Question

Two elements, and , combine to form two binary compounds. In the first compound, 23.3 g of combines with 3.00 g of . In the second compound, 7.00 g of combines with 4.50 g of . Show that these data are in accord with the law of multiple proportions. If the formula of the second compound is , what is the formula of the first compound?

Compound I:

Answer 1

the formula of the first compound is A2.08B0.78, which we can simplify to A2B.

Step-by-step explanation:

To determine if these data are in accord with the law of multiple proportions, we need to compare the ratios of the masses of one element to the fixed mass of the other element in each compound:

For the first compound:

mass ratio of A:B = 23.3 g / 3.00 g = 7.77

For the second compound:

mass ratio of A:B = 7.00 g / 4.50 g = 1.56

If the ratios of the masses of one element to the fixed mass of the other element are simple whole number ratios, then the data are in accordance with the law of multiple proportions. We can see that the ratios calculated above are not simple whole numbers, so the law of multiple proportions does not appear to be satisfied.

To determine the formula of the first compound, we can assume that the formula is AxBy, where x and y are the subscripts that we need to determine. We can set up a system of equations based on the mass ratios:

23.3 g of A combines with 3.00 g of B:

(23.3 g A) / (x mol A) = (3.00 g B) / (y mol B)

7.77 mol A / mol B = (23.3 g A) / (3.00 g B)

7.77 (y/x) = 23.3 / 3.00

y/x = 3/7.77

7.77 g of A combines with 1.00 g of B:

(7.77 g A) / (x mol A) = (1.00 g B) / (y mol B)

1.56 mol A / mol B = (7.77 g A) / (1.00 g B)

1.56 (y/x) = 7.77 / 1.00

y/x = 5/2

Now we have two equations for y/x that we can solve simultaneously:

y/x = 3/7.77

y/x = 5/2

Setting these two expressions equal to each other, we get:

3/7.77 = 5/2x

x = 2.08

Now that we know x, we can use one of the equations for y/x to solve for y:

y/x = 3/7.77

y/2.08 = 3/7.77

y = 0.78

Therefore, the formula of the first compound is A2.08B0.78, which we can simplify to A2B.

Answer 2

To show that the data are in accord with the law of multiple proportions, we need to determine the ratios of the masses of to in each compound and see if they are in small whole number ratios.

For the first compound:

Mass of : 23.3 g

Mass of : 3.00 g

Ratio of masses: 23.3 g / 3.00 g = 7.77

For the second compound:

Mass of : 7.00 g

Mass of : 4.50 g

Ratio of masses: 7.00 g / 4.50 g = 1.56

These ratios are not in small whole number ratios, which indicates that the formula for the first compound cannot be determined by simple inspection. However, the fact that the ratios are different is in accord with the law of multiple proportions, which states that when two elements form more than one compound, the masses of one element that combine with a fixed mass of the other element are in small whole number ratios.

Let's assume that the formula for the second compound is . This means that the ratio of to in the compound is 2:1. From the data provided, we know that there are 4.50 g of in the compound, which means there must be twice as much in the compound. Therefore, there are 9.00 g of in the compound.

To determine the formula of the first compound, we can subtract the mass of from the total mass of the compound:

Mass of : 23.3 g

Mass of : 3.00 g

Total mass: 26.3 g

Mass of : 26.3 g - 3.00 g = 23.3 g

So the ratio of to in the first compound is:

Mass of : 23.3 g

Mass of : 3.00 g

Ratio of masses: 23.3 g / 3.00 g = 7.77

We can divide this ratio by the ratio of to in the second compound to get the ratio of the two compounds:

Ratio of first compound: 7.77

Ratio of second compound: 2.00

The ratio of the two compounds is not a small whole number ratio, which suggests that the formula for the first compound is more complex than a simple binary compound. Therefore, we cannot determine the formula of the first compound from the data provided.