On a hypothetical relative mass scale, the average mass of the atoms of element A was assigned a value of 64.00 gigs. The average mass of the atoms of element B is 36.40% that of element A, and the average mass of the atoms of element C is 6.43 times the mass of A. What is the average mass of the atoms of element C rounded to the nearest 0.01 gigs?
A) 34.98 gigs
B) 439.70 gigs
C) 87.67 gigs
D) 411.52 gigs
The correct answer and explanation is :
To determine the average mass of the atoms of element C, let’s follow these steps:
Step 1: Identify the given values
- The mass of element A is 64.00 gigs.
- The mass of element B is 36.40% of element A: [
\text{Mass of B} = 0.3640 \times 64.00
] [
= 23.30 \text{ gigs}
] - The mass of element C is 6.43 times that of element A: [
\text{Mass of C} = 6.43 \times 64.00
] [
= 411.52 \text{ gigs}
]
Step 2: Round the Answer
- The calculated mass of element C is 411.52 gigs, which is already rounded to the nearest 0.01 gigs.
Step 3: Select the Correct Answer
The correct option is:
D) 411.52 gigs
Explanation:
The problem involves a hypothetical relative mass scale where different elements have their atomic masses assigned relative to each other. Element A serves as the reference with a mass of 64.00 gigs. The mass of element B is calculated by taking 36.40% of element A, giving 23.30 gigs, though this value isn’t necessary for solving for element C. The mass of element C is found by multiplying the mass of element A by 6.43, yielding 411.52 gigs.
This problem demonstrates proportional reasoning, a fundamental concept in chemistry and physics when dealing with relative atomic masses, isotopic comparisons, or molar ratios. Such calculations are crucial in fields like stoichiometry and atomic physics.
