An electric device delivers a current of [tex]$15.0 A$[/tex] for 30 seconds. How many electrons flow through it?
Answer (2)
Balance the chemical equation: 1 M g ( H C O 3 ) 2 → 1 M g C O 3 + 1 H 2 O + 1 C O 2 .
Count the number of atoms of each element on the reactant side.
Count the number of atoms of each element on the product side.
Complete the table with the counts: Mg: 1, H: 2, C: 2, O: 6 on both sides. M g ( H C O 3 ) 2 → M g C O 3 + H 2 O + C O 2
Explanation
Understanding the Problem We are asked to balance the chemical equation and complete the table showing the number of atoms of each element on both sides.
Objective The chemical equation is: M g ( H C O 3 ) 2 → M g C O 3 + H 2 O + C O 2 We need to find the smallest whole number coefficients to balance the equation. We need to complete the table showing the number of atoms of each element on both sides of the balanced equation.
Solution Plan
Balance the equation by adjusting the coefficients in front of each chemical formula.
Start by balancing Mg. In this case, Mg is already balanced.
Next, balance C. There are 2 C atoms on the left, so we need to make sure there are 2 C atoms on the right. The M g C O 3 already provides one C atom, so we need one more, which comes from C O 2 . Thus, the coefficient in front of C O 2 is 1.
Next, balance H. There are 2 H atoms on the left, so we need 2 H atoms on the right. The coefficient in front of H 2 O must be 1.
Finally, balance O. On the left, there are 2 × 3 = 6 O atoms in each H C O 3 group, and there are two such groups, so there are 6 × 2 = 12 O atoms in total. On the right, there are 3 O atoms in M g C O 3 , 1 O atom in H 2 O , and 2 O atoms in C O 2 . Thus, there are 3 + 1 + 2 = 6 O atoms. Let's check the balanced equation: M g ( H C O 3 ) 2 → M g C O 3 + H 2 O + C O 2 . On the left: 1 Mg, 2 H, 2 C, 6 O. On the right: 1 Mg, 2 H, 2 C, 6 O. The equation is balanced.
Balanced Equation The balanced equation is: 1 M g ( H C O 3 ) 2 → 1 M g C O 3 + 1 H 2 O + 1 C O 2 .
Completing the Table Complete the table with the number of atoms of each element on both sides of the balanced equation. Mg: Reactant = 1, Product = 1 H: Reactant = 2, Product = 2 C: Reactant = 2, Product = 2 O: Reactant = 6, Product = 6
Final Table
Element
Reactant
Products
Mg
1
1
H
2
2
C
2
2
O
6
6
Final Answer The balanced equation is: 1 M g ( H C O 3 ) 2 → 1 M g C O 3 + 1 H 2 O + 1 C O 2 The completed table is:
Element
Reactant
Products
Mg
1
1
H
2
2
C
2
2
O
6
6
Examples
Balancing chemical equations is essential in various real-world applications, such as in environmental science when assessing the impact of pollutants, in medicine for drug synthesis, and in cooking for understanding ingredient interactions. For example, in environmental science, knowing the balanced equation for the combustion of fossil fuels helps scientists calculate the amount of carbon dioxide released into the atmosphere, contributing to climate change models. In drug synthesis, precise balancing ensures the correct proportions of reactants are used to produce the desired pharmaceutical compound, avoiding unwanted side reactions and ensuring efficacy. In cooking, understanding the stoichiometry of reactions, such as baking soda reacting with an acid, helps achieve the desired texture and flavor in baked goods.
The total charge delivered by the device is 450 coulombs. This corresponds to approximately 2.81 x 10^21 electrons flowing through it in 30 seconds. Thus, when a current of 15.0 A is supplied for that duration, an immense number of electrons pass through the device.
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