Fill in the gaps to balance the equation.
Use the smallest set of whole numbers to balance the equation and include coefficients of "1" when appropriate.
$\square$ $NaNO _3+$ $\square$ 1 $Cr _2\left( CO _3\right)_3 \rightarrow$ $\square$ 3 $Na_2 CO_3+$ $\square$ 2 $Cr \left( NO _3\right)_3$
Complete the table to determine how many atoms of each element are present in the reactants and products.
| Element | Reactant | Products |
|---|---|---|
| Na | | |
| N | | |
| O | | |
| Cr | 2 | 2 |
| C | | |
Answer (2)
Balance the number of Na atoms: x = 2 y , where x is the coefficient of N a N O 3 and y is the coefficient of N a 2 C O 3 .
Balance the number of C atoms: y = 3 .
Solve for x: x = 2 ( 3 ) = 6 .
The balanced equation is 6 N a N O 3 + 1 C r 2 ( C O 3 ) 3 → 3 N a 2 C O 3 + 2 C r ( N O 3 ) 3 , and the table is completed with the number of atoms of each element on both sides.
The final balanced equation is: 6 N a N O 3 + 1 C r 2 ( C O 3 ) 3 → 3 N a 2 C O 3 + 2 C r ( N O 3 ) 3
Explanation
Problem Analysis We are given the unbalanced chemical equation:
□ N a N O 3 + □ 1 C r 2 ( C O 3 ) 3 → □ 3 N a 2 C O 3 + □ 2 C r ( N O 3 ) 3
Our goal is to find the smallest whole number coefficients that balance the equation and to complete the table showing the number of atoms of each element on both sides of the equation.
Balancing Sodium Atoms Let's start by balancing the equation. We can see that the number of Chromium (Cr) atoms is already balanced, with 2 Cr atoms on both the reactant and product sides.
Now, let's balance the Sodium (Na) atoms. Let x be the coefficient of N a N O 3 and y be the coefficient of N a 2 C O 3 . From the equation, we have:
x N a N O 3 + 1 C r 2 ( C O 3 ) 3 → y N a 2 C O 3 + 2 C r ( N O 3 ) 3
The number of Na atoms on the reactant side is x , and the number of Na atoms on the product side is 2 y . Therefore, we must have x = 2 y .
Balancing Carbon Atoms Next, let's balance the Carbon (C) atoms. There are 3 C atoms in C r 2 ( C O 3 ) 3 on the reactant side. On the product side, there are y C O 3 groups in y N a 2 C O 3 . Therefore, we must have y = 3 .
Finding the Coefficient of Sodium Nitrate Now we can find the value of x . Since y = 3 , we have x = 2 y = 2 ( 3 ) = 6 . So, the balanced equation is:
6 N a N O 3 + 1 C r 2 ( C O 3 ) 3 → 3 N a 2 C O 3 + 2 C r ( N O 3 ) 3
Completing the Table Now, let's complete the table to show the number of atoms of each element on both sides of the balanced equation:
Element
Reactant
Product
Na
6 × 1 = 6
3 × 2 = 6
N
6 × 1 = 6
2 × 3 = 6
O
( 6 × 3 ) + ( 1 × 3 × 3 ) = 18 + 9 = 27
( 3 × 3 ) + ( 2 × 3 × 3 ) = 9 + 18 = 27
Cr
1 × 2 = 2
2 × 1 = 2
C
1 × 3 = 3
3 × 1 = 3
Final Answer Therefore, the balanced equation is:
6 N a N O 3 + 1 C r 2 ( C O 3 ) 3 → 3 N a 2 C O 3 + 2 C r ( N O 3 ) 3
And the completed table is:
Element
Reactant
Product
Na
6
6
N
6
6
O
27
27
Cr
2
2
C
3
3
Examples
Balancing chemical equations is essential in various real-world applications, such as in the pharmaceutical industry when synthesizing new drugs, in environmental science when studying pollution and its effects, and in materials science when creating new materials with specific properties. For instance, when creating a new drug, chemists need to ensure that the reaction is balanced to produce the desired compound in the correct amount, minimizing waste and maximizing efficiency. Similarly, in environmental science, understanding the balanced chemical equations of pollutants helps scientists predict their behavior and develop strategies to mitigate their impact on the environment. In the kitchen, when baking, you need to balance the ingredients to get the desired result. If you add too much or too little of an ingredient, the recipe will not turn out as expected. Balancing chemical equations is like balancing a recipe.
The balanced chemical equation is 6 NaNO_3 + 1 Cr_2(CO_3)_3 → 3 Na_2CO_3 + 2 Cr(NO_3)_3. The table of atoms for each element confirms that both sides are balanced, with equal numbers of each type of atom. The balancing process involved ensuring that the number of atoms for sodium, carbon, and nitrogen matched between reactants and products.
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