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The following data are obtained when dinitrogen and dioxygen react together to form different compounds :
\(\begin{array}{cc} \text{Mass of dinitrogen Mass of dioxygen} & \text{Mass of dinitrogen Mass of dioxygen}\\ \text { (i) } 14 \mathrm{~g} & 16 \mathrm{~g} \\ \text { (ii) } 14 \mathrm{~g} & 32 \mathrm{~g} \\ \text { (iii) } 28 \mathrm{~g} & 32 \mathrm{~g} \\ \text { (iv) } 28 \mathrm{~g} & 80 \mathrm{~g}\end{array}\)
(a) Which law of chemical combination is obeyed by the above experimental data?
Give its statement.
(b) Fill in the blanks in the following conversions:
(i) \(1 \mathrm{~km}=\)\(\mathrm{mm}=\ldots \ldots \ldots . \mathrm{pm}\)
(ii) \(1 \mathrm{mg}=\) \(\mathbf{k g}=\ldots \ldots . \ldots . \ldots\)ng
(iii) \(1 \mathrm{~mL}=\) \(\mathbf{L}=\) \(\mathrm{dm}^3\)
\(\begin{array}{cc} \text{Mass of dinitrogen Mass of dioxygen} & \text{Mass of dinitrogen Mass of dioxygen}\\ \text { (i) } 14 \mathrm{~g} & 16 \mathrm{~g} \\ \text { (ii) } 14 \mathrm{~g} & 32 \mathrm{~g} \\ \text { (iii) } 28 \mathrm{~g} & 32 \mathrm{~g} \\ \text { (iv) } 28 \mathrm{~g} & 80 \mathrm{~g}\end{array}\)
(a) Which law of chemical combination is obeyed by the above experimental data?
Give its statement.
(b) Fill in the blanks in the following conversions:
(i) \(1 \mathrm{~km}=\)\(\mathrm{mm}=\ldots \ldots \ldots . \mathrm{pm}\)
(ii) \(1 \mathrm{mg}=\) \(\mathbf{k g}=\ldots \ldots . \ldots . \ldots\)ng
(iii) \(1 \mathrm{~mL}=\) \(\mathbf{L}=\) \(\mathrm{dm}^3\)
Solution:
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Verified Answer
(a) Fixing the mass of dinitrogen as \(28 \mathrm{~g}\), masses of dioxygen combined will be \(32,64,32\) and \(80 \mathrm{~g}\) in the given four oxides. These are in the ratio \(1: 2: 1: 2.5\) or \(2: 4: 2: 5\) which is a simple whole number ratio. Hence, the given data obey the law of multiple proportions.
Definition - When two elements combine to form two or more chemical compounds, then the masses of one of the elements which combine with a fixed mass of the other, bear a simple ratio to one another.
(b) (i) \(1 \mathrm{~km}=1 \mathrm{~km} \times \frac{1000 \mathrm{~m}}{1 \mathrm{~km}} \times \frac{10 \mathrm{~mm}}{1 \mathrm{~cm}}\)
\(\begin{aligned}
&=\frac{100 \mathrm{~cm}}{1 \mathrm{~m}} \times 10^6 \mathrm{~mm} \\
1 \mathrm{~km} &=1 \mathrm{~km} \times \frac{1000 \mathrm{~m}}{1 \mathrm{~km}} \times \frac{1 \mathrm{pm}}{10^{-12} \mathrm{~m}} \\
&=10^{15} \mathrm{pm}
\end{aligned}\)
(ii) \(1 \mathrm{mg}=1 \mathrm{mg} \times \frac{1 \mathrm{~g}}{1000 \mathrm{mg}} \times \frac{1 \mathrm{~kg}}{1000 \mathrm{~g}}\)
\(\begin{aligned}
&=10^{-6} \mathrm{~kg} \\
1 \mathrm{mg} &=1 \mathrm{mg} \times \frac{1 \mathrm{~g}}{1000 \mathrm{mg}} \times \frac{1 \mathrm{ng}}{10^{-9} \mathrm{~g}}=10^6 \mathrm{ng}
\end{aligned}\)
(iii) \(1 \mathrm{~mL}=1 \mathrm{~mL} \times \frac{1 \mathrm{~L}}{1000 \mathrm{~mL}}=10^{-3} \mathrm{~L}\)
\(1 \mathrm{~mL}=1 \mathrm{~cm}^3=\frac{1 \mathrm{~cm}^3 \times 1 \mathrm{dm} \times 1 \mathrm{dm} \times 1 \mathrm{dm}}{10 \mathrm{~cm} \times 10 \mathrm{~cm} \times 10 \mathrm{~cm}}\)
\(=10^{-3} \mathrm{dm}^3\)
Definition - When two elements combine to form two or more chemical compounds, then the masses of one of the elements which combine with a fixed mass of the other, bear a simple ratio to one another.
(b) (i) \(1 \mathrm{~km}=1 \mathrm{~km} \times \frac{1000 \mathrm{~m}}{1 \mathrm{~km}} \times \frac{10 \mathrm{~mm}}{1 \mathrm{~cm}}\)
\(\begin{aligned}
&=\frac{100 \mathrm{~cm}}{1 \mathrm{~m}} \times 10^6 \mathrm{~mm} \\
1 \mathrm{~km} &=1 \mathrm{~km} \times \frac{1000 \mathrm{~m}}{1 \mathrm{~km}} \times \frac{1 \mathrm{pm}}{10^{-12} \mathrm{~m}} \\
&=10^{15} \mathrm{pm}
\end{aligned}\)
(ii) \(1 \mathrm{mg}=1 \mathrm{mg} \times \frac{1 \mathrm{~g}}{1000 \mathrm{mg}} \times \frac{1 \mathrm{~kg}}{1000 \mathrm{~g}}\)
\(\begin{aligned}
&=10^{-6} \mathrm{~kg} \\
1 \mathrm{mg} &=1 \mathrm{mg} \times \frac{1 \mathrm{~g}}{1000 \mathrm{mg}} \times \frac{1 \mathrm{ng}}{10^{-9} \mathrm{~g}}=10^6 \mathrm{ng}
\end{aligned}\)
(iii) \(1 \mathrm{~mL}=1 \mathrm{~mL} \times \frac{1 \mathrm{~L}}{1000 \mathrm{~mL}}=10^{-3} \mathrm{~L}\)
\(1 \mathrm{~mL}=1 \mathrm{~cm}^3=\frac{1 \mathrm{~cm}^3 \times 1 \mathrm{dm} \times 1 \mathrm{dm} \times 1 \mathrm{dm}}{10 \mathrm{~cm} \times 10 \mathrm{~cm} \times 10 \mathrm{~cm}}\)
\(=10^{-3} \mathrm{dm}^3\)
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