A metal X forms two different chlorides. If 12.7g of chloride A and 16.3g of chloride B contain 7.1g and 10.7g of chlorine respectively, show that the figures agrees with the law of multiple proportions. Write their formulae
From Google:
Law of Multiple Proportions. John Dalton (1803) stated, "'When two elements combine with each other to form two or more compounds, the ratios of the masses of one element that combines with the fixed mass of the other are simple whole numbers'.Jun 5, 2019
So we have the two chlorides that are XyClw and XyClz. We need to show that the ratio w to z are small whole numbers.
Compound A = 12.7 g X and 7.1 g Cl so X must be 5.56 g
Compound B = 16.3 g X and 10.7 g Cl so X must 5.56 g.
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7.1 x (12.7/16.3) = 5.53 g Cl for each g X
10.7 x (12/7/16.3) = 8.34 g Cl for each g X so what is the ratio of the two Cl numbers: The easy way to do this is to divide both numbers by the smaller one. That is
5.53/5.53 = 1.00
8.34/5.53 = 1.508. If we round that 1.508 to 1.50 you can see that 1.0 to 1.5 is actually 2 to 3 and those are small whole numbers. Within experimental error the law of multiple proportions is proved.
The compounds must be XCl2 and XCl3. The problem doesn't ask but I worked out the formula and X is Fe so FeCl2 and FeCl3. are the compounds.
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What's the chemical formula
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Well, well, well! Looks like we have some chemists in the house, huh?
Let's break it down, my chemical connoisseur friend! The law of multiple proportions states that when two elements combine to form different compounds, the mass ratios of one element that combine with a fixed mass of the other element can be expressed as small whole numbers.
So, let's do some number crunching, shall we? The masses of chlorine in chlorides A and B are 7.1g and 10.7g, respectively. We can compare these masses to see if they follow the law of multiple proportions.
If we take the ratio of the masses of chlorine in chloride A and B, we get:
7.1g / 10.7g ≈ 0.663
Hmm, that's not a whole number, is it? But don't lose hope just yet! Let's simplify these numbers by dividing them by the smallest common factor, in this case, 0.663:
0.663 / 0.663 ≈ 1
1 / 0.663 ≈ 1.51
Ah, now we're talking! We have simplified the ratios to approximately 1:1.51. These ratios can be expressed as small whole numbers by multiplying them with a common factor:
1 x 2 ≈ 2
1.51 x 2 ≈ 3
So, it seems like the ratios of the masses of chlorine in chlorides A and B can be expressed as 2:3, which are indeed small whole numbers. This validates the law of multiple proportions!
Now, onto their formulae! Since chlorine is a halogen and usually has a charge of -1 in compounds, we can determine the formulae by looking at the ratio of chlorine to the metal X in each chloride.
In chloride A, we have a 1:2 ratio of chlorine to metal X. Therefore, the formula for chloride A could be XCl2.
In chloride B, we have a 1:3 ratio of chlorine to metal X. This suggests the formula for chloride B could be XCl3.
Keep in mind that other factors, such as charges of the metal X, need to be considered as well. This is just a superficial analysis based on the given information.
Stay curious, my chemist friend, and keep those reactions rockin'!
To show that the figures agree with the law of multiple proportions, we need to compare the ratios of the masses of chlorine in both chlorides.
For chloride A:
Mass of Chlorine = 7.1 g
Mass of Chloride A = 12.7 g
For chloride B:
Mass of Chlorine = 10.7 g
Mass of Chloride B = 16.3 g
Now, let's calculate the ratio of chlorine to chloride for each compound:
Chloride A ratio:
Chlorine/Chloride A = 7.1 g/12.7 g = 0.5591
Chloride B ratio:
Chlorine/Chloride B = 10.7 g/16.3 g = 0.6564
If these two ratios can be expressed as a simple ratio of whole numbers, then it supports the law of multiple proportions.
To find the simplest ratio, we can divide both ratios by the smallest value, which is 0.5591:
Chloride A ratio / Chloride A ratio = 0.5591 / 0.5591 = 1
Chloride B ratio / Chloride A ratio = 0.6564 / 0.5591 = 1.172
When rounded to the nearest whole number, the ratio is approximately 1:1 for chloride A and 1:1 for chloride B.
Based on these ratios, we can write their formulae:
Chloride A: XCl (where X represents the metal)
Chloride B: XCl2