Final answer:
To find the formula of compound X, analyze the given mass ratios of carbon to hydrogen and use the law of multiple proportions to get whole-number ratios. Divide the given mass of each element by the smaller number to find the ratio of moles and simplify to whole numbers. From there, we can derive the empirical formula.
Step-by-step explanation:
To determine the formula of compound X, we begin by analyzing the given mass ratios of carbon to hydrogen. The ratios are 14.13 g of carbon to 2.96 g of hydrogen and 19.91 g of carbon to 3.34 g of hydrogen. According to the law of multiple proportions, if two elements form more than one compound, the mass ratios of the elements in the compounds can express a ratio of small whole numbers. In this case, if we take the ratios of carbon to hydrogen of both mass ratios, we can simplify them to a whole-number ratio.
For the first mass ratio (14.13 g C to 2.96 g H), we divide each by the smallest number (2.96 g):
Carbon: 14.13 ÷ 2.96 = 4.77
Hydrogen: 2.96 ÷ 2.96 = 1
For the second mass ratio (19.91 g C to 3.34 g H), we also divide each by the smallest number (3.34 g):
Carbon: 19.91 ÷ 3.34 = 5.96
Hydrogen: 3.34 ÷ 3.34 = 1
These results suggest the compounds are different. The subscripts for carbon and hydrogen should be whole numbers. After deriving this basic ratio, we can determine the empirical formula by comparing the ratios of moles of carbon to moles of hydrogen, which should also give us small whole numbers. The final empirical formula for a compound can be obtained once we adjust these numbers to the smallest whole numbers.
As an example, if we have a compound Co.142H0.284, to get a simpler whole-number ratio, we would divide each subscript by the smaller subscript (0.142), giving us the empirical formula C1H2. However, without information about the molecular weight or additional details, we can only determine the empirical formula and not the molecular formula.