Question

A sample of C3H8 has 6.72 x 10^24 H atoms.
What is the total mass of the sample?

Answer 1

To find the total mass of a C3H8 sample with 6.72 × 1024 H atoms, we calculate the number of moles of C3H8 and multiply it by the compound's molar mass to get approximately 61.5 grams.

Step-by-step explanation:

The question asks us to calculate the total mass of a sample of C3H8 (propane) given the number of H atoms in the sample. First, we determine the number of moles of H atoms by dividing the given number of H atoms by Avogadro's number (6.022 × 1023 atoms per mole), then use the molar ratio of H to C3H8 to find the moles of C3H8. We can then multiply the moles of C3H8 by its molar mass (the sum of the mass of 3 carbon atoms and 8 hydrogen atoms) to find the total mass of the sample.

Using the provided information, C3H8 has 8 H atoms per molecule. Therefore, if there are 6.72 × 1024 H atoms, that constitutes 6.72 × 1024 ÷ 8 = 8.4 × 1023 molecules of C3H8. One mole of C3H8 contains 6.022 × 1023 molecules, so the sample contains 8.4 × 1023 ÷ (6.022 × 1023) ≈ 1.395 moles of C3H8.

Next, we calculate the molar mass of C3H8: (3 × 12.011 amu for C) + (8 × 1.0079 amu for H) ≈ 44.1 g/mol. The total mass of the sample is therefore 1.395 moles × 44.1 g/mol = 61.5 grams.

Answer 2

The answer is 492.8 g


1. Calculate a number of moles of a sample.
2. Calculate a molar mass of C3H8.
3. Calculate a mass of the sample.

1. Avogadro's number is the number of units (atoms, molecules) in 1 mole of substance: 6.023 × 10²³ units per 1 mole

6.023 × 10²³ atoms : 1 mol =6.72 × 10²⁴ atoms : n

n = 6.72 × 10²⁴ atoms * 1 mol : 6.023 × 10²³ atoms = 1.12 × 10 mol = 11.2 mol

2. Molar mass (Mr) of C3H8 is sum of atomic masses (Ar) of its elements:

Ar(C) = 12 g/mol

Ar(H) = 1 g/mol

Mr(C3H8) = 3 * Ar(C) + 8 * Ar(H) = 3 * 12 + 8 * 1 = 36 + 8 = 44 g/mol

3. Mass (m) of a sample is number of moles (n) multiplied by molar mass (Mr) of C3H8:

m = n * Mr = 11.2 mol * 44 g/mol = 492.8 g