Answer
7.219 kJ
Work Step by Step
There are 6.5g of sodium hydroxide dissolved in 100g of water in the calorimeter and the temperature rises from 21.6 to 37.8 C. The specific heat of water is 4.184 J/g*K so first we need to find the $\Delta T = 37.8 - 21.6 = 16.2 C $. Since a $\Delta T$ of 1 C is equivalent to a change of 1K then we can write 16.2C as 16.2K. Then, to find how much energy is released we do the following:
4.184 J/g*K * (100g+6.5g) * 16.2K = 7218.6J
Then to convert to kJ we divide by 1000:
7.219 kJ
