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Sagot :
Sure! To write the empirical formulas for ionic compounds, we need to combine ions in such a way that the total positive charge equals the total negative charge. Here’s a step-by-step solution for forming four such compounds from the given ions:
1. Combining [tex]\( \text{Fe}^{2+} \)[/tex] with [tex]\( \text{SO}_4^{2-} \)[/tex]:
The iron ion has a charge of [tex]\( 2+ \)[/tex] and the sulfate ion has a charge of [tex]\( 2- \)[/tex]. To balance the charges so that the total positive charge equals the total negative charge, we need one [tex]\( \text{Fe}^{2+} \)[/tex] ion and one [tex]\( \text{SO}_4^{2-} \)[/tex] ion.
Therefore, the empirical formula for this compound is [tex]\( \text{FeSO}_4 \)[/tex].
2. Combining [tex]\( \text{NH}_4^{+} \)[/tex] with [tex]\( \text{SO}_4^{2-} \)[/tex]:
The ammonium ion has a charge of [tex]\( 1+ \)[/tex] and the sulfate ion has a charge of [tex]\( 2- \)[/tex]. To balance the charges, we need two [tex]\( \text{NH}_4^{+} \)[/tex] ions for every one [tex]\( \text{SO}_4^{2-} \)[/tex] ion.
Therefore, the empirical formula for this compound is [tex]\( (\text{NH}_4)_2\text{SO}_4 \)[/tex].
3. Combining [tex]\( \text{Fe}^{2+} \)[/tex] with [tex]\( \text{MnO}_4^{-} \)[/tex]:
The iron ion has a charge of [tex]\( 2+ \)[/tex] and the permanganate ion has a charge of [tex]\( 1- \)[/tex]. To balance the charges, we need one [tex]\( \text{Fe}^{2+} \)[/tex] ion and two [tex]\( \text{MnO}_4^{-} \)[/tex] ions.
Therefore, the empirical formula for this compound is [tex]\( \text{Fe}(\text{MnO}_4)_2 \)[/tex].
4. Combining [tex]\( \text{NH}_4^{+} \)[/tex] with [tex]\( \text{MnO}_4^{-} \)[/tex]:
The ammonium ion has a charge of [tex]\( 1+ \)[/tex] and the permanganate ion has a charge of [tex]\( 1- \)[/tex]. To balance the charges, we need one [tex]\( \text{NH}_4^{+} \)[/tex] ion and one [tex]\( \text{MnO}_4^{-} \)[/tex] ion.
Therefore, the empirical formula for this compound is [tex]\( \text{NH}_4\text{MnO}_4 \)[/tex].
So, the empirical formulas for the four ionic compounds are:
1. [tex]\( \text{FeSO}_4 \)[/tex]
2. [tex]\( (\text{NH}_4)_2\text{SO}_4 \)[/tex]
3. [tex]\( \text{Fe}(\text{MnO}_4)_2 \)[/tex]
4. [tex]\( \text{NH}_4\text{MnO}_4 \)[/tex]
These formulas balance out the positive and negative charges and represent the correct ratio of ions in each compound.
1. Combining [tex]\( \text{Fe}^{2+} \)[/tex] with [tex]\( \text{SO}_4^{2-} \)[/tex]:
The iron ion has a charge of [tex]\( 2+ \)[/tex] and the sulfate ion has a charge of [tex]\( 2- \)[/tex]. To balance the charges so that the total positive charge equals the total negative charge, we need one [tex]\( \text{Fe}^{2+} \)[/tex] ion and one [tex]\( \text{SO}_4^{2-} \)[/tex] ion.
Therefore, the empirical formula for this compound is [tex]\( \text{FeSO}_4 \)[/tex].
2. Combining [tex]\( \text{NH}_4^{+} \)[/tex] with [tex]\( \text{SO}_4^{2-} \)[/tex]:
The ammonium ion has a charge of [tex]\( 1+ \)[/tex] and the sulfate ion has a charge of [tex]\( 2- \)[/tex]. To balance the charges, we need two [tex]\( \text{NH}_4^{+} \)[/tex] ions for every one [tex]\( \text{SO}_4^{2-} \)[/tex] ion.
Therefore, the empirical formula for this compound is [tex]\( (\text{NH}_4)_2\text{SO}_4 \)[/tex].
3. Combining [tex]\( \text{Fe}^{2+} \)[/tex] with [tex]\( \text{MnO}_4^{-} \)[/tex]:
The iron ion has a charge of [tex]\( 2+ \)[/tex] and the permanganate ion has a charge of [tex]\( 1- \)[/tex]. To balance the charges, we need one [tex]\( \text{Fe}^{2+} \)[/tex] ion and two [tex]\( \text{MnO}_4^{-} \)[/tex] ions.
Therefore, the empirical formula for this compound is [tex]\( \text{Fe}(\text{MnO}_4)_2 \)[/tex].
4. Combining [tex]\( \text{NH}_4^{+} \)[/tex] with [tex]\( \text{MnO}_4^{-} \)[/tex]:
The ammonium ion has a charge of [tex]\( 1+ \)[/tex] and the permanganate ion has a charge of [tex]\( 1- \)[/tex]. To balance the charges, we need one [tex]\( \text{NH}_4^{+} \)[/tex] ion and one [tex]\( \text{MnO}_4^{-} \)[/tex] ion.
Therefore, the empirical formula for this compound is [tex]\( \text{NH}_4\text{MnO}_4 \)[/tex].
So, the empirical formulas for the four ionic compounds are:
1. [tex]\( \text{FeSO}_4 \)[/tex]
2. [tex]\( (\text{NH}_4)_2\text{SO}_4 \)[/tex]
3. [tex]\( \text{Fe}(\text{MnO}_4)_2 \)[/tex]
4. [tex]\( \text{NH}_4\text{MnO}_4 \)[/tex]
These formulas balance out the positive and negative charges and represent the correct ratio of ions in each compound.
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