In a coffee cup calorimeter, 2.00 g of potassium hydroxide are mixed with 200.0 g of water at an initial temperature of 25.00C. After dissolving the salt, the final temperature of the solution is 27.33C. What is the heat change for the dissolution of potassium hydroxide in units of kJ per gram of potassium hydroxide. Assume the solution has a specific heat capacity identical to that of water.
heat generated = spec heat of water (202 grams)(27.33 - 25.00)
divide by 1000 if that is in Joules to get kJoules
divide by 2 grams to get kJ/gram
To calculate the heat change for the dissolution of potassium hydroxide in units of kJ per gram of potassium hydroxide, we need to use the equation:
q = mcΔT
Where:
q is the heat change (in joules),
m is the mass of the solution (in grams),
c is the specific heat capacity of the solution (in J/gºC), and
ΔT is the change in temperature (in ºC).
First, let's calculate the mass of the solution. We have 2.00 g of potassium hydroxide and 200.0 g of water, so the total mass of the solution is 2.00 g + 200.0 g = 202.0 g.
The specific heat capacity of the solution is given as identical to that of water. The specific heat capacity of water is approximately 4.18 J/gºC.
Now, calculate the change in temperature (ΔT):
ΔT = final temperature - initial temperature
ΔT = 27.33ºC - 25.00ºC
ΔT = 2.33ºC
Finally, substitute the values into the equation to find the heat change (q):
q = (202.0 g) * (4.18 J/gºC) * (2.33ºC)
q = 1969.76 J
To convert joules (J) to kilojoules (kJ), divide the value by 1000:
q = 1969.76 J / 1000
q = 1.96976 kJ
Therefore, the heat change for the dissolution of potassium hydroxide is 1.96976 kJ.
To calculate the heat change per gram of potassium hydroxide, we divide the heat change by the mass of potassium hydroxide:
Heat change per gram of potassium hydroxide = (1.96976 kJ) / (2.00 g)
Heat change per gram of potassium hydroxide = 0.98488 kJ/g
Therefore, the heat change for the dissolution of potassium hydroxide is approximately 0.98488 kJ per gram of potassium hydroxide.