Understanding the Law of Reciprocal Proportions
The Law of Reciprocal Proportions (also known as the Law of Equivalent Proportions) is one of the fundamental laws of chemical combination. It states:
If two different elements combine separately with a third element to form compounds, then the ratio in which they do so will be the same or a simple multiple of the ratio in which they combine with each other.
Solving the Provided Problem
To verify this law, we need to find the ratio in which the metal (M) and oxygen (O) combine with hydrogen (H), and compare that to their direct combination ratio.
Step 1: Ratio of Metal (M) to Oxygen (O)
From (a): 0.46 g of Metal combines with $(0.77 - 0.46) = 0.31$ g of Oxygen.
- Ratio M:O = $0.46 / 0.31 \approx 1.48:1$
Step 2: Ratio of Metal (M) to Hydrogen (H)
From (b): 0.805 g of Metal displaces 760 cc of $H_2$. Since 22400 cc of $H_2$ weighs 2.016 g, 760 cc weighs $(2.016 \times 760) / 22400 \approx 0.0684$ g.
- Ratio M:H = $0.805 / 0.0684 \approx 11.77:1$
Step 3: Ratio of Oxygen (O) to Hydrogen (H)
From (c): 1.12 g of Oxygen forms 1.26 g of water. Mass of H = $1.26 - 1.12 = 0.14$ g.
- Ratio O:H = $1.12 / 0.14 = 8:1$
Step 4: Verification
According to the law, the ratio in which M and O combine with H is:
- $(M \text{ combined with } H) / (O \text{ combined with } H) = 11.77 / 8 \approx 1.47:1$
Comparing this to the direct combination ratio from Step 1 ($1.48:1$), we see that the ratios are effectively the same (allowing for slight experimental variance), thus proving the Law of Reciprocal Proportions.