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 ratios of small whole numbers. Let's analyze each given pair of substances to determine which one illustrates this law:
### Option (a) CO and [tex]\( CO_2 \)[/tex]
1. CO (Carbon Monoxide):
- Contains carbon (C) and oxygen (O).
- The ratio by mass of carbon to oxygen in CO is 12:16 (since the atomic masses of C and O are approximately 12 and 16, respectively).
2. [tex]\( CO_2 \)[/tex] (Carbon Dioxide):
- Contains carbon (C) and oxygen (O).
- The ratio by mass of carbon to oxygen in [tex]\( CO_2 \)[/tex] is 12:32 (one carbon atom to two oxygen atoms, so 12: 16*2 = 12:32).
We see that in CO and [tex]\( CO_2 \)[/tex], the ratio of the masses of oxygen that combine with a fixed mass of carbon are in the ratio of 16:32, which simplifies to 1:2. This is a small whole number ratio, illustrating the law of multiple proportions.
### Option (b) [tex]\( H_2O \)[/tex] and [tex]\( D_2O \)[/tex]
1. [tex]\( H_2O \)[/tex] (Water):
- Contains hydrogen (H) and oxygen (O).
2. [tex]\( D_2O \)[/tex] (Heavy Water):
- Contains deuterium (D) and oxygen (O).
- Deuterium is an isotope of hydrogen, not a different element.
Since deuterium is not a different element but an isotope of hydrogen, these two substances do not involve different elements combining in different ratios. Therefore, this pair does not illustrate the law of multiple proportions.
### Option (c) NaCl and NaBr
1. NaCl (Sodium Chloride):
- Contains sodium (Na) and chlorine (Cl).
2. NaBr (Sodium Bromide):
- Contains sodium (Na) and bromine (Br).
In this case, we have sodium combining with two different elements, chlorine and bromine, rather than the same two elements in different ratios. Thus, this pair does not illustrate the law of multiple proportions.
### Option (d) MgO and [tex]\( Mg(OH)_2 \)[/tex]
1. MgO (Magnesium Oxide):
- Contains magnesium (Mg) and oxygen (O).
2. [tex]\( Mg(OH)_2 \)[/tex] (Magnesium Hydroxide):
- Contains magnesium (Mg), oxygen (O), and hydrogen (H).
The composition of these compounds involves more than two elements in different combinations. Therefore, this does not strictly illustrate the law of multiple proportions, as it doesn't examine the ratio of just two elements combined in multiple ways.
### Conclusion
The pair of substances that best illustrates the law of multiple proportions is:
(a) CO and [tex]\( CO_2 \)[/tex]. This is because they show oxygen combining with a fixed amount of carbon in simple multiple ratios (1:1 and 2:1).
