How is the mass percent of elements in a compound different for a 1.0-g sample versus a 100.-g sample versus a 1-mole sample of the compound?

The mass percent of an element in a compound is calculated using the following formula: \[ \text{Mass Percent} = \frac{\text{Mass of Element}}{\text{Total Mass of Compound}} * 100\]

We will now use this formula to compare the mass percent of an element in a compound for a 1.0-g, a 100-g, and a 1-mole sample of the compound. Note that, for any specific compound, the ratio \(\frac{\text{Mass of Element}}{\text{Total Mass of Compound}}\) will remain constant irrespective of the sample size. This is because the composition of a compound is defined by the mole ratio of its constituent elements.

Let's assume the given compound has a mass ratio of element A being x and element B being (1-x). So, in a 1.0-g sample: Mass of element A = 1.0 g * x Mass of element B = 1.0 g * (1-x) Calculating the mass percent of element A: \( \text{Mass Percent of A} = \frac{1.0 * x}{1.0} * 100 = 100x \% \)

In a 100-g sample, the mass of elements will be proportionate to their mass ratio in the compound: Mass of element A = 100 g * x Mass of element B = 100 g * (1-x) Calculating the mass percent of element A: \( \text{Mass Percent of A} = \frac{100 * x}{100} * 100 = 100x \% \)

In a 1-mole sample, first, we need to find the molar mass of the compound, which is the sum of the molar masses of its constituent elements. Let the molar masses for elements A and B be M_A and M_B, respectively. Molar Mass of the compound = (M_A * x) + (M_B * (1-x)) In a 1-mole sample: Mass of element A = (M_A * x) * 1 mol Mass of element B = (M_B * (1-x)) * 1 mol Calculating the mass percent of element A: \( \text{Mass Percent of A} = \frac{(M_A * x)}{[(M_A * x) + (M_B * (1-x))]} * 100 \) \( \text{Mass Percent of A} = \frac{(M_A * x)}{(M_A * x) + (M_B * (1-x))} * 100 \) Since the molar ratio of A and B is constant for the given compound, their mass ratio will also be constant, regardless of the number of moles. This means the mass percent of A, and in turn, B, will remain constant for any amount of the compound. #Conclusion# The mass percent of elements in a compound is the same for a 1.0-g sample, a 100-g sample, and a 1-mole sample of the compound. This is because mass percent is a property of the compound's composition and is independent of the sample size or the number of moles.