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an unknown compound was analyzed and found to contain 75.0% carbon, 5.05% hydrogen,and 20.0% oxygen by mass. the molar mass of the compound was also determined experimentally and was found to be 240.28 g/mol. what is the empirical and molar formula of the compound?

Sagot :

Solution (Empirical Formula):

Step 1: Assume that the mass of a compound is 100 g.

[tex]\text{mass C = 75.0 g}[/tex]

[tex]\text{mass H = 5.05 g}[/tex]

[tex]\text{mass O = 20.0 g}[/tex]

Step 2: Calculate the number of moles of each element.

[tex]n \: \text{C = 75.0 g} × \frac{\text{1 mol}}{\text{12.01 g}} = \text{6.24 mol}[/tex]

[tex]n \: \text{H = 5.05 g} × \frac{\text{1 mol}}{\text{1.008 g}} = \text{5.01 mol}[/tex]

[tex]n \: \text{O = 20.0 g} × \frac{\text{1 mol}}{\text{16.00 g}} = \text{1.25 mol}[/tex]

Step 3: Represent an empirical formula.

[tex]\text{empirical formula} = \text{C}_{x}\text{H}_{y}\text{O}_{z}[/tex]

Step 4: Divide the number of moles of each element by the least number of moles.

[tex]x = \frac{\text{6.24 mol}}{\text{1.25 mol}} = 5[/tex]

[tex]y = \frac{\text{5.01 mol}}{\text{1.25 mol}} = 4[/tex]

[tex]z = \frac{\text{1.25 mol}}{\text{1.25 mol}} = 1[/tex]

Step 5: Write the empirical formula.

[tex]\boxed{\text{empirical formula} = \text{C}_{5}\text{H}_{4}\text{O}}[/tex]

Solution (Molecular Formula):

Step 1: Represent a molecular formula.

[tex]\text{molecular formula} = (\text{C}_{5}\text{H}_{4}\text{O})_{n}[/tex]

Step 2: Calculate the empirical mass.

empirical mass = (12.01 g/mol × 5) + (1.008 g/mol × 4) + (16.00 g/mol × 1)

empirical mass = 80.082 g/mol

Step 3: Divide the molar mass by the empirical mass.

[tex]n = \frac{\text{molar mass}}{\text{empirical mass}}[/tex]

[tex]n = \frac{\text{240.28 g/mol}}{\text{80.082 g/mol}}[/tex]

[tex]n = 3[/tex]

Step 4: Multiply the subscripts by the value of n to obtain the molecular formula.

[tex]\text{molecular formula} = (\text{C}_{5}\text{H}_{4}\text{O})_{3}[/tex]

[tex]\boxed{\text{molecular formula} = \text{C}_{15}\text{H}_{12}\text{O}_{3}}[/tex]

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