To determine the charge \( x \) on the compound \( \text{AlSi}_3\text{O}_8^x \), we first need to calculate the overall charge contributed by each element in the formula.
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Oxidation States:
- Silicon (Si) has an oxidation number of +4.
- Aluminum (Al) has an oxidation number of +3.
- Oxygen (O) has an oxidation number of -2.
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Number of Atoms: In the formula \( \text{AlSi}_3\text{O}_8 \):
- There is 1 Aluminum (Al) atom.
- There are 3 Silicon (Si) atoms.
- There are 8 Oxygen (O) atoms.
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Calculate Total Contribution to Charge:
- Contribution from Aluminum: \[ 1 \times (+3) = +3 \]
- Contribution from Silicon: \[ 3 \times (+4) = +12 \]
- Contribution from Oxygen: \[ 8 \times (-2) = -16 \]
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Total Charge Calculation: Now, let's sum these contributions: \[ \text{Total Charge} = (+3) + (+12) + (-16) = 3 + 12 - 16 = -1 \]
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Determine the Charge \( x \): Given that the total charge from the \( \text{AlSi}_3\text{O}_8^x \) must equal the charge indicated by \( x \), we can set up the equation: \[ -1 + x = 0 \] This implies that: \[ x = +1 \]
Thus, the charge \( x \) on \( \text{AlSi}_3\text{O}_8^x \) is +1.