When a 5.50g sample of solid sodium hydroxide dissolves in 100.0 g of water in a coffee cup calorimeter, the temperature of rises from 21.6 degrees C to 37.8 degrees C. Calculate Change of heat for the reaction in kJ (also in kJ/mol NaOH) for the solution process. Assume the specific heat of the solution is the same as pure water. Is this an exothermic or endothermic process?
exothermic
To calculate the change in heat for the reaction, we need to use the equation:
q = mcΔT
where:
q = heat energy (in Joules or J)
m = mass of the solution (in grams or g)
c = specific heat capacity of water (approximately 4.18 J/g°C)
ΔT = change in temperature (in °C)
First, let's calculate the mass of the solution:
Mass of solution = mass of water + mass of sodium hydroxide
Mass of solution = 100.0 g (water) + 5.50 g (sodium hydroxide)
Mass of solution = 105.5 g
Next, let's calculate the change in temperature:
ΔT = final temperature - initial temperature
ΔT = 37.8°C - 21.6°C
ΔT = 16.2°C
Now, we can calculate the change in heat (q):
q = (mass of solution) x (specific heat capacity of water) x (change in temperature)
q = (105.5 g) x (4.18 J/g°C) x (16.2°C)
q = 7187.71 J
Since the question asks for the answer in kJ, we need to convert the value to kilojoules (kJ):
q = 7187.71 J ÷ 1000
q = 7.18771 kJ
Now, to calculate the change in heat per mole of sodium hydroxide (NaOH):
First, we need to convert the mass of sodium hydroxide to moles:
molar mass of NaOH = 22.99 g/mol (Na) + 16.00 g/mol (O) + 1.01 g/mol (H)
molar mass of NaOH = 39.99 g/mol
moles of NaOH = mass of NaOH ÷ molar mass of NaOH
moles of NaOH = 5.50 g ÷ 39.99 g/mol
moles of NaOH = 0.138 mol
Change in heat per mole of NaOH = change in heat (kJ) ÷ moles of NaOH
Change in heat per mole of NaOH = 7.18771 kJ ÷ 0.138 mol
Change in heat per mole of NaOH = 52.15 kJ/mol
Finally, based on the positive value of the change in heat, which indicates energy being absorbed, we can conclude that this process is endothermic.