An electric device delivers a current of [tex]$15.0 A$[/tex] for 30 seconds. How many electrons flow through it?
Answer (2)
Calculate the concentration of each solution using C o n ce n t r a t i o n = V o l u m e m o l es , where m o l es = M o l a r M a ss ma ss .
Determine the change in temperature ( D T ) using D T = T f ina l − T ini t ia l .
Classify each reaction as endothermic if D T < 0 or exothermic if 0"> D T > 0 .
Complete the table with calculated concentrations, temperature changes, and classifications.
The completed table (using example temperature values) provides the final results.
Explanation
Problem Analysis Let's analyze the data we have. We are given the masses of the solids used in each mixture and the fact that 100 mL of liquid is used in each case. We need to calculate the concentration of the solid after dissolving, the change in temperature ( D T ), and determine whether the reaction is endothermic or exothermic.
Calculating Concentrations First, we need to calculate the concentration of each solid after it dissolves. We'll use the formula: C o n ce n t r a t i o n ( M ) = V o l u m e ( L ) m o l es To find the number of moles, we use: m o l es = M o l a r M a ss ( g / m o l ) ma ss ( g ) We'll use the molar masses:
N H 4 N O 3 : 80.043 g/mol
C a C l 2 : 110.98 g/mol
K C H 3 COO : 98.142 g/mol
M g O : 40.304 g/mol The masses of the solids are:
N H 4 N O 3 : 2.0 g
C a C l 2 : 2.0 g
K C H 3 COO : 2.0 g
M g O : 4.0 g The volume of the solution is 100 mL, which is 0.1 L.
Concentration Calculations Now, let's calculate the concentrations:
N H 4 N O 3 :
m o l es = 80.043 g / m o l 2.0 g = 0.02499 m o l C o n ce n t r a t i o n = 0.1 L 0.02499 m o l = 0.2499 M
C a C l 2 :
m o l es = 110.98 g / m o l 2.0 g = 0.01802 m o l C o n ce n t r a t i o n = 0.1 L 0.01802 m o l = 0.1802 M
K C H 3 COO :
m o l es = 98.142 g / m o l 2.0 g = 0.02038 m o l C o n ce n t r a t i o n = 0.1 L 0.02038 m o l = 0.2038 M
M g O :
m o l es = 40.304 g / m o l 4.0 g = 0.09925 m o l C o n ce n t r a t i o n = 0.1 L 0.09925 m o l = 0.9925 M
Calculating Temperature Changes Next, we need to calculate the change in temperature ( D T ) for each mixture. The formula is: D T = T f ina l − T ini t ia l
We will assume some example values for T ini t ia l and T f ina l to demonstrate how to complete the table. Let's assume:
N H 4 N O 3 + H 2 O : T ini t ia l = 25.0 ∘ C , T f ina l = 22.0 ∘ C
C a C l 2 + H 2 O : T ini t ia l = 25.0 ∘ C , T f ina l = 28.0 ∘ C
K C H 3 COO + H 2 O : T ini t ia l = 25.0 ∘ C , T f ina l = 24.0 ∘ C
H Cl + M g O : T ini t ia l = 25.0 ∘ C , T f ina l = 35.0 ∘ C
Temperature Change Results Now, let's calculate D T for each mixture:
N H 4 N O 3 + H 2 O :
D T = 22.0 ∘ C − 25.0 ∘ C = − 3.0 ∘ C
C a C l 2 + H 2 O :
D T = 28.0 ∘ C − 25.0 ∘ C = 3.0 ∘ C
K C H 3 COO + H 2 O :
D T = 24.0 ∘ C − 25.0 ∘ C = − 1.0 ∘ C
H Cl + M g O :
D T = 35.0 ∘ C − 25.0 ∘ C = 10.0 ∘ C
Determining Endothermic or Exothermic Reactions Finally, we determine whether each reaction is endothermic or exothermic. If 0"> D T > 0 , the reaction is exothermic. If D T < 0 , the reaction is endothermic.
N H 4 N O 3 + H 2 O : D T = − 3.0 ∘ C (Endothermic)
C a C l 2 + H 2 O : D T = 3.0 ∘ C (Exothermic)
K C H 3 COO + H 2 O : D T = − 1.0 ∘ C (Endothermic)
H Cl + M g O : D T = 10.0 ∘ C (Exothermic)
Completed Table Here's the completed table with our example data:
Mixture
Mass of Solid (g)
Concentration of Solid after Dissolving (M)
T ini t ia l ( ∘ C )
T f ina l ( ∘ C )
D T ( ∘ C )
Endothermic or Exothermic?
N H 4 N O 3 + H 2 O
2.0
0.2499
25.0
22.0
-3.0
Endothermic
C a C l 2 + H 2 O
2.0
0.1802
25.0
28.0
3.0
Exothermic
K C H 3 COO + H 2 O
2.0
0.2038
25.0
24.0
-1.0
Endothermic
H Cl + M g O
4.0
0.9925
25.0
35.0
10.0
Exothermic
Examples
Understanding endothermic and exothermic reactions is crucial in many real-world applications. For instance, instant cold packs utilize endothermic reactions to cool down quickly, providing relief for injuries. Conversely, hand warmers employ exothermic reactions to generate heat, keeping your hands warm in cold weather. In the construction industry, the setting of cement is an exothermic process, and controlling the heat released is essential for preventing cracks. Moreover, these concepts are fundamental in designing efficient engines and chemical processes, where managing heat flow can significantly impact performance and safety.
When a device delivers a current of 15.0 A for 30 seconds, approximately 2.81 x 10^21 electrons flow through it. This is calculated using the relationship between current, charge, and the charge of an electron. Understanding these principles is essential in physics and electronics.
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