Antimony forms 2 chlorides having widely different properties. One of the chlorides is a solid that melts at 73*C and contains 46.5% chlorine by mass. The other is a liquid that boils at 140*C and contains 59.3% chlorine by mass. Show how these results illustrate the low of multiple proportions .

Sb(1)Cl(1) and Sb(2)Cl(2) means the first Sb compound and the second Sb compound.

.....Sb(1)...Cl(1).......Sb(2)...Cl(2)
.....53.5%..46.5%........40.7%..59.3%

What we want to do first is to determine the mass Cl that combines with 1 g Sb.
That is 46.5 x (1/53.5) = 0.869 for #1
That is 59.3 x (1/40.7) = 1.457 for #2

The numbers for #1 and #2 should be in the ratio of small whole numbers. Let's see if they are.
0.869 for #1
1.457 for #2.

The easy way to find the ratio is to divide the smallest number by itself which assures us of getting 1.00 for that value. Then we divide the other number by the same small number. This gives us
0.869/0.869 = 1.00
1.457/0.869 = 1.67
which shows that 1.00 to something doesn't work (1.67 isn't a whole number). BUT we can try other small numbers. To do this the easy way is to just multiply each of the numbers above by 2,3,4,5,6 etc as a trial and error and see if those small whole numbers will work.
1.00 x 2 = 2.00
1.67 x 2 = 3.34
No again since 3.34 isn't a whole number. Try 3
1.00 x 3 = 3.00
1.00 x 1.67 = 5.01 which can be rounded to 5.00. (Why is it not EXACTLY 5.0? Because we have rounded above and used only three significant figures.
Bingo! small whole numbers; therefore, the formula for the first one is SbCl3 and the formula for the second one is SbCl5. PLEASE NOTE that the formulas were determined WITHOUT using the atomic mass of Sb or Cl. This is an important concept since atomic masses were not known years and years ago BUT the formulas could be determined anyway.

Ah, the law of multiple proportions, a fancy way of saying "variety is the spice of chemistry." Allow me to explain using the tale of two chlorides.

The solid chloride, let's call it Clowntonium Chloride (CCl₂), has a melting point of 73°C. It is composed of 46.5% chlorine by mass. Now, imagine you're at a circus, and there are two performers on stage. One is juggling flaming torches, and the other is balancing on a unicycle. Different acts, different properties, right? Similarly, CCl₂ displays its own unique properties due to its composition.

Now, let's take a look at the liquid chloride, we'll call it Boilium Chloride (BCl₃). This clownish concoction has a boiling point of 140°C and contains 59.3% chlorine by mass. Just like finding a hidden banana peel at your doorstep, BCl₃ surprises us with its differing properties compared to CCl₂.

Now, here's where the law of multiple proportions comes into play. When we compare the masses of chlorine in each chloride, we notice a distinct pattern. In CCl₂, the mass ratio of chlorine to other elements is 46.5%. In BCl₃, this ratio jumps to 59.3%. It's like seeing an acrobat jump higher and higher with each attempt!

This pattern suggests that there is a fixed ratio between the mass of chlorine and the other elements in each chloride. In simpler terms, these clowns have a specific recipe, and they're not messing around when it comes to their proportions. Each clown chloride showcases different properties due to this unique ratio.

So, my friend, the law of multiple proportions tells us that when elements combine to form compounds, they do so in fixed ratios. Just like a group of clowns with their own distinct acts, these chlorides demonstrate the principle that proportions matter in chemistry.

The law of multiple proportions states that when two elements combine to form two or more different compounds, the ratios of the masses of one element that combine with a fixed mass of the other element are in small whole-number ratios.

In the case of antimony and chlorine, the two chlorides formed have different properties, which indicates that they are different compounds.

Let's compare the mass percentages of chlorine in each compound:

1. The solid chloride has a melting point of 73*C and contains 46.5% chlorine by mass. This means that for every 100 grams of the compound, 46.5 grams are chlorine.

2. The liquid chloride has a boiling point of 140*C and contains 59.3% chlorine by mass. This means that for every 100 grams of the compound, 59.3 grams are chlorine.

Now, let's compare the ratios of chlorine to antimony in each compound:

1. Solid chloride: 46.5 grams chlorine / 53.5 grams antimony = 0.869
2. Liquid chloride: 59.3 grams chlorine / 40.7 grams antimony = 1.455

These ratios are not whole numbers, indicating that the two compounds are different and do not follow the law of multiple proportions.

Therefore, the results illustrate the law of multiple proportions by showing that when antimony combines with chlorine, it can form two different compounds with different ratios of masses, which do not follow small whole-number ratios.

To understand how these results illustrate the law of multiple proportions, let's first define what the law states. The law of multiple proportions, proposed by John Dalton, states that if two elements can combine to form more than one compound, the masses of one element that combine with a fixed mass of the other element will be in ratios of small whole numbers.

In this case, we have antimony (Sb) and chlorine (Cl) forming two chlorides that have different properties.

The first chloride is a solid that melts at 73°C and contains 46.5% chlorine by mass. Let's call this chloride A. Its composition can be represented as SbX, where X represents chlorine. Since it contains 46.5% chlorine by mass, we can say that for every 100 grams of chloride A, it contains 46.5 grams of chlorine.

The second chloride is a liquid that boils at 140°C and contains 59.3% chlorine by mass. Let's call this chloride B. Its composition can be represented as SbY, where Y represents chlorine. Since it contains 59.3% chlorine by mass, we can say that for every 100 grams of chloride B, it contains 59.3 grams of chlorine.

Now, let's compare the ratios of chlorine in both chlorides. The ratio of chlorine in chloride A to chlorine in chloride B can be calculated as follows:

(Ratio of chlorine in chloride A) / (Ratio of chlorine in chloride B) = (46.5 g Cl / 100 g chloride A) / (59.3 g Cl / 100 g chloride B)

Simplifying this expression:

(Ratio of chlorine in chloride A) / (Ratio of chlorine in chloride B) = (46.5 / 100) / (59.3 / 100) = (46.5 / 59.3) ≈ 0.784

The result is approximately 0.784, which is close to a 3:4 ratio (or 0.75) when expressed as a small whole number ratio. This suggests that the ratio of chlorine in chloride A to chloride B is approximately 3:4.

By applying the law of multiple proportions, we can conclude that antimony forms two different chlorides (chloride A and chloride B) with chlorine, where the ratio of chlorine in these compounds follows a small whole number ratio of approximately 3:4. This observation supports the law of multiple proportions.