When a 5.00-g sample of KCl is dissolved in water in a calorimeter that has a total heat capacity of 3.978 kJ·K–1, the temperature decreases by 0.290 K. Calculate the molar heat of solution of KCl.
Ccal x delta T = q
q/g = heat soln/g
(q/g)*molar mass = q/mol
To calculate the molar heat of solution of KCl, we can use the equation:
q = n * ΔH
where q is the heat absorbed or released, n is the number of moles of solute (KCl), and ΔH is the molar heat of solution.
First, let's calculate the number of moles of KCl in the 5.00 g sample using its molar mass. The molar mass of KCl is 39.10 g/mol for K and 35.45 g/mol for Cl.
molar mass of KCl = 39.10 g/mol + 35.45 g/mol = 74.55 g/mol
moles of KCl = mass / molar mass
moles of KCl = 5.00 g / 74.55 g/mol
Next, let's convert the temperature change from Kelvin to Celsius:
ΔT = 0.290 K
Now, we can calculate the heat absorbed or released:
q = n * ΔH
Since the temperature decreased, heat was released, so q is negative.
q = -3.978 kJ/K * 0.290 K
Finally, we can solve for ΔH:
ΔH = q / n
ΔH = (-3.978 kJ/K * 0.290 K) / moles of KCl
Plug in the calculated values to find ΔH.
To calculate the molar heat of solution of KCl, we can use the equation:
q = m * C * ΔT
where:
q = heat absorbed or released by the system
m = mass of the substance (in this case, KCl)
C = heat capacity of the calorimeter
ΔT = change in temperature
Let's plug in the known values into the equation:
m = 5.00 g
C = 3.978 kJ·K–1 (convert to J·K–1 by multiplying by 1000)
ΔT = 0.290 K
First, let's convert the heat capacity to J·K–1:
C = 3.978 kJ·K–1 * 1000 J·kJ–1 = 3978 J·K–1
Now we can calculate the heat change, q:
q = 5.00 g * 3978 J·K–1 * 0.290 K
Next, we need to convert the mass of KCl to moles. We can use the molar mass of KCl, which is 74.55 g·mol–1.
moles of KCl = 5.00 g / 74.55 g·mol–1
Finally, we can calculate the molar heat of solution by dividing the heat change by the moles of KCl:
molar heat of solution = q / moles of KCl
By following these steps, you can calculate the molar heat of solution of KCl. Keep in mind to use the correct units and perform the necessary conversions.