Solution (a)
Step 1: Assume that the mass of a compound is 100 g.
[tex]\text{mass C = 84 g}[/tex]
[tex]\text{mass H = 16 g}[/tex]
Step 2: Calculate the number of moles of each element.
[tex]n \: \text{C = 84 g} × \frac{\text{1 mol}}{\text{12 g}} = \text{7 mol}[/tex]
[tex]n \: \text{H = 16 g} × \frac{\text{1 mol}}{\text{1 g}} = \text{16 mol}[/tex]
Step 3: Represent an empirical formula.
[tex]\text{empirical formula} = \text{C}_{x}\text{H}_{y}[/tex]
Step 4: Divide the number of moles of each element by the least number of moles.
[tex]x = \frac{\text{7 mol}}{\text{7 mol}} = 1 × 7 = 7[/tex]
[tex]y = \frac{\text{16 mol}}{\text{7 mol}} = 2.286 × 7 = 16[/tex]
Step 5: Write the empirical formula.
[tex]\boxed{\text{empirical formula} = \text{C}_{7}\text{H}_{16}}[/tex]
Solution (b)
Step 1: Represent a molecular formula.
[tex]\text{molecular formula} = (\text{C}_{7}\text{H}_{16})_{n}[/tex]
Step 2: Calculate the empirical mass.
empirical mass = (12 g/mol × 7) + (1 g/mol × 16)
empirical mass = 100 g/mol
Step 3: Divide the molecular mass by the empirical mass.
[tex]n = \frac{\text{molecular mass}}{\text{empirical mass}}[/tex]
[tex]n = \frac{\text{100 g/mol}}{\text{100 g/mol}}[/tex]
[tex]n = 1[/tex]
Step 4: Multiply the subscripts by the value of n to obtain the molecular formula.
[tex]\text{molecular formula} = (\text{C}_{7}\text{H}_{16})_{1}[/tex]
[tex]\boxed{\text{molecular formula} = \text{C}_{7}\text{H}_{16}}[/tex]
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