To find the number of atoms in each rectangle of the tape diagram, we need to keep in mind that methane (CHâ‚„) contains carbon and hydrogen atoms in the ratio of 1:4.
In this case, for every 1 carbon atom, there are 4 hydrogen atoms. Therefore, if we represent the total number of carbon atoms as \(C\) and the total number of hydrogen atoms as \(H\), the relationship can be expressed as:
- \(C = 1\)
- \(H = 4\)
Now, if we have a total of 90 atoms in the sample of methane, we can express this as:
\[ C + H = 90 \]
Substituting \(H\) in terms of \(C\):
\[ C + 4C = 90 \]
This simplifies to:
\[ 5C = 90 \]
Now, solving for \(C\):
\[ C = \frac{90}{5} = 18 \]
This means there are 18 carbon atoms. The number of hydrogen atoms can be calculated as:
\[ H = 4C = 4 \times 18 = 72 \]
Now, looking back at the tape diagram:
- The first section (representing carbon atoms) should be labeled with the number 18.
- The four sections (representing the hydrogen atoms) should each represent the total number of hydrogen atoms (72) divided by 4 (since there are 4 sections for hydrogen).
Calculating the value to be inserted into each rectangular section for hydrogen:
\[ \text{Value for each hydrogen section} = \frac{72}{4} = 18 \]
Thus, the answer is: The number 18 should be inserted into each rectangle.
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