Histamine is a substance that is released by cells in response to injury, infections, stings and materials that cause allergic responses, such as pollen. Histamine causes dilation of blood vessels and swelling due to accumulation of fluid in the tissues. People sometimes take antihistamine drugs to counteract the effects of histamine. A sample of histamine having a mass of 385 mg is composed of 208 mg of carbon, 31 mg of hydrogen and 146 mg of nitrogen. The molar mass of histamine is 111 g/mol. What is the molecular formula for histamine?

C₅H₉N₃

Explanation:

First, you need to find the empirical formula of the compound (histamine).

To find the empirical formula convert all the data given in mass units (miligrams) into mole numbers.

You do that by using the formula: number of moles = mass in grams / atomic mass.

To find the mass in grams divide the mass in miligrams by 1,000.

Build a table:

Element mass (g) atomic mass (g/mol) number of moles (mol)

C 0.208 12.011 0.0173

H 0.031 1.008 0.0307

N 0.146 14.007 0.0104

Now, find the ratio C:H:N, for which you divide every number of moles by the smallest number of moles: 0.0104:

C: 0.0173 / 0.0104 = 1.665 H: 0.0307 / 0.0104 = 2.957 N: 0.0104 / 0.104 = 1.002

You must find a multiple that yields 1.665 to a reasonably close integer.

Muliply every amount by 3:

C: 1.665 (3) = 4.995 ≈ 5 H: 2.957 (3) = 8.871 ≈ 9 N: 1.002 (3) = 3.007 ≈ 3

Hence, the empirical formula is C₅H₉N₃.

Now, find the mass of the empirical formula:

5 (12.011 g/mol) + 9 (1.008 g/mol) + 3 (14.007 g/mol) = 111.148 g/mol ≈ 111 g/mol.

Since the mass of the empirical formula is the same of the molecular formula, both formulae are the same.

Therefore, the answer is: C₅H₉N₃ ← molecular formula