the molar heat capacity of water at 25 degrees celsius is 75.29JK/mol. an exothermic reaction with -5.00kJ proceeded to completion in a 200mL dilute aqueous solution,initially at 16.0 degrees celsius. what is the final temperature of the solution ? clearly show all working
q = mass H2O x specific heat H2O x (Tfinal-Tinitial)
Solve for Tf. q = 5000 J.
To determine the final temperature of the solution, we can use the equation for heat transfer:
q = m × c × ΔT
where:
q is the heat transfer
m is the mass of the solution
c is the specific heat capacity of the solution
ΔT is the change in temperature
First, let's calculate the heat transferred during the reaction.
Given that the reaction is exothermic and releases -5.00 kJ of heat, the heat transfer (q) is -5.00 kJ.
Next, we need to determine the mass of the solution. The volume provided (200 mL) is for the aqueous solution initially at 16.0 degrees Celsius. However, we also need to consider the density of water.
The density of water at room temperature (25 degrees Celsius) is approximately 1 g/mL. Therefore, the mass of the solution can be calculated as follows:
mass = volume × density
mass = 200 mL × 1 g/mL
mass = 200 g
Now, let's calculate the change in temperature (ΔT) using the equation:
ΔT = q / (m × c)
Given:
q = -5.00 kJ = -5,000 J
m = 200 g
c = 75.29 J/(mol·K)
First, let's convert grams to moles of water:
moles = mass / molar mass
The molar mass of water is approximately 18 g/mol, so:
moles = 200 g / 18 g/mol
moles ≈ 11.11 mol
Now, we can substitute the values into the equation and solve for ΔT:
ΔT ≈ (-5,000 J) / (11.11 mol × 75.29 J/(mol·K))
Calculating this expression gives:
ΔT ≈ -6.53 K
The negative sign indicates a decrease in temperature. Therefore, the change in temperature is approximately -6.53 degrees Celsius.
Finally, to find the final temperature of the solution, we add the change in temperature to the initial temperature:
Final temperature = Initial temperature + ΔT
Final temperature = 16.0 degrees Celsius + (-6.53 degrees Celsius)
Final temperature ≈ 9.47 degrees Celsius
Therefore, the final temperature of the solution is approximately 9.47 degrees Celsius.