# Energy Calculations

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COMPARING THE ENERGY RELEASED BY FUELS

When fuels and foods react with oxygen, the reactions are exothermic.  Different amounts of energy are released by different fuels and foods.  The amount of energy released is usually measured in joules, but can also be measured in calories.  1 calorie = 4.2J.  We can use a calorimeter to measure the amount of energy released when substances burn.  A simple calorimeter is made using water in a glass beaker or metal can.  When a substance burns and heats the water, the temperature rise of the water depends on the amount of energy released.  The amount of energy transferred to the water is calculated using the equation:

Q = m x c x triangle t, where Q = the amount of energy transferred to the water in J, m = mass of water in g, c = specific heat capacity of water in J/goC, and triangle t = temperature change in oC.

Example:

0.5g of fuel was burned and used to heat 200g of water in a calorimeter.  The temperature of the water increased by 14oC.  The specific heat capacity of water is 4.2J/goC.

energy released = 200 x 4.2 x 14 = 11760J

energy released per gram of fuel = 11760/0.5 = 23520J or 23.52kJ

Simple calorimeters do not give accurate results for the energy released because much of the energy is used to heat the surroundings.  However, the results can be used to compare the amount of energy released by different fuels.  The energy change in kJ/mol can be calculated by multiplying the energy change in kJ/g by the relative formula mass of the substance.

ENERGY TRANSFER IN SOLUTIONS

When a reaction takes place in a solution, energy is transferred to or from the solution.  We can do the reactions in an insulated container to reduce energy transfer to the surroundings.  We can measure the temperature change of the solution and use this to calculate the energy change using the equation Q = m x c x triangle t.  In these calculations we assume the solution behaves like water.  This means that 1cm3 of the solution has a mass of 1g and the specific heat capacity of the solution is 4.2J/goC.

Example: a student added 25cm3 of dilute nitric acid to 25cm3 of potassium hydroxide solution in a polystyrene cup.  He recorded a temperature rise of 12oC. Calculate the energy change.

Q = m x c x triangle t.  Volume of solution = 25 + 25 = 50cm3 and therefore 50g.

50 x 4.2 x 12…