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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.
Solution :
Step 1: Given Variables & Conversion to SI Units
To calculate the distance, we must ensure all physical quantities are in base SI units (meters and seconds). The given parameters are:
- Speed of light ($v$) = $3.0 \times 10^8 \, m \, s^{-1}$
- Time ($t$) = $2.00 \, ns$
Applying the unit conversion for nanoseconds ($1 \, ns = 10^{-9} \, s$):
$t = 2.00 \times 10^{-9} \, s$ [Definition of the SI prefix 'nano']
Step 2: Selecting the Governing Physical Principle
Since the speed of light in a vacuum is constant, we utilize the fundamental kinematic relationship for uniform motion:
$d = v \times t$ [Per the definition of velocity: $v = \frac{\Delta x}{\Delta t}$]
Step 3: Algebraic Calculation
Substituting the values into the governing equation:
$d = (3.0 \times 10^8 \, m \, s^{-1}) \times (2.00 \times 10^{-9} \, s)$
Perform multiplication of the coefficients and powers of 10 independently:
$d = (3.0 \times 2.00) \times (10^8 \times 10^{-9}) \, m$
$d = 6.0 \times 10^{-1} \, m$
$d = 0.60 \, m$
Visual Representation of Light Propagation
Step 4: Significant Figures Analysis
In the multiplication $(3.0 \times 10^8) \times (2.00 \times 10^{-9})$:
- The speed $3.0$ has 2 significant figures.
- The time $2.00$ has 3 significant figures.
- Per the rules of significant figures, the final result must be rounded to the least number of significant figures used in the calculation, which is 2.
Our result $0.60 \, m$ correctly maintains 2 significant figures.
Final Solution: The distance covered by light in 2.00 ns is 0.60 m.
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 = ...................... $dm^3$
- Q1.23(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 ($CuSO_4$)?
- Q1.8: 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.
- 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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