Answer :
To determine the correct proportions in which \( \text{Cr}^{3+} \) (chromium ions) and \( \text{O}^{2-} \) (oxygen ions) combine to form a neutral compound, we need to balance the total positive and negative charges.
1. Charges of the Ions:
- The charge of a chromium ion \( \text{Cr}^{3+} \) is \( +3 \).
- The charge of an oxygen ion \( \text{O}^{2-} \) is \( -2 \).
2. Neutral Compound Requirement:
- A neutral compound has a net charge of zero. Therefore, the total positive charge must equal the total negative charge.
3. Setting Up the Equation:
- Let's say we have \( x \) chromium ions and \( y \) oxygen ions.
- The total positive charge contributed by \( x \) chromium ions is \( 3x \) (since each \( \text{Cr}^{3+} \) ion has a charge of \( +3 \)).
- The total negative charge contributed by \( y \) oxygen ions is \( 2y \) (since each \( \text{O}^{2-} \) ion has a charge of \( -2 \)).
4. Balancing the Charges:
- To form a neutral compound, the total positive charge must equal the total negative charge:
[tex]\[ 3x = 2y \][/tex]
5. Finding the Smallest Whole Number Ratio:
- Solving the equation for the smallest whole numbers that satisfy this condition, we can set \( x = 2 \) and \( y = 3 \):
[tex]\[ 3(2) = 2(3) = 6 \][/tex]
Hence, the smallest whole number ratio in which \( \text{Cr}^{3+} \) and \( \text{O}^{2-} \) combine to produce a neutral compound is \( 2:3 \).
Therefore, the correct answer is:
D. [tex]\( 2:3 \)[/tex]
1. Charges of the Ions:
- The charge of a chromium ion \( \text{Cr}^{3+} \) is \( +3 \).
- The charge of an oxygen ion \( \text{O}^{2-} \) is \( -2 \).
2. Neutral Compound Requirement:
- A neutral compound has a net charge of zero. Therefore, the total positive charge must equal the total negative charge.
3. Setting Up the Equation:
- Let's say we have \( x \) chromium ions and \( y \) oxygen ions.
- The total positive charge contributed by \( x \) chromium ions is \( 3x \) (since each \( \text{Cr}^{3+} \) ion has a charge of \( +3 \)).
- The total negative charge contributed by \( y \) oxygen ions is \( 2y \) (since each \( \text{O}^{2-} \) ion has a charge of \( -2 \)).
4. Balancing the Charges:
- To form a neutral compound, the total positive charge must equal the total negative charge:
[tex]\[ 3x = 2y \][/tex]
5. Finding the Smallest Whole Number Ratio:
- Solving the equation for the smallest whole numbers that satisfy this condition, we can set \( x = 2 \) and \( y = 3 \):
[tex]\[ 3(2) = 2(3) = 6 \][/tex]
Hence, the smallest whole number ratio in which \( \text{Cr}^{3+} \) and \( \text{O}^{2-} \) combine to produce a neutral compound is \( 2:3 \).
Therefore, the correct answer is:
D. [tex]\( 2:3 \)[/tex]
