An electric device delivers a current of [tex]$15.0 A$[/tex] for 30 seconds. How many electrons flow through it?
Answer (2)
Determine the number of protons for each species using the atomic number.
Calculate the number of electrons for each species based on its charge.
Find the absolute difference between the number of protons and electrons for each species.
Identify the species with the largest difference, which is C e 4 + .
Explanation
Problem Analysis We are given five species: T i 2 + , P 3 − , Mn, S e 2 − , and C e 4 + . Our task is to determine which of these species has the largest difference between the number of protons and the number of electrons. The number of protons is the same as the atomic number of the element, which can be found on the periodic table. The number of electrons is determined by the charge of the ion; a positive charge indicates a loss of electrons, while a negative charge indicates a gain of electrons.
Solution Strategy For each species, we will find the number of protons and electrons and then calculate the absolute difference between them.
Titanium Calculation (a) T i 2 + : Titanium (Ti) has an atomic number of 22, so it has 22 protons. The 2 + charge means it has lost 2 electrons, so it has 22 − 2 = 20 electrons. The difference is ∣22 − 20∣ = 2 .
Phosphorus Calculation (b) P 3 − : Phosphorus (P) has an atomic number of 15, so it has 15 protons. The 3 − charge means it has gained 3 electrons, so it has 15 + 3 = 18 electrons. The difference is ∣15 − 18∣ = 3 .
Manganese Calculation (c) Mn: Manganese (Mn) has an atomic number of 25, so it has 25 protons. Since it is neutral, it has 25 electrons. The difference is ∣25 − 25∣ = 0 .
Selenium Calculation (d) S e 2 − : Selenium (Se) has an atomic number of 34, so it has 34 protons. The 2 − charge means it has gained 2 electrons, so it has 34 + 2 = 36 electrons. The difference is ∣34 − 36∣ = 2 .
Cerium Calculation (e) C e 4 + : Cerium (Ce) has an atomic number of 58, so it has 58 protons. The 4 + charge means it has lost 4 electrons, so it has 58 − 4 = 54 electrons. The difference is ∣58 − 54∣ = 4 .
Final Comparison Comparing the differences, we have: T i 2 + (2), P 3 − (3), Mn (0), S e 2 − (2), and C e 4 + (4). The largest difference is 4, which corresponds to C e 4 + .
Conclusion Therefore, the species with the largest difference between the number of protons and the number of electrons is C e 4 + .
Examples
Understanding the difference between protons and electrons in ions is crucial in various fields. For example, in chemistry, it helps predict how elements will bond to form compounds. In environmental science, it's important for understanding how pollutants interact with soil and water. In medicine, understanding ionic imbalances is key to diagnosing and treating certain diseases. For instance, knowing that C e 4 + has a significant difference between protons and electrons helps in designing materials for catalytic converters to reduce harmful emissions.
By applying the formula for charge related to current and time, the total charge from a current of 15.0 A for 30 seconds is 450 C . Dividing the total charge by the charge of a single electron ( 1.6 × 1 0 − 19 C ) gives approximately 2.81 × 1 0 21 electrons. Thus, around 2.81 × 1 0 21 electrons flow through the device.
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