(b)
(i) 1 km = 1 km × \(\frac{1000\,m}{1 \,km}\times\frac{100\,cm}{1\,m}\times\frac{10\,mm}{1\,cm}\)
\(\therefore\) 1 km = 106 mm
1 km = 1 km × \(\frac{1000\,m}{1 \,km}\times\frac{1\,pm}{10^{-12}m}\)
\(\therefore\) 1 km = 1015 pm
Hence, 1 km = 106 mm = 1015 pm
(ii) 1 mg = 1 mg × \(\frac{1\,g}{1000\,mg}\times\frac{1\,kg}{1000\,g}\)
⇒ 1 mg = 10–6 kg
1 mg = 1 mg × \(\frac{1\,g}{1000\,mg}\times\frac{1\,ng}{10^{-9}\,g}\)
⇒ 1 mg = 106 ng
1 mg = 10–6 kg = 106 ng
(iii) 1 mL = 1 mL × \(\frac{1\,L}{1000\,mL}\)
⇒ 1 mL = 10–3 L
1 mL = 1 cm3 = 1 \(\frac{1\,dm\times1\,dm\times1\,dm}{10\,cm\times10\,cm\times10\,cm}\) cm3
⇒ 1 mL = 10–3 dm3
\(\therefore\) 1 mL = 10–3 L = 10–3 dm3
22. If the speed of light is 3.0 ×108 m s-1 , calculate the distance covered by light in 2.00 ns.
Answer:
According to the question:
Time taken to cover the distance
= 2.00 ns = 2.00 × 10–9 s
Speed of light = 3.0 × 108 ms–1
Distance travelled by light in 2.00 ns
= Speed of light × Time taken
= (3.0 × 108 ms –1) (2.00 × 10–9 s)
= 6.00 × 10–1 m
= 0.600 m
23. In a reaction
A + B2 → AB2
Identify the limiting reagent, if any, in the following reaction mixtures.
(i) 300 atoms of A + 200 molecules of B
(ii) 2 mol A + 3 mol B
(iii) 100 atoms of A + 100 molecules of B
(iv) 5 mol A + 2.5 mol B
(v) 2.5 mol A + 5 mol B
Answer:
A limiting reagent determines the extent of a reaction. It is the reactant which is the first to get consumed during a reaction, thereby causing the reaction to stop and limiting the amount of products formed.
(i) According to the given reaction, 1 atom of A reacts with 1 molecule of B.
Thus, 200 molecules of B will react with 200 atoms of A, thereby leaving 100 atoms of A unused. Hence, B is the limiting reagent.
(ii) According to the reaction, 1 mole of A reacts with 1 mole of B.
Thus, 2 mole of A will react with only 2 mole of B. As a result, 1 mole of A will not be consumed. Hence, A is the limiting reagent.
(iii) According to the given reaction, 1 atom of A combines with 1 molecule of B.
Thus, all 100 atoms of A will combine with all 100 molecules of B.
Hence, the mixture is stoichiometric where no limiting reagent is present.
(iv) 1 mole of atom A combines with 1 mole of molecule B.
Thus, 2.5 mole of B will combine with only 2.5 mole of A. As a result, 2.5 mole of A will be left as such.
Hence, B is the limiting reagent.
(v) According to the reaction, 1 mole of atom A combines with 1 mole of molecule B.
Thus, 2.5 mole of A will combine with only 2.5 mole of B and the remaining 2.5 mole of B will be left as such. Hence, A is the limiting reagent.
24. Dinitrogen and dihydrogen react with each other to produce ammonia according to the following chemical equation:
N2(g) + H2(g) → 2NH3(g)
(i) Calculate the mass of ammonia produced if 2.00 × 103 g dinitrogen reacts with 1.00 × 103 g of dihydrogen.
(ii) Will any of the two reactants remain unreacted?
(iii) If yes, which one and what would be its mass?
Answer:
(i) Balancing the given chemical equation,
N2(g) + 3H2(g) → 2NH3(g)
From the equation, 1 mole (28 g) of dinitrogen reacts with 3 mole (6 g) of dihydrogen to give 2 mole (34 g) of ammonia.
⇒ 2.00 × 103 g of dinitrogen will react with \(\frac{6\,g}{28\,g}\times2.00\times10^3 g\) dihydrogen
i.e., 2.00 × 103 g of dinitrogen will react with 428.6 g of dihydrogen.
Given,
Amount of dihydrogen = 1.00 × 103 g
Hence,
N2 is the limiting reagent.
\(\therefore\) 28 g of N2 produces 34 g of NH3.
Hence, mass of ammonia produced by 2000 g of N2 = \(\frac{34\,g}{28\,g}\times2000g\) = 2428.57 g
(ii) N2 is the limiting reagent and H2 is the excess reagent.
Hence, H2 will remain unreacted.
(iii) Mass of dihydrogen left unreacted = 1.00 × 103 g – 428.6 g
= 571.4 g
25. How are 0.50 mol Na2CO3 and 0.50 M Na2CO3 different?
Answer:
Molar mass of Na2CO3 = (2 × 23) + 12.00 + (3× 16) = 106 g mol–1
Now, 1 mole of Na2CO3 means 106 g of Na2CO3.
\(\therefore\) 0.5 mol of Na2CO3 = \(\frac{106\,g}{1\,mole}\times0.5\) mol Na2CO3
= 53 g Na2CO3
⇒ 0.50 M of Na2CO3 = 0.50 mol/L Na2CO3
Hence, 0.50 mol of Na2CO3 is present in 1 L of water or 53 g of Na2CO3 is present in 1 L of water.
26. If ten volumes of dihydrogen gas react with five volumes of dioxygen gas, how many volumes of water vapour would be produced?
Answer:
Reaction of dihydrogen with dioxygen can be written as:
\(2H_{2(g)}+O_{2(g)}\longrightarrow 2H_2O_{(g)}\)
Now, two volumes of dihydrogen react with one volume of dihydrogen to produce two volumes of water vapour.
Hence, ten volumes of dihydrogen will react with five volumes of dioxygen to produce ten volumes of water vapour.
27. Convert the following into basic units:
(i) 28.7 pm
(ii) 15.15 pm
(iii) 25365 mg
Answer:
(i) 28.7 pm:
1 pm = 10–12 m
\(\therefore\) 28.7 pm = 28.7 × 10–12 m
= 2.87 × 10–11 m
(ii) 15.15 pm:
1 pm = 10–12 m
\(\therefore\) 15.15 pm = 15.15 × 10–12 m
= 1.515 × 10–12 m
(iii) 25365 mg:
1 mg = 10–3 g
25365 mg = 2.5365 × 104 × 10–3 g
Since,
1 g = 10–3 kg
2.5365 × 101 g = 2.5365 × 10–1 × 10–3 kg
\(\therefore\) 25365 mg = 2.5365 × 10–2 kg