Two elements, R and Q, combine to form two binary compounds. In the first compound, 9.50 g of R combines with 3.00 g of Q. In the second compound, 7.00 g of R combines with 4.50 g of Q. Show that these data are in accord with the law of multiple proportions. If the formula of the second compound is RQ, what is the formula of the first compound?
To determine whether these data are in accord with the law of multiple proportions, we need to compare the ratios of the masses of R to Q in both compounds. According to the law of multiple proportions, when different elements combine to form different compounds, the mass ratios of the elements in the compounds will be a small whole number ratio.
Let's start by calculating the ratio of the mass of R to Q in the first compound:
Mass of R in the first compound = 9.50 g
Mass of Q in the first compound = 3.00 g
Ratio of R to Q in the first compound = (Mass of R / Mass of Q) = (9.50 g / 3.00 g)
Now, calculate the ratio of the mass of R to Q in the second compound:
Mass of R in the second compound = 7.00 g
Mass of Q in the second compound = 4.50 g
Ratio of R to Q in the second compound = (Mass of R / Mass of Q) = (7.00 g / 4.50 g)
Comparing the two ratios, we have:
Ratio in the first compound = (9.50 g / 3.00 g)
Ratio in the second compound = (7.00 g / 4.50 g)
Simplifying the ratios:
Ratio in the first compound = 3.17
Ratio in the second compound = 1.56
Since the ratios are not the same or a small whole number, we can conclude that these data are NOT in accord with the law of multiple proportions.
However, we are given that the formula of the second compound is RQ. Now, to find the formula of the first compound, we need to determine the ratio that would have resulted in small whole numbers.
Taking the ratio of R to Q in the first compound (3.17), we can try simplifying it by multiplying both the numerator and the denominator by the same number to get a smaller ratio:
Multiplying the ratio by 2:
(9.50 g / 3.00 g) * 2 = 19.00 g / 6.00 g
Simplifying this gives us a ratio of 3.17, which does not result in small whole numbers. Let's try a different number:
Multiplying the ratio by 3:
(9.50 g / 3.00 g) * 3 = 28.50 g / 9.00 g
Now we have a ratio of 3.17, which can be approximated as 3. This gives us a 3:1 ratio of R to Q, matching the small whole number ratio.
Therefore, based on the law of multiple proportions, the formula of the first compound can be represented as R3Q.