Please help with a heat capacity chemistry question!?

Question

experimentally it is found that 163 kJ of thermal energy (heat) is evolved when 10.0 g of Al2O3 is formed from the elements. To what final temperature would 1.00 gallon of water at 20 degrees C be heated by absorbing this quantity of heat?

the answer is 29 degrees Celsius but im not sure how to get that answer.. any help?? thanks so much :D

Answer 1

No prob.

What you need to know is the specific heat (capacity) of water. They have just made it a little bit interesting by mixing units from different measurement systems, but we will fix that.

The specific heat of water is 1 calorie/gram°C = 4.186 joule/gram°C. Now, rather than going through liters per gallon and all that, we'll just lift a number for the density of water in units we like from a convenient web source:

3785 g/gal

To heat 1 gallon of water through 1°C requires 3785 calories or

3785 x 4.186/1000 = 15.844 kJ

SO: the water will be heated through 163/15.844 = 10.29°C  That of course is for a US gallon. For an Imperial gallon, we must divide by 1.2, which gives us 8.6°C for the temperature increase.

Following Sherlock Holmes, I conclude you are using Imperial gallons.

One imperial gallon is approximately equal to 1.201 U.S. gallons.