When 40.0 mL of $1.00 M H _2 SO _4$ is added to 80.0 mL of 1.00 M NaOH at $20.00^{\circ} C$ in a coffee cup calorimeter, the temperature of the aqueous solution increases to $29.20^{\circ} C$. If the mass of the solution is 120.0 g and the specific heat of the calorimeter and solution is $4.184 J / g \cdot{ }^{\circ} C$, how much heat is given off in the reaction? (Ignore the mass of the calorimeter in the calculation.) Use $q=m C_p \Delta T$.
A. 4.62 kJ
B. 10.0 kJ
C. 14.7 kJ
D. 38.5 kJ
Answer (1)
Calculate the change in temperature: Δ T = 29.2 0 ∘ C − 20.0 0 ∘ C = 9. 2 ∘ C .
Calculate the heat released: q = ( 120.0 g ) × ( 4.184 J/g ⋅ ∘ C ) × ( 9. 2 ∘ C ) = 4619.136 J .
Convert the heat to kJoules: q = 1000 J/kJ 4619.136 J = 4.619136 kJ .
The heat given off in the reaction is 4.62 kJ .
Explanation
Problem Analysis We are given the following information:
Volume of H 2 S O 4 = 40.0 mL
Molarity of H 2 S O 4 = 1.00 M
Volume of NaOH = 80.0 mL
Molarity of NaOH = 1.00 M
Initial temperature = 20.0 0 ∘ C
Final temperature = 29.2 0 ∘ C
Mass of solution = 120.0 g
Specific heat of solution = 4.184 J / g ⋅ ∘ C
Ignore the mass of the calorimeter.
Use q = m C p Δ T
Our objective is to calculate the amount of heat given off in the reaction.
Calculating the Change in Temperature First, we need to calculate the change in temperature, which is the difference between the final and initial temperatures:
Δ T = T f ina l − T ini t ia l
Δ T = 29.2 0 ∘ C − 20.0 0 ∘ C = 9. 2 ∘ C
So, the change in temperature is 9. 2 ∘ C .
Calculating the Heat Released Next, we calculate the heat released using the formula q = m C p Δ T , where:
m is the mass of the solution (120.0 g)
C p is the specific heat of the solution ( 4.184 J / g ⋅ ∘ C )
Δ T is the change in temperature ( 9. 2 ∘ C )
q = ( 120.0 g ) × ( 4.184 J/g ⋅ ∘ C ) × ( 9. 2 ∘ C )
q = 4619.136 J
So, the heat released is 4619.136 J.
Converting to kJoules Finally, we convert the heat from Joules to kJoules by dividing by 1000:
q (in kJ) = 1000 J/kJ 4619.136 J = 4.619136 kJ
Rounding to two decimal places, the heat released is approximately 4.62 kJ.
Final Answer Therefore, the amount of heat given off in the reaction is approximately 4.62 kJ.
Examples
When an acid and a base react, heat is either released (exothermic) or absorbed (endothermic). In this case, sulfuric acid ( H 2 S O 4 ) reacts with sodium hydroxide (NaOH), releasing heat. This concept is used in various applications, such as designing chemical reactors where controlling the temperature is crucial for safety and efficiency. For example, in industrial processes, understanding the heat released during neutralization reactions helps engineers design cooling systems to prevent overheating and potential hazards. By quantifying the heat released, we can optimize reaction conditions and ensure safe operation.
