An electric device delivers a current of [tex]$15.0 A$[/tex] for 30 seconds. How many electrons flow through it?
Answer (2)
To find the number of electrons flowing through a device delivering 15.0 A of current for 30 seconds, we first calculate the total charge, which is 450 C. Then, we divide this total charge by the charge of a single electron (about 1.6 × 1 0 − 19 C) to find that approximately 2.81 × 1 0 21 electrons have flowed through the device. Therefore, around 2.81 × 1 0 21 electrons pass through the device during this time.
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Calculate the moles of A l ( O H ) 3 : $moles =
\frac{0.750 g}{78.00 g/mol} = 0.009615 mol$.
Determine the mole ratio between A l ( O H ) 3 and H Cl from the balanced equation: 1:3.
Calculate the moles of H Cl : $moles_HCl = 3
\times 0.009615 mol = 0.028846 mol$.
Calculate the mass of H Cl : $mass_HCl = 0.028846 mol
\times 36.46 g/mol = 1.0517 g . T h e f ina l an s w er i s \boxed{1.05 g}$.
Explanation
Problem Analysis and Given Data We are given the balanced chemical equation: A l ( O H ) 3 ( s ) + 3 H Cl ( a q ) → A lC l 3 ( a q ) + 3 H 2 O ( l ) We are also given that we have 0.750 g of A l ( O H ) 3 and we need to determine the mass of H Cl in grams that can react with it. From the table, we know that the molar mass of H Cl is 36.46 g / m o l and the molar mass of A l ( O H ) 3 is 78.00 g / m o l .
Calculate Moles of Aluminum Hydroxide First, we need to calculate the number of moles of A l ( O H ) 3 that we have. We can use the formula: m o l es = m o l a r _ ma ss ma ss So, the number of moles of A l ( O H ) 3 is: m o l es _ A l ( O H ) 3 = 78.00 g / m o l 0.750 g = 0.009615 m o l
Determine Mole Ratio From the balanced chemical equation, we can see that 1 mole of A l ( O H ) 3 reacts with 3 moles of H Cl . Therefore, the mole ratio between A l ( O H ) 3 and H Cl is 1:3.
Calculate Moles of Hydrochloric Acid Now, we can calculate the number of moles of H Cl required to react with 0.009615 m o l of A l ( O H ) 3 :
m o l es _ H Cl = 3 × m o l es _ A l ( O H ) 3 = 3 × 0.009615 m o l = 0.028846 m o l
Calculate Mass of Hydrochloric Acid Finally, we can calculate the mass of H Cl using the formula: ma ss = m o l es × m o l a r _ ma ss So, the mass of H Cl is: ma ss _ H Cl = 0.028846 m o l × 36.46 g / m o l = 1.0517 g Therefore, 1.0517 g of H Cl can react with 0.750 g of A l ( O H ) 3 .
Final Answer The mass of H Cl that can react with 0.750 g of A l ( O H ) 3 is approximately 1.05 g .
Examples
Understanding stoichiometry is crucial in various real-life applications, such as cooking, where precise ratios of ingredients are essential for a successful recipe. Similarly, in medicine, accurately calculating the dosage of drugs is vital for effective treatment while minimizing potential side effects. In environmental science, stoichiometry helps in assessing the impact of pollutants on ecosystems, ensuring that chemical reactions are balanced to maintain ecological equilibrium. This problem demonstrates how stoichiometry is used to determine the exact amount of reactants needed for a chemical reaction, which is fundamental in many scientific and industrial processes.
