The law of multiple proportions states that when two elements combine to form more than one compound, the masses of one element that combine with a fixed mass of the other element are in simple whole number ratios.
NO and NO\(_2\): Nitrogen combines with oxygen to form NO and NO\(_2\), and the ratio of oxygen in these two compounds follows the law of multiple proportions.
CuO and Cu\(_2\)O: Copper combines with oxygen to form these two compounds, and the mass of oxygen in CuO and Cu\(_2\)O follows the law of multiple proportions.
FeO and Fe\(_2\)O\(_3\): Iron combines with oxygen in different proportions to form FeO and Fe\(_2\)O\(_3\), which also follows the law of multiple proportions.
H\(_2\)O and H\(_2\)S: Water and hydrogen sulfide do not illustrate the law of multiple proportions because both compounds contain hydrogen in the same amount (2 atoms of H) but different non-metals (oxygen and sulfur), which doesn’t follow the rule of simple whole number ratios of mass.
Thus, H\(_2\)O and H\(_2\)S do not illustrate the law of multiple proportions.
The correct option is (D) : H2O and N2S
The Law of Multiple Proportions states that if two elements combine to form more than one compound, the masses of one element that combine with a fixed mass of the other element are in the ratio of small whole numbers.
Let's analyze the options:
1. NO and NO₂: Same elements (N and O), different ratios → ✔️ illustrate the law
2. CuO and Cu₂O: Same elements (Cu and O), different ratios → ✔️ illustrate the law
3. FeO and Fe₂O₃: Same elements (Fe and O), different ratios → ✔️ illustrate the law
4. H₂O and N₂S: Different elements → ✖️ do not illustrate the law of multiple proportions
5. NO and N₂O: Same elements (N and O), different ratios → ✔️ illustrate the law
✅ Correct answer: H₂O and N₂S – different elements, so the law of multiple proportions does not apply.
If $ X = A \times B $, $ A = \begin{bmatrix} 1 & 2 \\-1 & 1 \end{bmatrix} $, $ B = \begin{bmatrix} 3 & 6 \\5 & 7 \end{bmatrix} $, find $ x_1 + x_2 $.