Heat equation (Q = mcθ)

The heat equation, Q = mcθ, is the formula for the heat change in a thermochemistry experiment. Q is the heat in joules, m is the mass of the solution or water in grams, c is the specific heat capacity, and θ is the temperature change. Malay: persamaan haba · Chinese: 热量方程.

It is the engine of every calculation in this chapter. You measure a temperature change, multiply it by the mass of the surroundings and by the specific heat capacity, and out comes the heat energy transferred. Because the density of a dilute solution is taken as 1 g cm⁻³, a volume in cm³ gives the same number in grams, so you can use the total volume of solution directly as m.

Example. If 100 cm³ of solution rises in temperature during a neutralisation, you take m as the mass equal to that volume in grams, read c from the value the question gives, and multiply both by the temperature rise to find Q in joules. To turn Q into a heat of reaction you then divide by the number of moles and attach the sign.

Confusion to avoid. Q from this equation is not the final answer. Q is the total heat for the amount that actually reacted, in joules; a heat of reaction is Q converted to kJ and divided by the moles of the named substance, in kJ mol⁻¹. Stopping at Q, or mixing joules and kilojoules, is a common loss of marks.

Mastering Q = mcθ, and the per-mole step that follows it, is the single most useful skill in this SPM Chemistry chapter, because all four heats of reaction are found the same way. A safe routine is to write each quantity with its unit first, m in grams, c in J g⁻¹ °C⁻¹, θ in °C, so that you can see the unit of joules building up before you touch the calculator. After finding Q, convert it to kilojoules by dividing by 1000, then divide by the number of moles of the named substance, and only then does the number deserve to be called a heat of reaction, carried with its sign.