How many hydrogen atoms are in a 15.00 mg sample of glucose? (C6H1206)
To determine the number of hydrogen atoms in a given sample of glucose (C6H12O6), you need to consider the molecular formula of glucose and the molar mass of hydrogen.
Step 1: Determine the molar mass of glucose (C6H12O6)
The molecular formula of glucose (C6H12O6) indicates that it contains 6 carbon (C) atoms, 12 hydrogen (H) atoms, and 6 oxygen (O) atoms. The atomic masses are as follows:
- Carbon (C): 12.01 g/mol
- Hydrogen (H): 1.01 g/mol
- Oxygen (O): 16.00 g/mol
Calculate the molar mass of glucose by multiplying the number of atoms of each element in the formula by their respective atomic masses and summing them up:
Molar mass of glucose = (6 * C) + (12 * H) + (6 * O)
= (6 * 12.01) + (12 * 1.01) + (6 * 16.00)
= 72.06 + 12.12 + 96.00
= 180.18 g/mol
Step 2: Convert the mass of the sample to moles
Given that the sample mass is 15.00 mg (milligrams), we need to convert it to grams before calculating the number of moles.
1 g = 1000 mg
15.00 mg = 15.00 mg * (1 g/1000 mg)
= 0.015 g
Now, to convert grams to moles, divide the mass of the sample by the molar mass of glucose:
Number of moles = Mass of sample (g) / Molar mass of glucose (g/mol)
= 0.015 g / 180.18 g/mol
≈ 8.324 x 10^-5 mol
Step 3: Calculate the number of hydrogen atoms
Using the molecular formula of glucose, we know that there are 12 hydrogen (H) atoms in one mole of glucose.
Number of hydrogen atoms = Number of moles * Number of hydrogen atoms per mole
= 8.324 x 10^-5 mol * 12
= 0.0009989 mol
Since there are 0.0009989 moles of hydrogen atoms, we can convert this to the number of hydrogen atoms by multiplying by Avogadro's number (6.022 x 10^23 atoms/mol):
Number of hydrogen atoms = 0.0009989 mol * (6.022 x 10^23 atoms/mol)
≈ 6.02 x 10^20 hydrogen atoms
Therefore, in a 15.00 mg sample of glucose (C6H12O6), there are approximately 6.02 x 10^20 hydrogen atoms.