Final answer:
The percent composition by mass of hydrogen in NH₄HCO₃ is calculated by dividing the total mass of hydrogen in one mole of the compound by the molar mass of the entire compound and then converting to a percentage. Our calculation yields a result of 6.39%, which does not match any of the provided options.
Step-by-step explanation:
To calculate the percent composition by mass of hydrogen in NH₄HCO₃, you must first determine the molar mass of the compound and the total mass of hydrogen in one mole of the compound. The molar mass of NH₄HCO₃ is the sum of the molar mass of nitrogen (N), four hydrogen atoms (H₄), one hydrogen atom (H), carbon (C), and three oxygen atoms (O₃).
The molar mass of each element is as follows: N (14.01 g/mol), H (1.01 g/mol for each atom), C (12.01 g/mol), and O (16.00 g/mol for each atom). Therefore, the molar mass of NH₄HCO₃ is:
1(14.01 g/mol) + 5(1.01 g/mol) + 1(12.01 g/mol) + 3(16.00 g/mol) = 79.07 g/mol.
Next, we calculate the total mass of hydrogen in one mole of NH₄HCO₃, which is 5 hydrogen atoms times 1.01 g/mol, equaling 5.05 g/mol.
The percent composition of hydrogen is then:
(5.05 g/mol H / 79.07 g/mol NH₄HCO₃) × 100% = 6.39%
Looking at the given options, none of them match our calculated result of 6.39%, so there might be a mistake in the options provided or in our calculation.