Question

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 

1. Which law of chemical combination is obeyed by the above experimental data? Give its statement.
2. Fill in the blanks in the following conversions: 
   (i)1 km = ...................... mm = ...................... pm 
   (ii) 1 mg = ...................... kg = ...................... ng 
   (iii) 1 mL = ...................... L = ...................... dm³

Answer 1

(a) If we fix the mass of dinitrogen at \(28 \;g\), then the masses of dioxygen that will combine with the fixed mass of dinitrogen are \(32 \;g\), \(64 \;g\), \(32 \;g\), and \(80 \;g\). The masses of dioxygen bear a whole number ratio of \(1:2:2:5\). 
Hence, the given experimental data obeys the law of multiple proportions. 
The law states that if two elements combine to form more than one compound, then the masses of one element that combines with the fixed mass of another element are in the ratio of small whole numbers.

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(b) (i) \(1\; km =\) \(1\; km × \frac{1000 m }{ 1 km} × \frac{100 cm }{ 1 m} × \frac{10 mm }{ 1 cm}\)
\(1 km = 10 ^6 mm\)
\(1\; km =\) \(1 km × \frac{1000 m }{ 1 km} ×\frac{ 1 pm }{ 10 ^{-12} m}\)
∴ \(1\; km = 10 ^{15} pm\)

Hence, \(1\; km\) = \(10^ 6 mm\) = \(10 ^15 \;pm\)

(ii) \(1\; mg = 1\; mg ×\) \(\frac{1\, g }{ 1000 \,mg} × \frac{1 \,kg }{ 1000 \,g}\)
\(\Rightarrow 1\; mg =\) \(10 ^{-6}\; kg\)
\(1\; mg = 1\; mg × \frac{1 g }{ 1000 mg} × \frac{1 ng }{ 10^{-9} g}\)
\(\Rightarrow 1 \;mg = 10^ 6\; ng\)
∴ \(1 \;mg = 10 ^{-6}\; kg = 10 ^6 \; ng\)

(iii) \(1\; mL = 1 \;mL × \frac{1 \,L }{ 1000 \,mL}\)
\(\Rightarrow 1 \;mL = 10 ^{-3}\; L\)
\(1\; mL = 1\; cm^3 = 1 \;cm^3 \frac{1 dm × 1 dm × 1 dm}{  10 cm × 10 cm × 10 cm}\)
\(\Rightarrow 1\; mL = 10 ^{-3} dm^3\)
\(\therefore\) \(1\; mL = 10 ^{-3}\; L = 10 ^{-3} \;dm^3\)