An organic compound has the empirical formula \(CH_{2}\). If its molar mass is 42\(gmol^{-1}\), what is its molecular formula? (C = 12.0, H = 1.0)

Answer Details

The empirical formula of the organic compound is given as \(CH_{2}\), which means that the ratio of carbon to hydrogen atoms in the compound is 1:2. The molar mass of the compound is also given as 42\(gmol^{-1}\). To find the molecular formula, we need to determine the actual number of carbon and hydrogen atoms in the compound. Let's assume that the molecular formula of the compound is \(C_{x}H_{y}\). The molar mass of the compound can be calculated as follows: molar mass = (molar mass of carbon) x (number of carbon atoms) + (molar mass of hydrogen) x (number of hydrogen atoms) 42 = (12.0 g/mol) x (x) + (1.0 g/mol) x (y) Simplifying the equation, we get: 12x + y = 42 However, we also know that the ratio of carbon to hydrogen atoms in the compound is 1:2. This means that: x/y = 1/2 Multiplying both sides by y, we get: x = (1/2)y Substituting this value of x in the previous equation, we get: 12(1/2)y + y = 42 Simplifying the equation, we get: 18y = 42 y = 2.33 Since the number of atoms must be a whole number, we can round y to the nearest whole number, which is 2. This means that the molecular formula of the compound is \(C_{x}H_{2}\). Using the ratio of carbon to hydrogen atoms in the empirical formula, we know that x = 2. Therefore, the molecular formula of the compound is \(C_{2}H_{4}\). Hence, the answer is option A) \(C_{2}H_{4}\).