A cube of gold that is 1.00 cm on a side has a mass of 19.3 g. A single gold atom has a mass of 197.0 u. (c) What assumptions did you make in arriving at your answer for part (b)?

Verified step by step guidance

To solve this problem, we need to consider the assumptions made when calculating the number of gold atoms in the cube. Let's break down the assumptions step by step.

Assumption 1: The density of gold is uniform throughout the cube. This means that the mass of gold is evenly distributed, allowing us to use the given mass and volume to calculate the number of atoms.

Assumption 2: The cube is composed entirely of gold atoms. We assume there are no impurities or other elements present in the cube, which simplifies the calculation to only consider gold atoms.

Assumption 3: The mass of a single gold atom is constant and accurately represented by 197.0 u (atomic mass units). This allows us to use this value to determine the number of atoms by dividing the total mass of the cube by the mass of a single atom.

Assumption 4: The cube is a perfect geometric shape with precise dimensions of 1.00 cm on each side. This ensures that the volume calculation is straightforward and accurate, which is crucial for determining the number of atoms based on density.

Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Density

Density is defined as mass per unit volume and is a critical property of materials. For gold, the density can be calculated using the mass of the cube and its volume, which is derived from its dimensions. Understanding density helps in determining how many atoms are present in a given mass of a substance, which is essential for calculations involving atomic mass and moles.

Molar Mass and Avogadro's Number

Molar mass is the mass of one mole of a substance, typically expressed in grams per mole. For gold, the molar mass is approximately 197.0 g/mol, which indicates how many grams correspond to one mole of gold atoms. Avogadro's number (6.022 x 10²³) relates the number of atoms in a mole to the mass, allowing for conversions between atomic scale and macroscopic measurements.

Assumptions in Calculations

When performing calculations in chemistry, certain assumptions are often made to simplify the problem. For instance, one might assume that the gold cube is a perfect solid without any impurities or voids, and that the mass of a single gold atom is constant. These assumptions are crucial for deriving accurate results, but they can also introduce errors if the real-world conditions deviate from these idealized scenarios.

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