i) 1 km = ...................... mm = ...................... pm
- Q1.21(b)(ii): Fill in the blanks in the following conversions: (ii) 1 mg = ...................... kg = ...................... ng
- Q1.21(b)(iii): Fill in the blanks in the following conversions: (iii) 1 mL = ...................... L = ...................... $dm^3$
- Q1.22: If the speed of light is $3.0 \times 10^8 m s^{-1}$, calculate the distance covered by light in 2.00 ns.
- Q1.23(i): In a reaction $A + B_2 \rightarrow AB_2$ Identify the limiting reagent, if any, in the following reaction mixtures. (i) 300 atoms of A + 200 molecules of B
- Q1.23(ii): In a reaction $A + B_2 \rightarrow AB_2$ Identify the limiting reagent, if any, in the following reaction mixtures. (ii) 2 mol A + 3 mol B
- Q1.23(iii): In a reaction $A + B_2 \rightarrow AB_2$ Identify the limiting reagent, if any, in the following reaction mixtures. (iii) 100 atoms of A + 100 molecules of B
- Q1.23(iv): In a reaction $A + B_2 \rightarrow AB_2$ Identify the limiting reagent, if any, in the following reaction mixtures. (iv) 5 mol A + 2.5 mol B
- Q1.23(v): In a reaction $A + B_2 \rightarrow AB_2$ Identify the limiting reagent, if any, in the following reaction mixtures. (v) 2.5 mol A + 5 mol B
- Q1.24(i): Dinitrogen and dihydrogen react with each other to produce ammonia according to the following chemical equation: $N_2 (g) + H_2 (g) \rightarrow 2NH_3 (g)$ (i) Calculate the mass of ammonia produced if $2.00 \times 10^3$ g dinitrogen reacts with $1.00 \times 10^3$ g of dihydrogen.
- Q1.24(ii): Dinitrogen and dihydrogen react with each other to produce ammonia according to the following chemical equation: $N_2 (g) + H_2 (g) \rightarrow 2NH_3 (g)$ (ii) Will any of the two reactants remain unreacted?
- Q1.24(iii): Dinitrogen and dihydrogen react with each other to produce ammonia according to the following chemical equation: $N_2 (g) + H_2 (g) \rightarrow 2NH_3 (g)$ (iii) If yes, which one and what would be its mass?
- Q1.25: How are 0.50 mol $Na_2CO_3$ and 0.50 M $Na_2CO_3$ different?
- Q1.26: If 10 volumes of dihydrogen gas reacts with five volumes of dioxygen gas, how many volumes of water vapour would be produced?
- Q1.27(i): Convert the following into basic units: (i) 28.7 pm
- Q1.27(ii): Convert the following into basic units: (ii) 15.15 pm
- Q1.27(iii): Convert the following into basic units: (iii) 25365 mg
- Q1.28: Which one of the following will have the largest number of atoms?
- Q1.29: Calculate the molarity of a solution of ethanol in water, in which the mole fraction of ethanol is 0.040 (assume the density of water to be one).
- Q1.3: Determine the empirical formula of an oxide of iron, which has 69.9% iron and 30.1% dioxygen by mass.
- Q1.30: What will be the mass of one $^{12}C$ atom in g?
- Q1.31(i): How many significant figures should be present in the answer of the following calculations? (i) $\frac{0.02856 \times 298.15 \times 0.112}{0.5785}$
- Q1.31(ii): How many significant figures should be present in the answer of the following calculations? (ii) $5 \times 5.364$
- Q1.31(iii): How many significant figures should be present in the answer of the following calculations? (iii) 0.0125 + 0.7864 + 0.0215
- Q1.32: Use the data given in the following table to calculate the molar mass of naturally occuring argon isotopes: Isotope Isotopic molar mass Abundance $^{36}Ar$ 35.96755 g $mol^{-1}$ 0.337% $^{38}Ar$ 37.96272 g $mol^{-1}$ 0.063% $^{40}Ar$ 39.9624 g $mol^{-1}$ 99.600%
- Q1.33(i): Calculate the number of atoms in each of the following (i) 52 moles of Ar
- Q1.33(ii): Calculate the number of atoms in each of the following (ii) 52 u of He
- Q1.33(iii): Calculate the number of atoms in each of the following (iii) 52 g of He.
- Q1.34(i): A welding fuel gas contains carbon and hydrogen only. Burning a small sample of it in oxygen gives 3.38 g carbon dioxide, 0.690 g of water and no other products. A volume of 10.0 L (measured at STP) of this welding gas is found to weigh 11.6 g. Calculate (i) empirical formula
- Q1.34(ii): A welding fuel gas contains carbon and hydrogen only. Burning a small sample of it in oxygen gives 3.38 g carbon dioxide, 0.690 g of water and no other products. A volume of 10.0 L (measured at STP) of this welding gas is found to weigh 11.6 g. Calculate (ii) molar mass of the gas
- Q1.34(iii): A welding fuel gas contains carbon and hydrogen only. Burning a small sample of it in oxygen gives 3.38 g carbon dioxide, 0.690 g of water and no other products. A volume of 10.0 L (measured at STP) of this welding gas is found to weigh 11.6 g. Calculate (iii) molecular formula.
- Q1.35: Calcium carbonate reacts with aqueous HCl to give $CaCl_2$ and $CO_2$ according to the reaction, $CaCO_3 (s) + 2 HCl (aq) \rightarrow CaCl_2 (aq) + CO_2(g) + H_2O(l)$. What mass of $CaCO_3$ is required to react completely with 25 mL of 0.75 M HCl?
- Q1.36: Chlorine is prepared in the laboratory by treating manganese dioxide ($MnO_2$) with aqueous hydrochloric acid according to the reaction $4 HCl (aq) + MnO_2(s) \rightarrow 2H_2O (l) + MnCl_2(aq) + Cl_2 (g)$ How many grams of HCl react with 5.0 g of manganese dioxide?
- Q1.4(i): Calculate the amount of carbon dioxide that could be produced when (i) 1 mole of carbon is burnt in air.
- Q1.4(ii): Calculate the amount of carbon dioxide that could be produced when (ii) 1 mole of carbon is burnt in 16 g of dioxygen.
- Q1.4(iii): Calculate the amount of carbon dioxide that could be produced when (iii) 2 moles of carbon are burnt in 16 g of dioxygen.
- Q1.5: Calculate the mass of sodium acetate ($CH_3COONa$) required to make 500 mL of 0.375 molar aqueous solution. Molar mass of sodium acetate is 82.0245 g $mol^{-1}$.
- Q1.6: Calculate the concentration of nitric acid in moles per litre in a sample which has a density, 1.41 g $mL^{-1}$ and the mass per cent of nitric acid in it being 69%.
- Q1.7: How much copper can be obtained from 100 g of copper sulphate ($CuSO_4$)?
- Q1.9: Calculate the atomic mass (average) of chlorine using the following data: % natural abundance molar mass $^{35}Cl$ 75.77 34.9689 $^{37}Cl$ 24.23 36.9659
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