How many moles of silicon are present in a 140 g sample, given that the atomic mass of silicon is 28 g per mole?

Introduction / Context:
This numerical chemistry question tests the basic concept of the mole, which is central to stoichiometry and quantitative chemical calculations. It asks you to convert a given mass of an element into moles using its atomic mass.

Given Data / Assumptions:

• Mass of silicon sample = 140 g.
• Atomic mass of silicon = 28 g per mole.
• We assume pure silicon and standard atomic mass for calculations.
• We have to calculate the number of moles of silicon in the sample.

Concept / Approach:
The mole concept states that one mole of a substance contains a fixed number of particles (Avogadro number) and has a mass in grams equal to its molar or atomic mass. The relationship between mass, molar mass and moles is simple: moles = given mass / molar mass. By inserting the given mass of silicon and its molar mass into this formula, we can directly compute the number of moles in the sample.

Step-by-Step Solution:
1) Write the formula: number of moles = given mass (g) / molar mass (g per mole).2) For silicon, molar mass = 28 g per mole.3) Given mass of silicon sample = 140 g.4) Substitute into the formula: moles of silicon = 140 / 28.5) Perform the division: 140 / 28 = 5, so there are 5 moles of silicon in the sample.

Verification / Alternative check:
We can check the arithmetic by noting that 28 * 5 = 140, which confirms that 5 moles of silicon have a mass of 140 g. We could also set up a simple proportion: 28 g corresponds to 1 mole, so 140 g corresponds to x moles. Then x = 140 * 1 / 28 = 5 moles, which matches the earlier calculation.

Why Other Options Are Wrong:
10: This would correspond to a mass of 10 * 28 = 280 g, not the given 140 g.
28: This represents the atomic mass in grams per mole, not the number of moles for a 140 g sample.
140: This is the mass in grams, not the number of moles; confusing mass with moles is a common error.
4: This would correspond to a mass of 4 * 28 = 112 g, which is less than the given 140 g.

Common Pitfalls:
Students sometimes mix up the roles of molar mass and moles, treating the atomic mass number itself as the answer. Others may forget to divide the given mass by molar mass and instead multiply. To avoid these mistakes, always remember the simple relationship moles = mass / molar mass and double check units to ensure grams cancel correctly, leaving moles as the final unit.

Final Answer:
The 140 g sample of silicon contains 5 moles of silicon atoms.