Final answer:
To complete the table with equivalent ratios of sulfur to oxygen atoms, we need to maintain the original 1:2 ratio given (15 sulfur atoms to 30 oxygen atoms). By scaling the number of sulfur atoms and applying the same factor to the number of oxygen atoms, we can find the corresponding numbers of oxygen atoms for each amount of sulfur atoms given.
Step-by-step explanation:
The problem provided is a mathematics question related to ratios. We're given a ratio of sulfur atoms to oxygen atoms and need to find equivalent ratios when the number of sulfur atoms changes. Let's start with the ratio given in the question.
For every 15 sulfur atoms, we have 30 oxygen atoms, which simplifies to a 1:2 ratio. This means for every sulfur atom, there are two oxygen atoms.
To find the equivalent ratios for different amounts of sulfur atoms, we use this proportional relationship:
- For 18 sulfur atoms, since 18 is 15 multiplied by 1.2, we need to multiply the number of oxygen atoms by the same factor to maintain the ratio. So, we multiply 30 by 1.2 to get 36 oxygen atoms.
- For 21 sulfur atoms, since 21 is 15 multiplied by 1.4, we multiply the number of oxygen atoms by the same factor. So, we multiply 30 by 1.4 to get 42 oxygen atoms.
- For the case where we're given 54 oxygen atoms, we can work backwards to find the number of sulfur atoms by dividing 54 by 2, which results in 27 sulfur atoms.
Thus, the completed table with equivalent ratios is:
- Sulfur atoms: 15, 18, 21, 27
- Oxygen atoms: 30, 36, 42, 54