What are the missing coefficients for the skeleton equation below?
[tex]Al_2(SO_4)_3 + \underline{\qquad} KOH \rightarrow \underline{\qquad} Al(OH)_3 + \underline{\qquad} K_2SO_4[/tex]
A. 1, 6, 2, 3
B. 1, 3, 2, 3
C. 4, 6, 2, 3
D. 2, 12, 4, 6
Answer (2)
Balance the number of Aluminum (Al) atoms: A l 2 ( S O 4 ) 3 + ... K O H → 2 A l ( O H ) 3 + ... K 2 S O 4 .
Balance the number of Sulfate ( S O 4 ) ions: A l 2 ( S O 4 ) 3 + ... K O H → 2 A l ( O H ) 3 + 3 K 2 S O 4 .
Balance the number of Potassium (K) atoms: A l 2 ( S O 4 ) 3 + 6 K O H → 2 A l ( O H ) 3 + 3 K 2 S O 4 .
The balanced equation is: A l 2 ( S O 4 ) 3 + 6 K O H → 2 A l ( O H ) 3 + 3 K 2 S O 4 . The missing coefficients are 6 , 2 , 3 .
Explanation
Analyzing the Problem We are given the skeleton equation:
A l 2 ( S O 4 ) 3 + ... K O H → ... A l ( O H ) 3 + ... K 2 S O 4
Our goal is to find the missing coefficients to balance this chemical equation.
Balancing Aluminum
Balance Aluminum (Al):
There are 2 Al atoms on the left side ( A l 2 ( S O 4 ) 3 ).
To balance Al, we need 2 Al atoms on the right side. So, we put a coefficient of 2 in front of A l ( O H ) 3 .
The equation now looks like this: A l 2 ( S O 4 ) 3 + ... K O H → 2 A l ( O H ) 3 + ... K 2 S O 4
Balancing Sulfate
Balance Sulfate ( S O 4 ):
There are 3 S O 4 groups on the left side ( A l 2 ( S O 4 ) 3 ).
To balance S O 4 , we need 3 S O 4 groups on the right side. So, we put a coefficient of 3 in front of K 2 S O 4 .
The equation now looks like this: A l 2 ( S O 4 ) 3 + ... K O H → 2 A l ( O H ) 3 + 3 K 2 S O 4
Balancing Potassium
Balance Potassium (K):
There are now 3 x 2 = 6 K atoms on the right side ( 3 K 2 S O 4 ).
To balance K, we need 6 K atoms on the left side. So, we put a coefficient of 6 in front of K O H .
The equation now looks like this: A l 2 ( S O 4 ) 3 + 6 K O H → 2 A l ( O H ) 3 + 3 K 2 S O 4
Balancing Hydroxide
Balance Hydroxide (OH):
On the left side, we have 6 O H groups ( 6 K O H ).
On the right side, we have 2 x 3 = 6 O H groups ( 2 A l ( O H ) 3 ).
The O H groups are already balanced.
Final Balanced Equation
The balanced equation:
The balanced equation is: A l 2 ( S O 4 ) 3 + 6 K O H → 2 A l ( O H ) 3 + 3 K 2 S O 4
The missing coefficients are 6, 2, and 3.
Conclusion Therefore, the missing coefficients are 6 for K O H , 2 for A l ( O H ) 3 , and 3 for K 2 S O 4 . The correct answer is:
A l 2 ( S O 4 ) 3 + 6 K O H → 2 A l ( O H ) 3 + 3 K 2 S O 4
Examples
Balancing chemical equations is essential in various real-life applications, such as in the pharmaceutical industry when synthesizing new drugs, in environmental science when studying pollution control, and in manufacturing when optimizing chemical processes. For instance, when producing fertilizers, chemists must ensure the correct proportions of reactants to maximize yield and minimize waste. Similarly, in wastewater treatment, understanding the stoichiometry of chemical reactions helps in designing effective treatment processes to remove pollutants.
The missing coefficients are 6 for KOH, 2 for Al(OH)3, and 3 for K2SO4, making the balanced equation Al2(SO4)3 + 6 KOH → 2 Al(OH)3 + 3 K2SO4. Therefore, the correct answer is option A: 1, 6, 2, 3.
;
